external/boringssl: Sync to b1cbe1979008debd0541621584b00e010d9935dd.
This includes the following changes:
https://boringssl.googlesource.com/boringssl/+log/ba94746eb2b4b59a0eb72047e4ca2d2d54454c87..b1cbe1979008debd0541621584b00e010d9935dd
Test: BoringSSL CTS Presubmits.
Change-Id: I143290c32ebd3d98f5a35ec8899df44983b73b8a
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 1f2f6ba..338f212 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -338,6 +338,7 @@
add_library(crypto_test_data OBJECT crypto_test_data.cc)
add_subdirectory(crypto)
+add_subdirectory(third_party/fiat)
add_subdirectory(ssl)
add_subdirectory(ssl/test)
add_subdirectory(fipstools)
diff --git a/src/LICENSE b/src/LICENSE
index a25996f..ff4116f 100644
--- a/src/LICENSE
+++ b/src/LICENSE
@@ -6,7 +6,9 @@
https://cla.developers.google.com/clas
Some files from Intel are under yet another license, which is also included
-underneath.
+underneath. Files in third_party/ have their own licenses, as described
+therein. The MIT license, for third_party/fiat, which, unlike other third_party
+directories, is compiled into non-test libraries, is included below.
The OpenSSL toolkit stays under a dual license, i.e. both the conditions of the
OpenSSL License and the original SSLeay license apply to the toolkit. See below
@@ -190,3 +192,27 @@
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+The code in third_party/fiat carries the MIT license:
+
+Copyright (c) 2015-2016 the fiat-crypto authors (see
+https://github.com/mit-plv/fiat-crypto/blob/master/AUTHORS).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/src/crypto/CMakeLists.txt b/src/crypto/CMakeLists.txt
index ae5d0b6..640f206 100644
--- a/src/crypto/CMakeLists.txt
+++ b/src/crypto/CMakeLists.txt
@@ -179,6 +179,7 @@
$<TARGET_OBJECTS:chacha>
$<TARGET_OBJECTS:poly1305>
$<TARGET_OBJECTS:curve25519>
+ $<TARGET_OBJECTS:fiat>
$<TARGET_OBJECTS:buf>
$<TARGET_OBJECTS:bn_extra>
$<TARGET_OBJECTS:bio>
diff --git a/src/crypto/conf/conf.c b/src/crypto/conf/conf.c
index f8ff613..b1982f8 100644
--- a/src/crypto/conf/conf.c
+++ b/src/crypto/conf/conf.c
@@ -791,13 +791,13 @@
}
}
-int CONF_modules_load_file(CONF_MUST_BE_NULL *filename, const char *appname,
+int CONF_modules_load_file(const char *filename, const char *appname,
unsigned long flags) {
return 1;
}
void CONF_modules_free(void) {}
-void OPENSSL_config(CONF_MUST_BE_NULL *config_name) {}
+void OPENSSL_config(const char *config_name) {}
void OPENSSL_no_config(void) {}
diff --git a/src/crypto/curve25519/CMakeLists.txt b/src/crypto/curve25519/CMakeLists.txt
index c6004d3..6f51d54 100644
--- a/src/crypto/curve25519/CMakeLists.txt
+++ b/src/crypto/curve25519/CMakeLists.txt
@@ -21,7 +21,6 @@
OBJECT
- curve25519.c
spake25519.c
x25519-x86_64.c
diff --git a/src/crypto/curve25519/curve25519.c b/src/crypto/curve25519/curve25519.c
deleted file mode 100644
index e49a8b3..0000000
--- a/src/crypto/curve25519/curve25519.c
+++ /dev/null
@@ -1,4938 +0,0 @@
-/* Copyright (c) 2015, Google Inc.
- *
- * Permission to use, copy, modify, and/or distribute this software for any
- * purpose with or without fee is hereby granted, provided that the above
- * copyright notice and this permission notice appear in all copies.
- *
- * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
- * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
- * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
- * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
- * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
- * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
- * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
-
-// This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
-// 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
-// public domain but this file has the ISC license just to keep licencing
-// simple.
-//
-// The field functions are shared by Ed25519 and X25519 where possible.
-
-#include <openssl/curve25519.h>
-
-#include <string.h>
-
-#include <openssl/cpu.h>
-#include <openssl/mem.h>
-#include <openssl/rand.h>
-#include <openssl/sha.h>
-
-#include "internal.h"
-#include "../internal.h"
-
-
-static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
-static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
-static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000);
-static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000);
-
-static uint64_t load_3(const uint8_t *in) {
- uint64_t result;
- result = (uint64_t)in[0];
- result |= ((uint64_t)in[1]) << 8;
- result |= ((uint64_t)in[2]) << 16;
- return result;
-}
-
-static uint64_t load_4(const uint8_t *in) {
- uint64_t result;
- result = (uint64_t)in[0];
- result |= ((uint64_t)in[1]) << 8;
- result |= ((uint64_t)in[2]) << 16;
- result |= ((uint64_t)in[3]) << 24;
- return result;
-}
-
-static void fe_frombytes(fe h, const uint8_t *s) {
- // Ignores top bit of h.
- int64_t h0 = load_4(s);
- int64_t h1 = load_3(s + 4) << 6;
- int64_t h2 = load_3(s + 7) << 5;
- int64_t h3 = load_3(s + 10) << 3;
- int64_t h4 = load_3(s + 13) << 2;
- int64_t h5 = load_4(s + 16);
- int64_t h6 = load_3(s + 20) << 7;
- int64_t h7 = load_3(s + 23) << 5;
- int64_t h8 = load_3(s + 26) << 4;
- int64_t h9 = (load_3(s + 29) & 8388607) << 2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
- carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
- carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-// Preconditions:
-// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Write p=2^255-19; q=floor(h/p).
-// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
-//
-// Proof:
-// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
-// Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
-//
-// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
-// Then 0<y<1.
-//
-// Write r=h-pq.
-// Have 0<=r<=p-1=2^255-20.
-// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
-//
-// Write x=r+19(2^-255)r+y.
-// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
-//
-// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
-// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
-static void fe_tobytes(uint8_t *s, const fe h) {
- int32_t h0 = h[0];
- int32_t h1 = h[1];
- int32_t h2 = h[2];
- int32_t h3 = h[3];
- int32_t h4 = h[4];
- int32_t h5 = h[5];
- int32_t h6 = h[6];
- int32_t h7 = h[7];
- int32_t h8 = h[8];
- int32_t h9 = h[9];
- int32_t q;
-
- q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
- q = (h0 + q) >> 26;
- q = (h1 + q) >> 25;
- q = (h2 + q) >> 26;
- q = (h3 + q) >> 25;
- q = (h4 + q) >> 26;
- q = (h5 + q) >> 25;
- q = (h6 + q) >> 26;
- q = (h7 + q) >> 25;
- q = (h8 + q) >> 26;
- q = (h9 + q) >> 25;
-
- // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
- h0 += 19 * q;
- // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
-
- h1 += h0 >> 26; h0 &= kBottom26Bits;
- h2 += h1 >> 25; h1 &= kBottom25Bits;
- h3 += h2 >> 26; h2 &= kBottom26Bits;
- h4 += h3 >> 25; h3 &= kBottom25Bits;
- h5 += h4 >> 26; h4 &= kBottom26Bits;
- h6 += h5 >> 25; h5 &= kBottom25Bits;
- h7 += h6 >> 26; h6 &= kBottom26Bits;
- h8 += h7 >> 25; h7 &= kBottom25Bits;
- h9 += h8 >> 26; h8 &= kBottom26Bits;
- h9 &= kBottom25Bits;
- // h10 = carry9
-
- // Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- // Have h0+...+2^230 h9 between 0 and 2^255-1;
- // evidently 2^255 h10-2^255 q = 0.
- // Goal: Output h0+...+2^230 h9.
-
- s[0] = h0 >> 0;
- s[1] = h0 >> 8;
- s[2] = h0 >> 16;
- s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
- s[4] = h1 >> 6;
- s[5] = h1 >> 14;
- s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
- s[7] = h2 >> 5;
- s[8] = h2 >> 13;
- s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
- s[10] = h3 >> 3;
- s[11] = h3 >> 11;
- s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
- s[13] = h4 >> 2;
- s[14] = h4 >> 10;
- s[15] = h4 >> 18;
- s[16] = h5 >> 0;
- s[17] = h5 >> 8;
- s[18] = h5 >> 16;
- s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
- s[20] = h6 >> 7;
- s[21] = h6 >> 15;
- s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
- s[23] = h7 >> 5;
- s[24] = h7 >> 13;
- s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
- s[26] = h8 >> 4;
- s[27] = h8 >> 12;
- s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
- s[29] = h9 >> 2;
- s[30] = h9 >> 10;
- s[31] = h9 >> 18;
-}
-
-// h = f
-static void fe_copy(fe h, const fe f) {
- OPENSSL_memmove(h, f, sizeof(int32_t) * 10);
-}
-
-// h = 0
-static void fe_0(fe h) { OPENSSL_memset(h, 0, sizeof(int32_t) * 10); }
-
-// h = 1
-static void fe_1(fe h) {
- OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
- h[0] = 1;
-}
-
-// h = f + g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-// |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static void fe_add(fe h, const fe f, const fe g) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = f[i] + g[i];
- }
-}
-
-// h = f - g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-// |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static void fe_sub(fe h, const fe f, const fe g) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = f[i] - g[i];
- }
-}
-
-// h = f * g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
-// |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
-//
-// Notes on implementation strategy:
-//
-// Using schoolbook multiplication.
-// Karatsuba would save a little in some cost models.
-//
-// Most multiplications by 2 and 19 are 32-bit precomputations;
-// cheaper than 64-bit postcomputations.
-//
-// There is one remaining multiplication by 19 in the carry chain;
-// one *19 precomputation can be merged into this,
-// but the resulting data flow is considerably less clean.
-//
-// There are 12 carries below.
-// 10 of them are 2-way parallelizable and vectorizable.
-// Can get away with 11 carries, but then data flow is much deeper.
-//
-// With tighter constraints on inputs can squeeze carries into int32.
-static void fe_mul(fe h, const fe f, const fe g) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t g0 = g[0];
- int32_t g1 = g[1];
- int32_t g2 = g[2];
- int32_t g3 = g[3];
- int32_t g4 = g[4];
- int32_t g5 = g[5];
- int32_t g6 = g[6];
- int32_t g7 = g[7];
- int32_t g8 = g[8];
- int32_t g9 = g[9];
- int32_t g1_19 = 19 * g1; // 1.959375*2^29
- int32_t g2_19 = 19 * g2; // 1.959375*2^30; still ok
- int32_t g3_19 = 19 * g3;
- int32_t g4_19 = 19 * g4;
- int32_t g5_19 = 19 * g5;
- int32_t g6_19 = 19 * g6;
- int32_t g7_19 = 19 * g7;
- int32_t g8_19 = 19 * g8;
- int32_t g9_19 = 19 * g9;
- int32_t f1_2 = 2 * f1;
- int32_t f3_2 = 2 * f3;
- int32_t f5_2 = 2 * f5;
- int32_t f7_2 = 2 * f7;
- int32_t f9_2 = 2 * f9;
- int64_t f0g0 = f0 * (int64_t) g0;
- int64_t f0g1 = f0 * (int64_t) g1;
- int64_t f0g2 = f0 * (int64_t) g2;
- int64_t f0g3 = f0 * (int64_t) g3;
- int64_t f0g4 = f0 * (int64_t) g4;
- int64_t f0g5 = f0 * (int64_t) g5;
- int64_t f0g6 = f0 * (int64_t) g6;
- int64_t f0g7 = f0 * (int64_t) g7;
- int64_t f0g8 = f0 * (int64_t) g8;
- int64_t f0g9 = f0 * (int64_t) g9;
- int64_t f1g0 = f1 * (int64_t) g0;
- int64_t f1g1_2 = f1_2 * (int64_t) g1;
- int64_t f1g2 = f1 * (int64_t) g2;
- int64_t f1g3_2 = f1_2 * (int64_t) g3;
- int64_t f1g4 = f1 * (int64_t) g4;
- int64_t f1g5_2 = f1_2 * (int64_t) g5;
- int64_t f1g6 = f1 * (int64_t) g6;
- int64_t f1g7_2 = f1_2 * (int64_t) g7;
- int64_t f1g8 = f1 * (int64_t) g8;
- int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
- int64_t f2g0 = f2 * (int64_t) g0;
- int64_t f2g1 = f2 * (int64_t) g1;
- int64_t f2g2 = f2 * (int64_t) g2;
- int64_t f2g3 = f2 * (int64_t) g3;
- int64_t f2g4 = f2 * (int64_t) g4;
- int64_t f2g5 = f2 * (int64_t) g5;
- int64_t f2g6 = f2 * (int64_t) g6;
- int64_t f2g7 = f2 * (int64_t) g7;
- int64_t f2g8_19 = f2 * (int64_t) g8_19;
- int64_t f2g9_19 = f2 * (int64_t) g9_19;
- int64_t f3g0 = f3 * (int64_t) g0;
- int64_t f3g1_2 = f3_2 * (int64_t) g1;
- int64_t f3g2 = f3 * (int64_t) g2;
- int64_t f3g3_2 = f3_2 * (int64_t) g3;
- int64_t f3g4 = f3 * (int64_t) g4;
- int64_t f3g5_2 = f3_2 * (int64_t) g5;
- int64_t f3g6 = f3 * (int64_t) g6;
- int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
- int64_t f3g8_19 = f3 * (int64_t) g8_19;
- int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
- int64_t f4g0 = f4 * (int64_t) g0;
- int64_t f4g1 = f4 * (int64_t) g1;
- int64_t f4g2 = f4 * (int64_t) g2;
- int64_t f4g3 = f4 * (int64_t) g3;
- int64_t f4g4 = f4 * (int64_t) g4;
- int64_t f4g5 = f4 * (int64_t) g5;
- int64_t f4g6_19 = f4 * (int64_t) g6_19;
- int64_t f4g7_19 = f4 * (int64_t) g7_19;
- int64_t f4g8_19 = f4 * (int64_t) g8_19;
- int64_t f4g9_19 = f4 * (int64_t) g9_19;
- int64_t f5g0 = f5 * (int64_t) g0;
- int64_t f5g1_2 = f5_2 * (int64_t) g1;
- int64_t f5g2 = f5 * (int64_t) g2;
- int64_t f5g3_2 = f5_2 * (int64_t) g3;
- int64_t f5g4 = f5 * (int64_t) g4;
- int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
- int64_t f5g6_19 = f5 * (int64_t) g6_19;
- int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
- int64_t f5g8_19 = f5 * (int64_t) g8_19;
- int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
- int64_t f6g0 = f6 * (int64_t) g0;
- int64_t f6g1 = f6 * (int64_t) g1;
- int64_t f6g2 = f6 * (int64_t) g2;
- int64_t f6g3 = f6 * (int64_t) g3;
- int64_t f6g4_19 = f6 * (int64_t) g4_19;
- int64_t f6g5_19 = f6 * (int64_t) g5_19;
- int64_t f6g6_19 = f6 * (int64_t) g6_19;
- int64_t f6g7_19 = f6 * (int64_t) g7_19;
- int64_t f6g8_19 = f6 * (int64_t) g8_19;
- int64_t f6g9_19 = f6 * (int64_t) g9_19;
- int64_t f7g0 = f7 * (int64_t) g0;
- int64_t f7g1_2 = f7_2 * (int64_t) g1;
- int64_t f7g2 = f7 * (int64_t) g2;
- int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
- int64_t f7g4_19 = f7 * (int64_t) g4_19;
- int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
- int64_t f7g6_19 = f7 * (int64_t) g6_19;
- int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
- int64_t f7g8_19 = f7 * (int64_t) g8_19;
- int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
- int64_t f8g0 = f8 * (int64_t) g0;
- int64_t f8g1 = f8 * (int64_t) g1;
- int64_t f8g2_19 = f8 * (int64_t) g2_19;
- int64_t f8g3_19 = f8 * (int64_t) g3_19;
- int64_t f8g4_19 = f8 * (int64_t) g4_19;
- int64_t f8g5_19 = f8 * (int64_t) g5_19;
- int64_t f8g6_19 = f8 * (int64_t) g6_19;
- int64_t f8g7_19 = f8 * (int64_t) g7_19;
- int64_t f8g8_19 = f8 * (int64_t) g8_19;
- int64_t f8g9_19 = f8 * (int64_t) g9_19;
- int64_t f9g0 = f9 * (int64_t) g0;
- int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
- int64_t f9g2_19 = f9 * (int64_t) g2_19;
- int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
- int64_t f9g4_19 = f9 * (int64_t) g4_19;
- int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
- int64_t f9g6_19 = f9 * (int64_t) g6_19;
- int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
- int64_t f9g8_19 = f9 * (int64_t) g8_19;
- int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
- int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
- int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
- int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
- int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
- int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
- int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
- int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
- int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
- int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
- int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- // |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
- // i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
- // |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
- // i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- // |h0| <= 2^25
- // |h4| <= 2^25
- // |h1| <= 1.71*2^59
- // |h5| <= 1.71*2^59
-
- carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
- carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- // |h1| <= 2^24; from now on fits into int32
- // |h5| <= 2^24; from now on fits into int32
- // |h2| <= 1.41*2^60
- // |h6| <= 1.41*2^60
-
- carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
- carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- // |h2| <= 2^25; from now on fits into int32 unchanged
- // |h6| <= 2^25; from now on fits into int32 unchanged
- // |h3| <= 1.71*2^59
- // |h7| <= 1.71*2^59
-
- carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
- carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
- // |h3| <= 2^24; from now on fits into int32 unchanged
- // |h7| <= 2^24; from now on fits into int32 unchanged
- // |h4| <= 1.72*2^34
- // |h8| <= 1.41*2^60
-
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
- // |h4| <= 2^25; from now on fits into int32 unchanged
- // |h8| <= 2^25; from now on fits into int32 unchanged
- // |h5| <= 1.01*2^24
- // |h9| <= 1.71*2^59
-
- carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- // |h9| <= 2^24; from now on fits into int32 unchanged
- // |h0| <= 1.1*2^39
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- // |h0| <= 2^25; from now on fits into int32 unchanged
- // |h1| <= 1.01*2^24
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-// h = f * f
-// Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
-//
-// See fe_mul.c for discussion of implementation strategy.
-static void fe_sq(fe h, const fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t f0_2 = 2 * f0;
- int32_t f1_2 = 2 * f1;
- int32_t f2_2 = 2 * f2;
- int32_t f3_2 = 2 * f3;
- int32_t f4_2 = 2 * f4;
- int32_t f5_2 = 2 * f5;
- int32_t f6_2 = 2 * f6;
- int32_t f7_2 = 2 * f7;
- int32_t f5_38 = 38 * f5; // 1.959375*2^30
- int32_t f6_19 = 19 * f6; // 1.959375*2^30
- int32_t f7_38 = 38 * f7; // 1.959375*2^30
- int32_t f8_19 = 19 * f8; // 1.959375*2^30
- int32_t f9_38 = 38 * f9; // 1.959375*2^30
- int64_t f0f0 = f0 * (int64_t) f0;
- int64_t f0f1_2 = f0_2 * (int64_t) f1;
- int64_t f0f2_2 = f0_2 * (int64_t) f2;
- int64_t f0f3_2 = f0_2 * (int64_t) f3;
- int64_t f0f4_2 = f0_2 * (int64_t) f4;
- int64_t f0f5_2 = f0_2 * (int64_t) f5;
- int64_t f0f6_2 = f0_2 * (int64_t) f6;
- int64_t f0f7_2 = f0_2 * (int64_t) f7;
- int64_t f0f8_2 = f0_2 * (int64_t) f8;
- int64_t f0f9_2 = f0_2 * (int64_t) f9;
- int64_t f1f1_2 = f1_2 * (int64_t) f1;
- int64_t f1f2_2 = f1_2 * (int64_t) f2;
- int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
- int64_t f1f4_2 = f1_2 * (int64_t) f4;
- int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
- int64_t f1f6_2 = f1_2 * (int64_t) f6;
- int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
- int64_t f1f8_2 = f1_2 * (int64_t) f8;
- int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
- int64_t f2f2 = f2 * (int64_t) f2;
- int64_t f2f3_2 = f2_2 * (int64_t) f3;
- int64_t f2f4_2 = f2_2 * (int64_t) f4;
- int64_t f2f5_2 = f2_2 * (int64_t) f5;
- int64_t f2f6_2 = f2_2 * (int64_t) f6;
- int64_t f2f7_2 = f2_2 * (int64_t) f7;
- int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
- int64_t f2f9_38 = f2 * (int64_t) f9_38;
- int64_t f3f3_2 = f3_2 * (int64_t) f3;
- int64_t f3f4_2 = f3_2 * (int64_t) f4;
- int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
- int64_t f3f6_2 = f3_2 * (int64_t) f6;
- int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
- int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
- int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
- int64_t f4f4 = f4 * (int64_t) f4;
- int64_t f4f5_2 = f4_2 * (int64_t) f5;
- int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
- int64_t f4f7_38 = f4 * (int64_t) f7_38;
- int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
- int64_t f4f9_38 = f4 * (int64_t) f9_38;
- int64_t f5f5_38 = f5 * (int64_t) f5_38;
- int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
- int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
- int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
- int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
- int64_t f6f6_19 = f6 * (int64_t) f6_19;
- int64_t f6f7_38 = f6 * (int64_t) f7_38;
- int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
- int64_t f6f9_38 = f6 * (int64_t) f9_38;
- int64_t f7f7_38 = f7 * (int64_t) f7_38;
- int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
- int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
- int64_t f8f8_19 = f8 * (int64_t) f8_19;
- int64_t f8f9_38 = f8 * (int64_t) f9_38;
- int64_t f9f9_38 = f9 * (int64_t) f9_38;
- int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
- int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
- int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
- int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
- int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
- int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
- int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
- int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
- int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
- int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-
- carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
- carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-
- carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
- carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-
- carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
- carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
- carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-static void fe_invert(fe out, const fe z) {
- fe t0;
- fe t1;
- fe t2;
- fe t3;
- int i;
-
- fe_sq(t0, z);
- fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t2, t0);
- fe_mul(t1, t1, t2);
- fe_sq(t2, t1);
- for (i = 1; i < 5; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t2, t1);
- for (i = 1; i < 10; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t2, t2, t1);
- fe_sq(t3, t2);
- for (i = 1; i < 20; ++i) {
- fe_sq(t3, t3);
- }
- fe_mul(t2, t3, t2);
- fe_sq(t2, t2);
- for (i = 1; i < 10; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t2, t1);
- for (i = 1; i < 50; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t2, t2, t1);
- fe_sq(t3, t2);
- for (i = 1; i < 100; ++i) {
- fe_sq(t3, t3);
- }
- fe_mul(t2, t3, t2);
- fe_sq(t2, t2);
- for (i = 1; i < 50; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(out, t1, t0);
-}
-
-// h = -f
-//
-// Preconditions:
-// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-static void fe_neg(fe h, const fe f) {
- unsigned i;
- for (i = 0; i < 10; i++) {
- h[i] = -f[i];
- }
-}
-
-// Replace (f,g) with (g,g) if b == 1;
-// replace (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-static void fe_cmov(fe f, const fe g, unsigned b) {
- b = 0-b;
- unsigned i;
- for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
- x &= b;
- f[i] ^= x;
- }
-}
-
-// return 0 if f == 0
-// return 1 if f != 0
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static int fe_isnonzero(const fe f) {
- uint8_t s[32];
- fe_tobytes(s, f);
-
- static const uint8_t zero[32] = {0};
- return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
-}
-
-// return 1 if f is in {1,3,5,...,q-2}
-// return 0 if f is in {0,2,4,...,q-1}
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static int fe_isnegative(const fe f) {
- uint8_t s[32];
- fe_tobytes(s, f);
- return s[0] & 1;
-}
-
-// h = 2 * f * f
-// Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
-//
-// See fe_mul.c for discussion of implementation strategy.
-static void fe_sq2(fe h, const fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t f0_2 = 2 * f0;
- int32_t f1_2 = 2 * f1;
- int32_t f2_2 = 2 * f2;
- int32_t f3_2 = 2 * f3;
- int32_t f4_2 = 2 * f4;
- int32_t f5_2 = 2 * f5;
- int32_t f6_2 = 2 * f6;
- int32_t f7_2 = 2 * f7;
- int32_t f5_38 = 38 * f5; // 1.959375*2^30
- int32_t f6_19 = 19 * f6; // 1.959375*2^30
- int32_t f7_38 = 38 * f7; // 1.959375*2^30
- int32_t f8_19 = 19 * f8; // 1.959375*2^30
- int32_t f9_38 = 38 * f9; // 1.959375*2^30
- int64_t f0f0 = f0 * (int64_t) f0;
- int64_t f0f1_2 = f0_2 * (int64_t) f1;
- int64_t f0f2_2 = f0_2 * (int64_t) f2;
- int64_t f0f3_2 = f0_2 * (int64_t) f3;
- int64_t f0f4_2 = f0_2 * (int64_t) f4;
- int64_t f0f5_2 = f0_2 * (int64_t) f5;
- int64_t f0f6_2 = f0_2 * (int64_t) f6;
- int64_t f0f7_2 = f0_2 * (int64_t) f7;
- int64_t f0f8_2 = f0_2 * (int64_t) f8;
- int64_t f0f9_2 = f0_2 * (int64_t) f9;
- int64_t f1f1_2 = f1_2 * (int64_t) f1;
- int64_t f1f2_2 = f1_2 * (int64_t) f2;
- int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
- int64_t f1f4_2 = f1_2 * (int64_t) f4;
- int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
- int64_t f1f6_2 = f1_2 * (int64_t) f6;
- int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
- int64_t f1f8_2 = f1_2 * (int64_t) f8;
- int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
- int64_t f2f2 = f2 * (int64_t) f2;
- int64_t f2f3_2 = f2_2 * (int64_t) f3;
- int64_t f2f4_2 = f2_2 * (int64_t) f4;
- int64_t f2f5_2 = f2_2 * (int64_t) f5;
- int64_t f2f6_2 = f2_2 * (int64_t) f6;
- int64_t f2f7_2 = f2_2 * (int64_t) f7;
- int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
- int64_t f2f9_38 = f2 * (int64_t) f9_38;
- int64_t f3f3_2 = f3_2 * (int64_t) f3;
- int64_t f3f4_2 = f3_2 * (int64_t) f4;
- int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
- int64_t f3f6_2 = f3_2 * (int64_t) f6;
- int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
- int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
- int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
- int64_t f4f4 = f4 * (int64_t) f4;
- int64_t f4f5_2 = f4_2 * (int64_t) f5;
- int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
- int64_t f4f7_38 = f4 * (int64_t) f7_38;
- int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
- int64_t f4f9_38 = f4 * (int64_t) f9_38;
- int64_t f5f5_38 = f5 * (int64_t) f5_38;
- int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
- int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
- int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
- int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
- int64_t f6f6_19 = f6 * (int64_t) f6_19;
- int64_t f6f7_38 = f6 * (int64_t) f7_38;
- int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
- int64_t f6f9_38 = f6 * (int64_t) f9_38;
- int64_t f7f7_38 = f7 * (int64_t) f7_38;
- int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
- int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
- int64_t f8f8_19 = f8 * (int64_t) f8_19;
- int64_t f8f9_38 = f8 * (int64_t) f9_38;
- int64_t f9f9_38 = f9 * (int64_t) f9_38;
- int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
- int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
- int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
- int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
- int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
- int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
- int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
- int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
- int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
- int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- h0 += h0;
- h1 += h1;
- h2 += h2;
- h3 += h3;
- h4 += h4;
- h5 += h5;
- h6 += h6;
- h7 += h7;
- h8 += h8;
- h9 += h9;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
-
- carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
- carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
-
- carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
- carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
-
- carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
- carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
- carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-static void fe_pow22523(fe out, const fe z) {
- fe t0;
- fe t1;
- fe t2;
- int i;
-
- fe_sq(t0, z);
- fe_sq(t1, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t0, t0);
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 20; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
- for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
- for (i = 1; i < 100; ++i) {
- fe_sq(t2, t2);
- }
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
- for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
- }
- fe_mul(t0, t1, t0);
- fe_sq(t0, t0);
- for (i = 1; i < 2; ++i) {
- fe_sq(t0, t0);
- }
- fe_mul(out, t0, z);
-}
-
-void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) {
- fe recip;
- fe x;
- fe y;
-
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
-
-static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
- fe recip;
- fe x;
- fe y;
-
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
-}
-
-static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
- -8787816, -6275908, -3247719, -18696448, -12055116};
-
-static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482};
-
-int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
- fe u;
- fe v;
- fe v3;
- fe vxx;
- fe check;
-
- fe_frombytes(h->Y, s);
- fe_1(h->Z);
- fe_sq(u, h->Y);
- fe_mul(v, u, d);
- fe_sub(u, u, h->Z); // u = y^2-1
- fe_add(v, v, h->Z); // v = dy^2+1
-
- fe_sq(v3, v);
- fe_mul(v3, v3, v); // v3 = v^3
- fe_sq(h->X, v3);
- fe_mul(h->X, h->X, v);
- fe_mul(h->X, h->X, u); // x = uv^7
-
- fe_pow22523(h->X, h->X); // x = (uv^7)^((q-5)/8)
- fe_mul(h->X, h->X, v3);
- fe_mul(h->X, h->X, u); // x = uv^3(uv^7)^((q-5)/8)
-
- fe_sq(vxx, h->X);
- fe_mul(vxx, vxx, v);
- fe_sub(check, vxx, u); // vx^2-u
- if (fe_isnonzero(check)) {
- fe_add(check, vxx, u); // vx^2+u
- if (fe_isnonzero(check)) {
- return -1;
- }
- fe_mul(h->X, h->X, sqrtm1);
- }
-
- if (fe_isnegative(h->X) != (s[31] >> 7)) {
- fe_neg(h->X, h->X);
- }
-
- fe_mul(h->T, h->X, h->Y);
- return 0;
-}
-
-static void ge_p2_0(ge_p2 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
-}
-
-static void ge_p3_0(ge_p3 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
- fe_0(h->T);
-}
-
-static void ge_cached_0(ge_cached *h) {
- fe_1(h->YplusX);
- fe_1(h->YminusX);
- fe_1(h->Z);
- fe_0(h->T2d);
-}
-
-static void ge_precomp_0(ge_precomp *h) {
- fe_1(h->yplusx);
- fe_1(h->yminusx);
- fe_0(h->xy2d);
-}
-
-// r = p
-static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
- fe_copy(r->X, p->X);
- fe_copy(r->Y, p->Y);
- fe_copy(r->Z, p->Z);
-}
-
-static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
- 15978800, -12551817, -6495438, 29715968, 9444199};
-
-// r = p
-void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
- fe_add(r->YplusX, p->Y, p->X);
- fe_sub(r->YminusX, p->Y, p->X);
- fe_copy(r->Z, p->Z);
- fe_mul(r->T2d, p->T, d2);
-}
-
-// r = p
-void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
-}
-
-// r = p
-void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
- fe_mul(r->T, p->X, p->Y);
-}
-
-// r = p
-static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) {
- ge_p3 t;
- x25519_ge_p1p1_to_p3(&t, p);
- x25519_ge_p3_to_cached(r, &t);
-}
-
-// r = 2 * p
-static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
- fe t0;
-
- fe_sq(r->X, p->X);
- fe_sq(r->Z, p->Y);
- fe_sq2(r->T, p->Z);
- fe_add(r->Y, p->X, p->Y);
- fe_sq(t0, r->Y);
- fe_add(r->Y, r->Z, r->X);
- fe_sub(r->Z, r->Z, r->X);
- fe_sub(r->X, t0, r->Y);
- fe_sub(r->T, r->T, r->Z);
-}
-
-// r = 2 * p
-static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
- ge_p2 q;
- ge_p3_to_p2(&q, p);
- ge_p2_dbl(r, &q);
-}
-
-// r = p + q
-static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yplusx);
- fe_mul(r->Y, r->Y, q->yminusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
-}
-
-// r = p - q
-static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yminusx);
- fe_mul(r->Y, r->Y, q->yplusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
-}
-
-// r = p + q
-void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YplusX);
- fe_mul(r->Y, r->Y, q->YminusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
-}
-
-// r = p - q
-void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
-
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YminusX);
- fe_mul(r->Y, r->Y, q->YplusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
-}
-
-static uint8_t equal(signed char b, signed char c) {
- uint8_t ub = b;
- uint8_t uc = c;
- uint8_t x = ub ^ uc; // 0: yes; 1..255: no
- uint32_t y = x; // 0: yes; 1..255: no
- y -= 1; // 4294967295: yes; 0..254: no
- y >>= 31; // 1: yes; 0: no
- return y;
-}
-
-static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
- fe_cmov(t->yplusx, u->yplusx, b);
- fe_cmov(t->yminusx, u->yminusx, b);
- fe_cmov(t->xy2d, u->xy2d, b);
-}
-
-void x25519_ge_scalarmult_small_precomp(
- ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) {
- // precomp_table is first expanded into matching |ge_precomp|
- // elements.
- ge_precomp multiples[15];
-
- unsigned i;
- for (i = 0; i < 15; i++) {
- const uint8_t *bytes = &precomp_table[i*(2 * 32)];
- fe x, y;
- fe_frombytes(x, bytes);
- fe_frombytes(y, bytes + 32);
-
- ge_precomp *out = &multiples[i];
- fe_add(out->yplusx, y, x);
- fe_sub(out->yminusx, y, x);
- fe_mul(out->xy2d, x, y);
- fe_mul(out->xy2d, out->xy2d, d2);
- }
-
- // See the comment above |k25519SmallPrecomp| about the structure of the
- // precomputed elements. This loop does 64 additions and 64 doublings to
- // calculate the result.
- ge_p3_0(h);
-
- for (i = 63; i < 64; i--) {
- unsigned j;
- signed char index = 0;
-
- for (j = 0; j < 4; j++) {
- const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
- index |= (bit << j);
- }
-
- ge_precomp e;
- ge_precomp_0(&e);
-
- for (j = 1; j < 16; j++) {
- cmov(&e, &multiples[j-1], equal(index, j));
- }
-
- ge_cached cached;
- ge_p1p1 r;
- x25519_ge_p3_to_cached(&cached, h);
- x25519_ge_add(&r, h, &cached);
- x25519_ge_p1p1_to_p3(h, &r);
-
- ge_madd(&r, h, &e);
- x25519_ge_p1p1_to_p3(h, &r);
- }
-}
-
-#if defined(OPENSSL_SMALL)
-
-// This block of code replaces the standard base-point table with a much smaller
-// one. The standard table is 30,720 bytes while this one is just 960.
-//
-// This table contains 15 pairs of group elements, (x, y), where each field
-// element is serialised with |fe_tobytes|. If |i| is the index of the group
-// element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
-// is the most significant bit). The value of the group element is then:
-// (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator.
-static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
- 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
- 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
- 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
- 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
- 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
- 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
- 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
- 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
- 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
- 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
- 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
- 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
- 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
- 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
- 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
- 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
- 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
- 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
- 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
- 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
- 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
- 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
- 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
- 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
- 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
- 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
- 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
- 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
- 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
- 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
- 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
- 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
- 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
- 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
- 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
- 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
- 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
- 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
- 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
- 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
- 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
- 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
- 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
- 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
- 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
- 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
- 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
- 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
- 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
- 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
- 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
- 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
- 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
- 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
- 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
- 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
- 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
- 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
- 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
- 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
- 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
- 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
- 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
- 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
- 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
- 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
- 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
- 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
- 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
- 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
- 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
- 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
- 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
- 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
- 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
- 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
- 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
- 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
-};
-
-void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
- x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp);
-}
-
-#else
-
-// k25519Precomp[i][j] = (j+1)*256^i*B
-static const ge_precomp k25519Precomp[32][8] = {
- {
- {
- {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
- 27544626, -11754271, -6079156, 2047605},
- {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378},
- {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
- 29287919, 11864899, -24514362, -4438546},
- },
- {
- {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
- -11717903, -3814571, -358445, -10211303},
- {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
- -15616551, 11189268, -26829678, -5319081},
- {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
- -3128826, -9541118, -15472047, -4166697},
- },
- {
- {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
- 27787600, -14772189, 28944400, -1550024},
- {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
- 16354577, -11775962, 7689662, 11199574},
- {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
- 7512774, 10017326, -17749093, -9920357},
- },
- {
- {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
- -28926210, 15006023, 3284568, -6276540},
- {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
- 7464579, 9656445, 13059162, 10374397},
- {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
- -3839045, -641708, -101325},
- },
- {
- {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
- 32867885, 14515107, -15438304, 10819380},
- {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306},
- {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
- 28542350, 13850243, -23678021, -15815942},
- },
- {
- {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
- -19188627, -15224819, -9818940, -12085777},
- {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
- -15689887, 1762328, 14866737},
- {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
- -28236412, 3959421, 27914454, 4383652},
- },
- {
- {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766},
- {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
- 20654025, 16520125, 30598449, 7715701},
- {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
- -31400660, 1370708, 29794553, -1409300},
- },
- {
- {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
- 30290735, 10876454, -33154098, 2381726},
- {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
- -6236617, 3696005, -32300832, 15351955},
- {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
- -32961401, -2970515, 29551813, 10109425},
- },
- },
- {
- {
- {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
- -2378284, -1627556, 10092783, -4764171},
- {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
- -32508754, 12005538, -17810127, 12803510},
- {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
- 30364213, -9038194, 18016357, 4397660},
- },
- {
- {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
- -26619106, 14544525, -17477504, 982639},
- {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
- -4120128, -21047696, 9934963},
- {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
- -14747930, 4559895, -30123922, -10897950},
- },
- {
- {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
- 24191034, 4541697, -13338309, 5500568},
- {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
- -17430592, 12264343, 10874051, 13524335},
- {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
- 5080568, -22528059, 5376628},
- },
- {
- {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
- -22321305, -9447443, 4535768, 1569007},
- {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
- -30494562, 3044290, 31848280, 12543772},
- {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
- -27377195, -2062731, 7718482, 14474653},
- },
- {
- {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
- -7236665, 24316168, -5253567},
- {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
- 33040651, -13424532, -20729456, 8321686},
- {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
- 23845965, -11874838, -9984458, 608372},
- },
- {
- {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
- 1123968, -6780577, 27229399, 23887},
- {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
- 12797024, -6440308, -1633405, 16678954},
- {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
- -1508144, -4795045, -17169265, 4904953},
- },
- {
- {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
- 5169211, 16191880, 2128236, -4326833},
- {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
- -29806336, 916033, -6882542, -2986532},
- {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
- 285431, 2763829, 15736322, 4143876},
- },
- {
- {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
- -14594663, 23527084, -16458268},
- {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
- -32625340, 4087881, -15188911, -14416214},
- {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
- 4357868, -4774191, -16323038},
- },
- },
- {
- {
- {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
- 23365147, -3949732, 7390890, 2759800},
- {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
- -4264057, 1244380, -12919645},
- {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
- 9208236, 15886429, 16489664},
- },
- {
- {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
- -13693198, 398369, -30606455, -712933},
- {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
- 13348553, 12076947, -30836462, 5113182},
- {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
- -30341101, -7336386, 13847711, 5387222},
- },
- {
- {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
- 8763061, 3617786, -19600662, 10370991},
- {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
- 14554437, -8746092, 32232924, 16763880},
- {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
- 11094161, 15689506, 3140038, -16510092},
- },
- {
- {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
- -27224800, 9448613, -28774454, 366295},
- {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
- 28344573, 8041113, 719605, 11671788},
- {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
- -15266516, 27000813, -10195553},
- },
- {
- {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
- 5336097, 6750977, -14521026},
- {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
- 1695823, -8819122, 8169720, 16220347},
- {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
- -11144307, -2627664, -5990708, -14166033},
- },
- {
- {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
- 27884329, 2847284, 2655861, 1738395},
- {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
- 21651608, -3239336, -19087449, -11005278},
- {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
- 5821408, 10478196, 8544890},
- },
- {
- {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
- 19270449, 12217473, 17789017, -3395995},
- {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
- 15479401, -3853233, 30460520, 1052596},
- {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
- 27491595, -4612359, 3179268, -9478891},
- },
- {
- {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
- -14756777, -16411740, 19072640, -9511060},
- {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
- 5977896, -5215017, 473099, 5040608},
- {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
- 28326862, 1721092, -19558642, -3131606},
- },
- },
- {
- {
- {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
- 8076149, -27868496, 11538389},
- {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
- 8754525, 7446702, -5676054, 5797016},
- {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
- 2014099, -9050574, -2369172, -5877341},
- },
- {
- {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
- 1192730, -3714199, 15123619, 10811505},
- {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
- 15776356, -28886779, -11974553},
- {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
- -20654173, -16484855, 4714547, -9600655},
- },
- {
- {15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
- 24611599, -4543832, -11745876, 12340220},
- {12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
- 9613953, 8241152, 15370987, 9608631},
- {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
- 15866074, -28210621, -8814099},
- },
- {
- {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233,
- 858697, 20571223, 8420556},
- {14620715, 13067227, -15447274, 8264467, 14106269, 15080814,
- 33531827, 12516406, -21574435, -12476749},
- {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519,
- 7256740, 8791136, 15069930},
- },
- {
- {1276410, -9371918, 22949635, -16322807, -23493039, -5702186,
- 14711875, 4874229, -30663140, -2331391},
- {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
- -7912378, -33069337, 9234253},
- {20590503, -9018988, 31529744, -7352666, -2706834, 10650548,
- 31559055, -11609587, 18979186, 13396066},
- },
- {
- {24474287, 4968103, 22267082, 4407354, 24063882, -8325180,
- -18816887, 13594782, 33514650, 7021958},
- {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421,
- -25948728, -3916677, -21480480, 12868082},
- {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208,
- -21446107, 2244500, -12455797, -8089383},
- },
- {
- {-30595528, 13793479, -5852820, 319136, -25723172, -6263899,
- 33086546, 8957937, -15233648, 5540521},
- {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908,
- -23710744, -1568984, -16128528, -14962807},
- {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819,
- 892185, -11513277, -15205948},
- },
- {
- {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819,
- 4763127, -19179614, 5867134},
- {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500,
- 27846559, 5931263, -29749703, -16108455},
- {27461885, -2977536, 22380810, 1815854, -23033753, -3031938,
- 7283490, -15148073, -19526700, 7734629},
- },
- },
- {
- {
- {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885,
- 7585295, -3176626, 18549497, 15302069},
- {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381,
- 10458790, -6418461, -8872242, 8424746},
- {24687205, 8613276, -30667046, -3233545, 1863892, -1830544,
- 19206234, 7134917, -11284482, -828919},
- },
- {
- {11334899, -9218022, 8025293, 12707519, 17523892, -10476071,
- 10243738, -14685461, -5066034, 16498837},
- {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
- -14124238, 6536641, 10543906},
- {-28946384, 15479763, -17466835, 568876, -1497683, 11223454,
- -2669190, -16625574, -27235709, 8876771},
- },
- {
- {-25742899, -12566864, -15649966, -846607, -33026686, -796288,
- -33481822, 15824474, -604426, -9039817},
- {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697,
- -4890037, 1657394, 3084098},
- {10477963, -7470260, 12119566, -13250805, 29016247, -5365589,
- 31280319, 14396151, -30233575, 15272409},
- },
- {
- {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466,
- -25173957, -12636138, -25014757, 1950504},
- {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630,
- -8384306, -8767532, 15341279, 8373727},
- {28685821, 7759505, -14378516, -12002860, -31971820, 4079242,
- 298136, -10232602, -2878207, 15190420},
- },
- {
- {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928,
- 8669718, 2742393, -26033313, -6875003},
- {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854,
- 9291594, -16247779, -12154742, 6048605},
- {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163,
- 13934231, 5128323, 11213262, 9168384},
- },
- {
- {-26280513, 11007847, 19408960, -940758, -18592965, -4328580,
- -5088060, -11105150, 20470157, -16398701},
- {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560,
- -22783952, 14461608, 14042978, 5230683},
- {29969567, -2741594, -16711867, -8552442, 9175486, -2468974,
- 21556951, 3506042, -5933891, -12449708},
- },
- {
- {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683,
- -21284170, 8971513, -28539189, 15326563},
- {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669,
- -15523050, 15300988, -20514118, 9168260},
- {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939,
- -28948358, 9601605, 33087103, -9011387},
- },
- {
- {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461,
- -27444329, -15000531, -5996870, 15664672},
- {23294591, -16632613, -22650781, -8470978, 27844204, 11461195,
- 13099750, -2460356, 18151676, 13417686},
- {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065,
- 1661597, -12551441, 15271676, -15452665},
- },
- },
- {
- {
- {11433042, -13228665, 8239631, -5279517, -1985436, -725718,
- -18698764, 2167544, -6921301, -13440182},
- {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379,
- -9917708, -8638997, 12215110, 12028277},
- {14098400, 6555944, 23007258, 5757252, -15427832, -12950502,
- 30123440, 4617780, -16900089, -655628},
- },
- {
- {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385,
- -15819999, 10154009, 23973261, -12684474},
- {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355,
- 18341390, -11419951, 32013174, -10103539},
- {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104,
- 21911214, 6354752, 4425632, -837822},
- },
- {
- {-10433389, -14612966, 22229858, -3091047, -13191166, 776729,
- -17415375, -12020462, 4725005, 14044970},
- {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390,
- -1411784, -19522291, -16109756},
- {-24864089, 12986008, -10898878, -5558584, -11312371, -148526,
- 19541418, 8180106, 9282262, 10282508},
- },
- {
- {-26205082, 4428547, -8661196, -13194263, 4098402, -14165257,
- 15522535, 8372215, 5542595, -10702683},
- {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360,
- -2781891, 6993761, -18093885, 10114655},
- {-20107055, -929418, 31422704, 10427861, -7110749, 6150669,
- -29091755, -11529146, 25953725, -106158},
- },
- {
- {-4234397, -8039292, -9119125, 3046000, 2101609, -12607294,
- 19390020, 6094296, -3315279, 12831125},
- {-15998678, 7578152, 5310217, 14408357, -33548620, -224739,
- 31575954, 6326196, 7381791, -2421839},
- {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640,
- 6295303, 8082724, -15362489, 12339664},
- },
- {
- {27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414,
- 15768922, 25091167, 14856294},
- {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300,
- -12695493, -22182473, -9012899},
- {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039,
- -27260765, 13866390, 30146206, 9142070},
- },
- {
- {3924129, -15307516, -13817122, -10054960, 12291820, -668366,
- -27702774, 9326384, -8237858, 4171294},
- {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944,
- 26396185, 3731949, 345228, -5462949},
- {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387,
- 2031539, -12391231, -16253183, -13582083},
- },
- {
- {31016211, -16722429, 26371392, -14451233, -5027349, 14854137,
- 17477601, 3842657, 28012650, -16405420},
- {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560,
- -9189873, 16292057, -8867157, 3507940},
- {29439664, 3537914, 23333589, 6997794, -17555561, -11018068,
- -15209202, -15051267, -9164929, 6580396},
- },
- },
- {
- {
- {-12185861, -7679788, 16438269, 10826160, -8696817, -6235611,
- 17860444, -9273846, -2095802, 9304567},
- {20714564, -4336911, 29088195, 7406487, 11426967, -5095705,
- 14792667, -14608617, 5289421, -477127},
- {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462,
- 17271490, 12349094, 26939669, -3752294},
- },
- {
- {-12889898, 9373458, 31595848, 16374215, 21471720, 13221525,
- -27283495, -12348559, -3698806, 117887},
- {22263325, -6560050, 3984570, -11174646, -15114008, -566785,
- 28311253, 5358056, -23319780, 541964},
- {16259219, 3261970, 2309254, -15534474, -16885711, -4581916,
- 24134070, -16705829, -13337066, -13552195},
- },
- {
- {9378160, -13140186, -22845982, -12745264, 28198281, -7244098,
- -2399684, -717351, 690426, 14876244},
- {24977353, -314384, -8223969, -13465086, 28432343, -1176353,
- -13068804, -12297348, -22380984, 6618999},
- {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193,
- 8044829, -13817328, 32239829, -5652762},
- },
- {
- {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647,
- -10350059, 32779359, 5095274},
- {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423,
- -24601656, 14506724, 21639561, -2630236},
- {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318,
- -1289502, -6863535, 17874574, 558605},
- },
- {
- {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700,
- 33499487, 5080151, 2085892, 5119761},
- {-22205145, -2519528, -16381601, 414691, -25019550, 2170430,
- 30634760, -8363614, -31999993, -5759884},
- {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256,
- 27534430, -7192145, -22351378, 12961482},
- },
- {
- {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287,
- 16533930, 8206996, -30194652, -5159638},
- {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630,
- 7031275, 7589640, 8945490},
- {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393,
- 7251489, -11182180, 24099109, -14456170},
- },
- {
- {5019558, -7907470, 4244127, -14714356, -26933272, 6453165,
- -19118182, -13289025, -6231896, -10280736},
- {10853594, 10721687, 26480089, 5861829, -22995819, 1972175,
- -1866647, -10557898, -3363451, -6441124},
- {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661,
- -2008168, -13866408, 7421392},
- },
- {
- {8139927, -6546497, 32257646, -5890546, 30375719, 1886181,
- -21175108, 15441252, 28826358, -4123029},
- {6267086, 9695052, 7709135, -16603597, -32869068, -1886135,
- 14795160, -7840124, 13746021, -1742048},
- {28584902, 7787108, -6732942, -15050729, 22846041, -7571236,
- -3181936, -363524, 4771362, -8419958},
- },
- },
- {
- {
- {24949256, 6376279, -27466481, -8174608, -18646154, -9930606,
- 33543569, -12141695, 3569627, 11342593},
- {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886,
- 4608608, 7325975, -14801071},
- {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312,
- -27400540, 10258390, -17646694, -8186692},
- },
- {
- {11431204, 15823007, 26570245, 14329124, 18029990, 4796082,
- -31446179, 15580664, 9280358, -3973687},
- {-160783, -10326257, -22855316, -4304997, -20861367, -13621002,
- -32810901, -11181622, -15545091, 4387441},
- {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370,
- -24513992, 8548137, 20617071, -7482001},
- },
- {
- {-938825, -3930586, -8714311, 16124718, 24603125, -6225393,
- -13775352, -11875822, 24345683, 10325460},
- {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528,
- 16318175, -1010689, 4766743, 3552007},
- {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514,
- 14481909, 10988822, -3994762},
- },
- {
- {15564307, -14311570, 3101243, 5684148, 30446780, -8051356,
- 12677127, -6505343, -8295852, 13296005},
- {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379,
- 31521204, 9614054, -30000824, 12074674},
- {4771191, -135239, 14290749, -13089852, 27992298, 14998318,
- -1413936, -1556716, 29832613, -16391035},
- },
- {
- {7064884, -7541174, -19161962, -5067537, -18891269, -2912736,
- 25825242, 5293297, -27122660, 13101590},
- {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445,
- 32512469, -5317593, -30356070, -4190957},
- {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044,
- 14413974, 9515896, 19568978, 9628812},
- },
- {
- {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894,
- -6106839, -6291786, 3437740},
- {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290,
- -22961733, 70104, 7463304, 4176122},
- {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117,
- -32719404, -5322751, 24216882, 5944158},
- },
- {
- {8894125, 7450974, -2664149, -9765752, -28080517, -12389115,
- 19345746, 14680796, 11632993, 5847885},
- {26942781, -2315317, 9129564, -4906607, 26024105, 11769399,
- -11518837, 6367194, -9727230, 4782140},
- {19916461, -4828410, -22910704, -11414391, 25606324, -5972441,
- 33253853, 8220911, 6358847, -1873857},
- },
- {
- {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388,
- -4480480, -13538503, 1387155},
- {19646058, 5720633, -11416706, 12814209, 11607948, 12749789,
- 14147075, 15156355, -21866831, 11835260},
- {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523,
- 15467869, -26560550, 5052483},
- },
- },
- {
- {
- {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123,
- -12618185, 12228557, -7003677},
- {32944382, 14922211, -22844894, 5188528, 21913450, -8719943,
- 4001465, 13238564, -6114803, 8653815},
- {22865569, -4652735, 27603668, -12545395, 14348958, 8234005,
- 24808405, 5719875, 28483275, 2841751},
- },
- {
- {-16420968, -1113305, -327719, -12107856, 21886282, -15552774,
- -1887966, -315658, 19932058, -12739203},
- {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912,
- 3999228, 13239134, -4777469, -13910208},
- {1382174, -11694719, 17266790, 9194690, -13324356, 9720081,
- 20403944, 11284705, -14013818, 3093230},
- },
- {
- {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424,
- 16271225, -24049421, -6691850},
- {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293,
- 24123614, 15193618, -21652117, -16739389},
- {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484,
- 31870908, 14690798, 17361620, 11864968},
- },
- {
- {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200,
- -12331205, -7486601, -25578460, -16240689},
- {14668462, -12270235, 26039039, 15305210, 25515617, 4542480,
- 10453892, 6577524, 9145645, -6443880},
- {5974874, 3053895, -9433049, -10385191, -31865124, 3225009,
- -7972642, 3936128, -5652273, -3050304},
- },
- {
- {30625386, -4729400, -25555961, -12792866, -20484575, 7695099,
- 17097188, -16303496, -27999779, 1803632},
- {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700,
- 14911344, 12196514, -21405489, 7047412},
- {20093277, 9920966, -11138194, -5343857, 13161587, 12044805,
- -32856851, 4124601, -32343828, -10257566},
- },
- {
- {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605,
- 4752377, -8714640, -21679658, 2288038},
- {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457,
- 29457502, 14625692, -24819617, 12570232},
- {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109,
- -21159943, -3498680, -11974704, 4724943},
- },
- {
- {17960970, -11775534, -4140968, -9702530, -8876562, -1410617,
- -12907383, -8659932, -29576300, 1903856},
- {23134274, -14279132, -10681997, -1611936, 20684485, 15770816,
- -12989750, 3190296, 26955097, 14109738},
- {15308788, 5320727, -30113809, -14318877, 22902008, 7767164,
- 29425325, -11277562, 31960942, 11934971},
- },
- {
- {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669,
- 20638173, 4875028, 10491392, 1379718},
- {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801,
- 33518459, 16176658, 21432314, 12180697},
- {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205,
- 1465425, 12689540, -10301319, -13872883},
- },
- },
- {
- {
- {5414091, -15386041, -21007664, 9643570, 12834970, 1186149,
- -2622916, -1342231, 26128231, 6032912},
- {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156,
- 3604025, 8316894, -25875034, -10437358},
- {3296484, 6223048, 24680646, -12246460, -23052020, 5903205,
- -8862297, -4639164, 12376617, 3188849},
- },
- {
- {29190488, -14659046, 27549113, -1183516, 3520066, -10697301,
- 32049515, -7309113, -16109234, -9852307},
- {-14744486, -9309156, 735818, -598978, -20407687, -5057904,
- 25246078, -15795669, 18640741, -960977},
- {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252,
- -31638386, -494430, 10530747, 1053335},
- },
- {
- {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384,
- -31462369, -2948985, 24018831, 15026644},
- {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631,
- 25310643, 13003497, -2314791, -15145616},
- {-27419985, -603321, -8043984, -1669117, -26092265, 13987819,
- -27297622, 187899, -23166419, -2531735},
- },
- {
- {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473,
- 9716667, 16266922, -5070217, 726099},
- {29370922, -6053998, 7334071, -15342259, 9385287, 2247707,
- -13661962, -4839461, 30007388, -15823341},
- {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109,
- 730663, 9835848, 4555336},
- },
- {
- {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977,
- 17693930, 544696, -11985298, 12422646},
- {31117226, -12215734, -13502838, 6561947, -9876867, -12757670,
- -5118685, -4096706, 29120153, 13924425},
- {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820,
- -9383939, -11317700, 7240931, -237388},
- },
- {
- {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771,
- 1222336, 4389483, 3293637, -15551743},
- {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533,
- -24319580, 7733547, 12796905, -6335822},
- {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811,
- -28253339, 3647836, 3222231, -11160462},
- },
- {
- {18606113, 1693100, -25448386, -15170272, 4112353, 10045021,
- 23603893, -2048234, -7550776, 2484985},
- {9255317, -3131197, -12156162, -1004256, 13098013, -9214866,
- 16377220, -2102812, -19802075, -3034702},
- {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502,
- -31718148, 9936966, -30097688, -10618797},
- },
- {
- {21878590, -5001297, 4338336, 13643897, -3036865, 13160960,
- 19708896, 5415497, -7360503, -4109293},
- {27736861, 10103576, 12500508, 8502413, -3413016, -9633558,
- 10436918, -1550276, -23659143, -8132100},
- {19492550, -12104365, -29681976, -852630, -3208171, 12403437,
- 30066266, 8367329, 13243957, 8709688},
- },
- },
- {
- {
- {12015105, 2801261, 28198131, 10151021, 24818120, -4743133,
- -11194191, -5645734, 5150968, 7274186},
- {2831366, -12492146, 1478975, 6122054, 23825128, -12733586,
- 31097299, 6083058, 31021603, -9793610},
- {-2529932, -2229646, 445613, 10720828, -13849527, -11505937,
- -23507731, 16354465, 15067285, -14147707},
- },
- {
- {7840942, 14037873, -33364863, 15934016, -728213, -3642706,
- 21403988, 1057586, -19379462, -12403220},
- {915865, -16469274, 15608285, -8789130, -24357026, 6060030,
- -17371319, 8410997, -7220461, 16527025},
- {32922597, -556987, 20336074, -16184568, 10903705, -5384487,
- 16957574, 52992, 23834301, 6588044},
- },
- {
- {32752030, 11232950, 3381995, -8714866, 22652988, -10744103,
- 17159699, 16689107, -20314580, -1305992},
- {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943,
- 7924251, -2752281, 1976123, -7249027},
- {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041,
- -3371252, 12331345, -8237197},
- },
- {
- {8651614, -4477032, -16085636, -4996994, 13002507, 2950805,
- 29054427, -5106970, 10008136, -4667901},
- {31486080, 15114593, -14261250, 12951354, 14369431, -7387845,
- 16347321, -13662089, 8684155, -10532952},
- {19443825, 11385320, 24468943, -9659068, -23919258, 2187569,
- -26263207, -6086921, 31316348, 14219878},
- },
- {
- {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801,
- 27146014, 6992409, 29126555, 9207390},
- {32382935, 1110093, 18477781, 11028262, -27411763, -7548111,
- -4980517, 10843782, -7957600, -14435730},
- {2814918, 7836403, 27519878, -7868156, -20894015, -11553689,
- -21494559, 8550130, 28346258, 1994730},
- },
- {
- {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307,
- -19516951, 7174894, 22628102, 8115180},
- {-30405132, 955511, -11133838, -15078069, -32447087, -13278079,
- -25651578, 3317160, -9943017, 930272},
- {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177,
- 24091212, -1388970, -22765376, -10650715},
- },
- {
- {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053,
- -14839018, -16554220, -1867018, 8398970},
- {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670,
- 22981545, -6291273, 18009408, -15772772},
- {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469,
- 29551787, -3727419, 19288549, 1325865},
- },
- {
- {15100157, -15835752, -23923978, -1005098, -26450192, 15509408,
- 12376730, -3479146, 33166107, -8042750},
- {20909231, 13023121, -9209752, 16251778, -5778415, -8094914,
- 12412151, 10018715, 2213263, -13878373},
- {32529814, -11074689, 30361439, -16689753, -9135940, 1513226,
- 22922121, 6382134, -5766928, 8371348},
- },
- },
- {
- {
- {9923462, 11271500, 12616794, 3544722, -29998368, -1721626,
- 12891687, -8193132, -26442943, 10486144},
- {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726,
- 2610596, -23921530, -11455195},
- {5408411, -1136691, -4969122, 10561668, 24145918, 14240566,
- 31319731, -4235541, 19985175, -3436086},
- },
- {
- {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976,
- -17577068, 8849297, 65030, 8370684},
- {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277,
- -19442942, 6922164, 12743482, -9800518},
- {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717,
- 23783145, 11038569, 18800704, 255233},
- },
- {
- {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847,
- 9066957, 19258688, -14753793},
- {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541,
- -31934921, 2209390, -1524053, 2055794},
- {580882, 16705327, 5468415, -2683018, -30926419, -14696000,
- -7203346, -8994389, -30021019, 7394435},
- },
- {
- {23838809, 1822728, -15738443, 15242727, 8318092, -3733104,
- -21672180, -3492205, -4821741, 14799921},
- {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804,
- 13496856, -9056018, 7402518},
- {2286874, -4435931, -20042458, -2008336, -13696227, 5038122,
- 11006906, -15760352, 8205061, 1607563},
- },
- {
- {14414086, -8002132, 3331830, -3208217, 22249151, -5594188,
- 18364661, -2906958, 30019587, -9029278},
- {-27688051, 1585953, -10775053, 931069, -29120221, -11002319,
- -14410829, 12029093, 9944378, 8024},
- {4368715, -3709630, 29874200, -15022983, -20230386, -11410704,
- -16114594, -999085, -8142388, 5640030},
- },
- {
- {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887,
- -16694564, 15219798, -14327783},
- {27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605,
- -1173195, -18342183, 9742717},
- {6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614,
- 7406442, 12420155, 1994844},
- },
- {
- {14012521, -5024720, -18384453, -9578469, -26485342, -3936439,
- -13033478, -10909803, 24319929, -6446333},
- {16412690, -4507367, 10772641, 15929391, -17068788, -4658621,
- 10555945, -10484049, -30102368, -4739048},
- {22397382, -7767684, -9293161, -12792868, 17166287, -9755136,
- -27333065, 6199366, 21880021, -12250760},
- },
- {
- {-4283307, 5368523, -31117018, 8163389, -30323063, 3209128,
- 16557151, 8890729, 8840445, 4957760},
- {-15447727, 709327, -6919446, -10870178, -29777922, 6522332,
- -21720181, 12130072, -14796503, 5005757},
- {-2114751, -14308128, 23019042, 15765735, -25269683, 6002752,
- 10183197, -13239326, -16395286, -2176112},
- },
- },
- {
- {
- {-19025756, 1632005, 13466291, -7995100, -23640451, 16573537,
- -32013908, -3057104, 22208662, 2000468},
- {3065073, -1412761, -25598674, -361432, -17683065, -5703415,
- -8164212, 11248527, -3691214, -7414184},
- {10379208, -6045554, 8877319, 1473647, -29291284, -12507580,
- 16690915, 2553332, -3132688, 16400289},
- },
- {
- {15716668, 1254266, -18472690, 7446274, -8448918, 6344164,
- -22097271, -7285580, 26894937, 9132066},
- {24158887, 12938817, 11085297, -8177598, -28063478, -4457083,
- -30576463, 64452, -6817084, -2692882},
- {13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710,
- -3418511, -4688006, 2364226},
- },
- {
- {16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024,
- -11697457, 15445875, -7798101},
- {29004207, -7867081, 28661402, -640412, -12794003, -7943086,
- 31863255, -4135540, -278050, -15759279},
- {-6122061, -14866665, -28614905, 14569919, -10857999, -3591829,
- 10343412, -6976290, -29828287, -10815811},
- },
- {
- {27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636,
- 15372179, 17293797, 960709},
- {20263915, 11434237, -5765435, 11236810, 13505955, -10857102,
- -16111345, 6493122, -19384511, 7639714},
- {-2830798, -14839232, 25403038, -8215196, -8317012, -16173699,
- 18006287, -16043750, 29994677, -15808121},
- },
- {
- {9769828, 5202651, -24157398, -13631392, -28051003, -11561624,
- -24613141, -13860782, -31184575, 709464},
- {12286395, 13076066, -21775189, -1176622, -25003198, 4057652,
- -32018128, -8890874, 16102007, 13205847},
- {13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170,
- 8525972, 10151379, 10394400},
- },
- {
- {4024660, -16137551, 22436262, 12276534, -9099015, -2686099,
- 19698229, 11743039, -33302334, 8934414},
- {-15879800, -4525240, -8580747, -2934061, 14634845, -698278,
- -9449077, 3137094, -11536886, 11721158},
- {17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229,
- 8835153, -9205489, -1280045},
- },
- {
- {-461409, -7830014, 20614118, 16688288, -7514766, -4807119,
- 22300304, 505429, 6108462, -6183415},
- {-5070281, 12367917, -30663534, 3234473, 32617080, -8422642,
- 29880583, -13483331, -26898490, -7867459},
- {-31975283, 5726539, 26934134, 10237677, -3173717, -605053,
- 24199304, 3795095, 7592688, -14992079},
- },
- {
- {21594432, -14964228, 17466408, -4077222, 32537084, 2739898,
- 6407723, 12018833, -28256052, 4298412},
- {-20650503, -11961496, -27236275, 570498, 3767144, -1717540,
- 13891942, -1569194, 13717174, 10805743},
- {-14676630, -15644296, 15287174, 11927123, 24177847, -8175568,
- -796431, 14860609, -26938930, -5863836},
- },
- },
- {
- {
- {12962541, 5311799, -10060768, 11658280, 18855286, -7954201,
- 13286263, -12808704, -4381056, 9882022},
- {18512079, 11319350, -20123124, 15090309, 18818594, 5271736,
- -22727904, 3666879, -23967430, -3299429},
- {-6789020, -3146043, 16192429, 13241070, 15898607, -14206114,
- -10084880, -6661110, -2403099, 5276065},
- },
- {
- {30169808, -5317648, 26306206, -11750859, 27814964, 7069267,
- 7152851, 3684982, 1449224, 13082861},
- {10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382,
- 15056736, -21016438, -8202000},
- {-33150110, 3261608, 22745853, 7948688, 19370557, -15177665,
- -26171976, 6482814, -10300080, -11060101},
- },
- {
- {32869458, -5408545, 25609743, 15678670, -10687769, -15471071,
- 26112421, 2521008, -22664288, 6904815},
- {29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737,
- 3841096, -29003639, -6657642},
- {10340844, -6630377, -18656632, -2278430, 12621151, -13339055,
- 30878497, -11824370, -25584551, 5181966},
- },
- {
- {25940115, -12658025, 17324188, -10307374, -8671468, 15029094,
- 24396252, -16450922, -2322852, -12388574},
- {-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390,
- 12641087, 20603771, -6561742},
- {-18882287, -11673380, 24849422, 11501709, 13161720, -4768874,
- 1925523, 11914390, 4662781, 7820689},
- },
- {
- {12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456,
- 12172924, 16136752, 15264020},
- {-10349955, -14680563, -8211979, 2330220, -17662549, -14545780,
- 10658213, 6671822, 19012087, 3772772},
- {3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732,
- -15762884, 20527771, 12988982},
- },
- {
- {-14822485, -5797269, -3707987, 12689773, -898983, -10914866,
- -24183046, -10564943, 3299665, -12424953},
- {-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197,
- 6461331, -25583147, 8991218},
- {-17226263, 1816362, -1673288, -6086439, 31783888, -8175991,
- -32948145, 7417950, -30242287, 1507265},
- },
- {
- {29692663, 6829891, -10498800, 4334896, 20945975, -11906496,
- -28887608, 8209391, 14606362, -10647073},
- {-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695,
- 9761487, 4170404, -2085325},
- {-11587470, 14855945, -4127778, -1531857, -26649089, 15084046,
- 22186522, 16002000, -14276837, -8400798},
- },
- {
- {-4811456, 13761029, -31703877, -2483919, -3312471, 7869047,
- -7113572, -9620092, 13240845, 10965870},
- {-7742563, -8256762, -14768334, -13656260, -23232383, 12387166,
- 4498947, 14147411, 29514390, 4302863},
- {-13413405, -12407859, 20757302, -13801832, 14785143, 8976368,
- -5061276, -2144373, 17846988, -13971927},
- },
- },
- {
- {
- {-2244452, -754728, -4597030, -1066309, -6247172, 1455299,
- -21647728, -9214789, -5222701, 12650267},
- {-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813,
- 13770293, -19134326, 10958663},
- {22470984, 12369526, 23446014, -5441109, -21520802, -9698723,
- -11772496, -11574455, -25083830, 4271862},
- },
- {
- {-25169565, -10053642, -19909332, 15361595, -5984358, 2159192,
- 75375, -4278529, -32526221, 8469673},
- {15854970, 4148314, -8893890, 7259002, 11666551, 13824734,
- -30531198, 2697372, 24154791, -9460943},
- {15446137, -15806644, 29759747, 14019369, 30811221, -9610191,
- -31582008, 12840104, 24913809, 9815020},
- },
- {
- {-4709286, -5614269, -31841498, -12288893, -14443537, 10799414,
- -9103676, 13438769, 18735128, 9466238},
- {11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821,
- -10896103, -22728655, 16199064},
- {14576810, 379472, -26786533, -8317236, -29426508, -10812974,
- -102766, 1876699, 30801119, 2164795},
- },
- {
- {15995086, 3199873, 13672555, 13712240, -19378835, -4647646,
- -13081610, -15496269, -13492807, 1268052},
- {-10290614, -3659039, -3286592, 10948818, 23037027, 3794475,
- -3470338, -12600221, -17055369, 3565904},
- {29210088, -9419337, -5919792, -4952785, 10834811, -13327726,
- -16512102, -10820713, -27162222, -14030531},
- },
- {
- {-13161890, 15508588, 16663704, -8156150, -28349942, 9019123,
- -29183421, -3769423, 2244111, -14001979},
- {-5152875, -3800936, -9306475, -6071583, 16243069, 14684434,
- -25673088, -16180800, 13491506, 4641841},
- {10813417, 643330, -19188515, -728916, 30292062, -16600078,
- 27548447, -7721242, 14476989, -12767431},
- },
- {
- {10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937,
- -1644259, -27912810, 12651324},
- {-31185513, -813383, 22271204, 11835308, 10201545, 15351028,
- 17099662, 3988035, 21721536, -3148940},
- {10202177, -6545839, -31373232, -9574638, -32150642, -8119683,
- -12906320, 3852694, 13216206, 14842320},
- },
- {
- {-15815640, -10601066, -6538952, -7258995, -6984659, -6581778,
- -31500847, 13765824, -27434397, 9900184},
- {14465505, -13833331, -32133984, -14738873, -27443187, 12990492,
- 33046193, 15796406, -7051866, -8040114},
- {30924417, -8279620, 6359016, -12816335, 16508377, 9071735,
- -25488601, 15413635, 9524356, -7018878},
- },
- {
- {12274201, -13175547, 32627641, -1785326, 6736625, 13267305,
- 5237659, -5109483, 15663516, 4035784},
- {-2951309, 8903985, 17349946, 601635, -16432815, -4612556,
- -13732739, -15889334, -22258478, 4659091},
- {-16916263, -4952973, -30393711, -15158821, 20774812, 15897498,
- 5736189, 15026997, -2178256, -13455585},
- },
- },
- {
- {
- {-8858980, -2219056, 28571666, -10155518, -474467, -10105698,
- -3801496, 278095, 23440562, -290208},
- {10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275,
- 11551483, -16571960, -7442864},
- {17932739, -12437276, -24039557, 10749060, 11316803, 7535897,
- 22503767, 5561594, -3646624, 3898661},
- },
- {
- {7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531,
- 7152530, 21831162, 1245233},
- {26958459, -14658026, 4314586, 8346991, -5677764, 11960072,
- -32589295, -620035, -30402091, -16716212},
- {-12165896, 9166947, 33491384, 13673479, 29787085, 13096535,
- 6280834, 14587357, -22338025, 13987525},
- },
- {
- {-24349909, 7778775, 21116000, 15572597, -4833266, -5357778,
- -4300898, -5124639, -7469781, -2858068},
- {9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781,
- 6439245, -14581012, 4091397},
- {-8426427, 1470727, -28109679, -1596990, 3978627, -5123623,
- -19622683, 12092163, 29077877, -14741988},
- },
- {
- {5269168, -6859726, -13230211, -8020715, 25932563, 1763552,
- -5606110, -5505881, -20017847, 2357889},
- {32264008, -15407652, -5387735, -1160093, -2091322, -3946900,
- 23104804, -12869908, 5727338, 189038},
- {14609123, -8954470, -6000566, -16622781, -14577387, -7743898,
- -26745169, 10942115, -25888931, -14884697},
- },
- {
- {20513500, 5557931, -15604613, 7829531, 26413943, -2019404,
- -21378968, 7471781, 13913677, -5137875},
- {-25574376, 11967826, 29233242, 12948236, -6754465, 4713227,
- -8940970, 14059180, 12878652, 8511905},
- {-25656801, 3393631, -2955415, -7075526, -2250709, 9366908,
- -30223418, 6812974, 5568676, -3127656},
- },
- {
- {11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
- -17408753, -13504373, -14395196, 8070818},
- {27117696, -10007378, -31282771, -5570088, 1127282, 12772488,
- -29845906, 10483306, -11552749, -1028714},
- {10637467, -5688064, 5674781, 1072708, -26343588, -6982302,
- -1683975, 9177853, -27493162, 15431203},
- },
- {
- {20525145, 10892566, -12742472, 12779443, -29493034, 16150075,
- -28240519, 14943142, -15056790, -7935931},
- {-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767,
- -3239766, -3356550, 9594024},
- {-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683,
- -6492290, 13352335, -10977084},
- },
- {
- {-1931799, -5407458, 3304649, -12884869, 17015806, -4877091,
- -29783850, -7752482, -13215537, -319204},
- {20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742,
- 15077870, -22750759, 14523817},
- {27406042, -6041657, 27423596, -4497394, 4996214, 10002360,
- -28842031, -4545494, -30172742, -4805667},
- },
- },
- {
- {
- {11374242, 12660715, 17861383, -12540833, 10935568, 1099227,
- -13886076, -9091740, -27727044, 11358504},
- {-12730809, 10311867, 1510375, 10778093, -2119455, -9145702,
- 32676003, 11149336, -26123651, 4985768},
- {-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043,
- 13794114, -19414307, -15621255},
- },
- {
- {6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603,
- 6970005, -1691065, -9004790},
- {1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622,
- -5475723, -16796596, -5031438},
- {-22273315, -13524424, -64685, -4334223, -18605636, -10921968,
- -20571065, -7007978, -99853, -10237333},
- },
- {
- {17747465, 10039260, 19368299, -4050591, -20630635, -16041286,
- 31992683, -15857976, -29260363, -5511971},
- {31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999,
- -3744247, 4882242, -10626905},
- {29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198,
- 3272828, -5190932, -4162409},
- },
- {
- {12501286, 4044383, -8612957, -13392385, -32430052, 5136599,
- -19230378, -3529697, 330070, -3659409},
- {6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522,
- -8573892, -271295, 12071499},
- {-8365515, -4042521, 25133448, -4517355, -6211027, 2265927,
- -32769618, 1936675, -5159697, 3829363},
- },
- {
- {28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550,
- -6567787, 26333140, 14267664},
- {-11067219, 11871231, 27385719, -10559544, -4585914, -11189312,
- 10004786, -8709488, -21761224, 8930324},
- {-21197785, -16396035, 25654216, -1725397, 12282012, 11008919,
- 1541940, 4757911, -26491501, -16408940},
- },
- {
- {13537262, -7759490, -20604840, 10961927, -5922820, -13218065,
- -13156584, 6217254, -15943699, 13814990},
- {-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681,
- 9257833, -1956526, -1776914},
- {-25045300, -10191966, 15366585, 15166509, -13105086, 8423556,
- -29171540, 12361135, -18685978, 4578290},
- },
- {
- {24579768, 3711570, 1342322, -11180126, -27005135, 14124956,
- -22544529, 14074919, 21964432, 8235257},
- {-6528613, -2411497, 9442966, -5925588, 12025640, -1487420,
- -2981514, -1669206, 13006806, 2355433},
- {-16304899, -13605259, -6632427, -5142349, 16974359, -10911083,
- 27202044, 1719366, 1141648, -12796236},
- },
- {
- {-12863944, -13219986, -8318266, -11018091, -6810145, -4843894,
- 13475066, -3133972, 32674895, 13715045},
- {11423335, -5468059, 32344216, 8962751, 24989809, 9241752,
- -13265253, 16086212, -28740881, -15642093},
- {-1409668, 12530728, -6368726, 10847387, 19531186, -14132160,
- -11709148, 7791794, -27245943, 4383347},
- },
- },
- {
- {
- {-28970898, 5271447, -1266009, -9736989, -12455236, 16732599,
- -4862407, -4906449, 27193557, 6245191},
- {-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898,
- 3260492, 22510453, 8577507},
- {-12632451, 11257346, -32692994, 13548177, -721004, 10879011,
- 31168030, 13952092, -29571492, -3635906},
- },
- {
- {3877321, -9572739, 32416692, 5405324, -11004407, -13656635,
- 3759769, 11935320, 5611860, 8164018},
- {-16275802, 14667797, 15906460, 12155291, -22111149, -9039718,
- 32003002, -8832289, 5773085, -8422109},
- {-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725,
- 12376320, 31632953, 190926},
- },
- {
- {-24593607, -16138885, -8423991, 13378746, 14162407, 6901328,
- -8288749, 4508564, -25341555, -3627528},
- {8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941,
- -14786005, -1672488, 827625},
- {-32720583, -16289296, -32503547, 7101210, 13354605, 2659080,
- -1800575, -14108036, -24878478, 1541286},
- },
- {
- {2901347, -1117687, 3880376, -10059388, -17620940, -3612781,
- -21802117, -3567481, 20456845, -1885033},
- {27019610, 12299467, -13658288, -1603234, -12861660, -4861471,
- -19540150, -5016058, 29439641, 15138866},
- {21536104, -6626420, -32447818, -10690208, -22408077, 5175814,
- -5420040, -16361163, 7779328, 109896},
- },
- {
- {30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390,
- 12180118, 23177719, -554075},
- {26572847, 3405927, -31701700, 12890905, -19265668, 5335866,
- -6493768, 2378492, 4439158, -13279347},
- {-22716706, 3489070, -9225266, -332753, 18875722, -1140095,
- 14819434, -12731527, -17717757, -5461437},
- },
- {
- {-5056483, 16566551, 15953661, 3767752, -10436499, 15627060,
- -820954, 2177225, 8550082, -15114165},
- {-18473302, 16596775, -381660, 15663611, 22860960, 15585581,
- -27844109, -3582739, -23260460, -8428588},
- {-32480551, 15707275, -8205912, -5652081, 29464558, 2713815,
- -22725137, 15860482, -21902570, 1494193},
- },
- {
- {-19562091, -14087393, -25583872, -9299552, 13127842, 759709,
- 21923482, 16529112, 8742704, 12967017},
- {-28464899, 1553205, 32536856, -10473729, -24691605, -406174,
- -8914625, -2933896, -29903758, 15553883},
- {21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572,
- 14513274, 19375923, -12647961},
- },
- {
- {8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818,
- -6222716, 2862653, 9455043},
- {29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124,
- -2990080, 15511449, 4789663},
- {-20679756, 7004547, 8824831, -9434977, -4045704, -3750736,
- -5754762, 108893, 23513200, 16652362},
- },
- },
- {
- {
- {-33256173, 4144782, -4476029, -6579123, 10770039, -7155542,
- -6650416, -12936300, -18319198, 10212860},
- {2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801,
- 2600940, -9988298, -12506466},
- {-24645692, 13317462, -30449259, -15653928, 21365574, -10869657,
- 11344424, 864440, -2499677, -16710063},
- },
- {
- {-26432803, 6148329, -17184412, -14474154, 18782929, -275997,
- -22561534, 211300, 2719757, 4940997},
- {-1323882, 3911313, -6948744, 14759765, -30027150, 7851207,
- 21690126, 8518463, 26699843, 5276295},
- {-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586,
- 149635, -15452774, 7159369},
- },
- {
- {9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009,
- 8312176, 22477218, -8403385},
- {18155857, -16504990, 19744716, 9006923, 15154154, -10538976,
- 24256460, -4864995, -22548173, 9334109},
- {2986088, -4911893, 10776628, -3473844, 10620590, -7083203,
- -21413845, 14253545, -22587149, 536906},
- },
- {
- {4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
- 10589625, 10838060, -15420424},
- {-19342404, 867880, 9277171, -3218459, -14431572, -1986443,
- 19295826, -15796950, 6378260, 699185},
- {7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039,
- 15693155, -5045064, -13373962},
- },
- {
- {-7737563, -5869402, -14566319, -7406919, 11385654, 13201616,
- 31730678, -10962840, -3918636, -9669325},
- {10188286, -15770834, -7336361, 13427543, 22223443, 14896287,
- 30743455, 7116568, -21786507, 5427593},
- {696102, 13206899, 27047647, -10632082, 15285305, -9853179,
- 10798490, -4578720, 19236243, 12477404},
- },
- {
- {-11229439, 11243796, -17054270, -8040865, -788228, -8167967,
- -3897669, 11180504, -23169516, 7733644},
- {17800790, -14036179, -27000429, -11766671, 23887827, 3149671,
- 23466177, -10538171, 10322027, 15313801},
- {26246234, 11968874, 32263343, -5468728, 6830755, -13323031,
- -15794704, -101982, -24449242, 10890804},
- },
- {
- {-31365647, 10271363, -12660625, -6267268, 16690207, -13062544,
- -14982212, 16484931, 25180797, -5334884},
- {-586574, 10376444, -32586414, -11286356, 19801893, 10997610,
- 2276632, 9482883, 316878, 13820577},
- {-9882808, -4510367, -2115506, 16457136, -11100081, 11674996,
- 30756178, -7515054, 30696930, -3712849},
- },
- {
- {32988917, -9603412, 12499366, 7910787, -10617257, -11931514,
- -7342816, -9985397, -32349517, 7392473},
- {-8855661, 15927861, 9866406, -3649411, -2396914, -16655781,
- -30409476, -9134995, 25112947, -2926644},
- {-2504044, -436966, 25621774, -5678772, 15085042, -5479877,
- -24884878, -13526194, 5537438, -13914319},
- },
- },
- {
- {
- {-11225584, 2320285, -9584280, 10149187, -33444663, 5808648,
- -14876251, -1729667, 31234590, 6090599},
- {-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721,
- 15878753, -6970405, -9034768},
- {-27757857, 247744, -15194774, -9002551, 23288161, -10011936,
- -23869595, 6503646, 20650474, 1804084},
- },
- {
- {-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995,
- -10329713, 27842616, -202328},
- {-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656,
- 5031932, -11375082, 12714369},
- {20807691, -7270825, 29286141, 11421711, -27876523, -13868230,
- -21227475, 1035546, -19733229, 12796920},
- },
- {
- {12076899, -14301286, -8785001, -11848922, -25012791, 16400684,
- -17591495, -12899438, 3480665, -15182815},
- {-32361549, 5457597, 28548107, 7833186, 7303070, -11953545,
- -24363064, -15921875, -33374054, 2771025},
- {-21389266, 421932, 26597266, 6860826, 22486084, -6737172,
- -17137485, -4210226, -24552282, 15673397},
- },
- {
- {-20184622, 2338216, 19788685, -9620956, -4001265, -8740893,
- -20271184, 4733254, 3727144, -12934448},
- {6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594,
- 7975683, 31123697, -10958981},
- {30069250, -11435332, 30434654, 2958439, 18399564, -976289,
- 12296869, 9204260, -16432438, 9648165},
- },
- {
- {32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266,
- 5248604, -26008332, -11377501},
- {17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711,
- 15298639, 2662509, -16297073},
- {-1172927, -7558695, -4366770, -4287744, -21346413, -8434326,
- 32087529, -1222777, 32247248, -14389861},
- },
- {
- {14312628, 1221556, 17395390, -8700143, -4945741, -8684635,
- -28197744, -9637817, -16027623, -13378845},
- {-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502,
- 9803137, 17597934, 2346211},
- {18510800, 15337574, 26171504, 981392, -22241552, 7827556,
- -23491134, -11323352, 3059833, -11782870},
- },
- {
- {10141598, 6082907, 17829293, -1947643, 9830092, 13613136,
- -25556636, -5544586, -33502212, 3592096},
- {33114168, -15889352, -26525686, -13343397, 33076705, 8716171,
- 1151462, 1521897, -982665, -6837803},
- {-32939165, -4255815, 23947181, -324178, -33072974, -12305637,
- -16637686, 3891704, 26353178, 693168},
- },
- {
- {30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294,
- -400668, 31375464, 14369965},
- {-14370654, -7772529, 1510301, 6434173, -18784789, -6262728,
- 32732230, -13108839, 17901441, 16011505},
- {18171223, -11934626, -12500402, 15197122, -11038147, -15230035,
- -19172240, -16046376, 8764035, 12309598},
- },
- },
- {
- {
- {5975908, -5243188, -19459362, -9681747, -11541277, 14015782,
- -23665757, 1228319, 17544096, -10593782},
- {5811932, -1715293, 3442887, -2269310, -18367348, -8359541,
- -18044043, -15410127, -5565381, 12348900},
- {-31399660, 11407555, 25755363, 6891399, -3256938, 14872274,
- -24849353, 8141295, -10632534, -585479},
- },
- {
- {-12675304, 694026, -5076145, 13300344, 14015258, -14451394,
- -9698672, -11329050, 30944593, 1130208},
- {8247766, -6710942, -26562381, -7709309, -14401939, -14648910,
- 4652152, 2488540, 23550156, -271232},
- {17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737,
- -5908146, -408818, -137719},
- },
- {
- {16091085, -16253926, 18599252, 7340678, 2137637, -1221657,
- -3364161, 14550936, 3260525, -7166271},
- {-4910104, -13332887, 18550887, 10864893, -16459325, -7291596,
- -23028869, -13204905, -12748722, 2701326},
- {-8574695, 16099415, 4629974, -16340524, -20786213, -6005432,
- -10018363, 9276971, 11329923, 1862132},
- },
- {
- {14763076, -15903608, -30918270, 3689867, 3511892, 10313526,
- -21951088, 12219231, -9037963, -940300},
- {8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216,
- -2909717, -15438168, 11595570},
- {15214962, 3537601, -26238722, -14058872, 4418657, -15230761,
- 13947276, 10730794, -13489462, -4363670},
- },
- {
- {-2538306, 7682793, 32759013, 263109, -29984731, -7955452,
- -22332124, -10188635, 977108, 699994},
- {-12466472, 4195084, -9211532, 550904, -15565337, 12917920,
- 19118110, -439841, -30534533, -14337913},
- {31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237,
- -10051775, 12493932, -5409317},
- },
- {
- {-25680606, 5260744, -19235809, -6284470, -3695942, 16566087,
- 27218280, 2607121, 29375955, 6024730},
- {842132, -2794693, -4763381, -8722815, 26332018, -12405641,
- 11831880, 6985184, -9940361, 2854096},
- {-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645,
- 960770, 12121869, 16648078},
- },
- {
- {-15218652, 14667096, -13336229, 2013717, 30598287, -464137,
- -31504922, -7882064, 20237806, 2838411},
- {-19288047, 4453152, 15298546, -16178388, 22115043, -15972604,
- 12544294, -13470457, 1068881, -12499905},
- {-9558883, -16518835, 33238498, 13506958, 30505848, -1114596,
- -8486907, -2630053, 12521378, 4845654},
- },
- {
- {-28198521, 10744108, -2958380, 10199664, 7759311, -13088600,
- 3409348, -873400, -6482306, -12885870},
- {-23561822, 6230156, -20382013, 10655314, -24040585, -11621172,
- 10477734, -1240216, -3113227, 13974498},
- {12966261, 15550616, -32038948, -1615346, 21025980, -629444,
- 5642325, 7188737, 18895762, 12629579},
- },
- },
- {
- {
- {14741879, -14946887, 22177208, -11721237, 1279741, 8058600,
- 11758140, 789443, 32195181, 3895677},
- {10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575,
- -3566119, -8982069, 4429647},
- {-2453894, 15725973, -20436342, -10410672, -5803908, -11040220,
- -7135870, -11642895, 18047436, -15281743},
- },
- {
- {-25173001, -11307165, 29759956, 11776784, -22262383, -15820455,
- 10993114, -12850837, -17620701, -9408468},
- {21987233, 700364, -24505048, 14972008, -7774265, -5718395,
- 32155026, 2581431, -29958985, 8773375},
- {-25568350, 454463, -13211935, 16126715, 25240068, 8594567,
- 20656846, 12017935, -7874389, -13920155},
- },
- {
- {6028182, 6263078, -31011806, -11301710, -818919, 2461772,
- -31841174, -5468042, -1721788, -2776725},
- {-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845,
- -4166698, 28408820, 6816612},
- {-10358094, -8237829, 19549651, -12169222, 22082623, 16147817,
- 20613181, 13982702, -10339570, 5067943},
- },
- {
- {-30505967, -3821767, 12074681, 13582412, -19877972, 2443951,
- -19719286, 12746132, 5331210, -10105944},
- {30528811, 3601899, -1957090, 4619785, -27361822, -15436388,
- 24180793, -12570394, 27679908, -1648928},
- {9402404, -13957065, 32834043, 10838634, -26580150, -13237195,
- 26653274, -8685565, 22611444, -12715406},
- },
- {
- {22190590, 1118029, 22736441, 15130463, -30460692, -5991321,
- 19189625, -4648942, 4854859, 6622139},
- {-8310738, -2953450, -8262579, -3388049, -10401731, -271929,
- 13424426, -3567227, 26404409, 13001963},
- {-31241838, -15415700, -2994250, 8939346, 11562230, -12840670,
- -26064365, -11621720, -15405155, 11020693},
- },
- {
- {1866042, -7949489, -7898649, -10301010, 12483315, 13477547,
- 3175636, -12424163, 28761762, 1406734},
- {-448555, -1777666, 13018551, 3194501, -9580420, -11161737,
- 24760585, -4347088, 25577411, -13378680},
- {-24290378, 4759345, -690653, -1852816, 2066747, 10693769,
- -29595790, 9884936, -9368926, 4745410},
- },
- {
- {-9141284, 6049714, -19531061, -4341411, -31260798, 9944276,
- -15462008, -11311852, 10931924, -11931931},
- {-16561513, 14112680, -8012645, 4817318, -8040464, -11414606,
- -22853429, 10856641, -20470770, 13434654},
- {22759489, -10073434, -16766264, -1871422, 13637442, -10168091,
- 1765144, -12654326, 28445307, -5364710},
- },
- {
- {29875063, 12493613, 2795536, -3786330, 1710620, 15181182,
- -10195717, -8788675, 9074234, 1167180},
- {-26205683, 11014233, -9842651, -2635485, -26908120, 7532294,
- -18716888, -9535498, 3843903, 9367684},
- {-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123,
- 8601684, -139197, 4242895},
- },
- },
- {
- {
- {22092954, -13191123, -2042793, -11968512, 32186753, -11517388,
- -6574341, 2470660, -27417366, 16625501},
- {-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857,
- 2602725, -27351616, 14247413},
- {6314175, -10264892, -32772502, 15957557, -10157730, 168750,
- -8618807, 14290061, 27108877, -1180880},
- },
- {
- {-8586597, -7170966, 13241782, 10960156, -32991015, -13794596,
- 33547976, -11058889, -27148451, 981874},
- {22833440, 9293594, -32649448, -13618667, -9136966, 14756819,
- -22928859, -13970780, -10479804, -16197962},
- {-7768587, 3326786, -28111797, 10783824, 19178761, 14905060,
- 22680049, 13906969, -15933690, 3797899},
- },
- {
- {21721356, -4212746, -12206123, 9310182, -3882239, -13653110,
- 23740224, -2709232, 20491983, -8042152},
- {9209270, -15135055, -13256557, -6167798, -731016, 15289673,
- 25947805, 15286587, 30997318, -6703063},
- {7392032, 16618386, 23946583, -8039892, -13265164, -1533858,
- -14197445, -2321576, 17649998, -250080},
- },
- {
- {-9301088, -14193827, 30609526, -3049543, -25175069, -1283752,
- -15241566, -9525724, -2233253, 7662146},
- {-17558673, 1763594, -33114336, 15908610, -30040870, -12174295,
- 7335080, -8472199, -3174674, 3440183},
- {-19889700, -5977008, -24111293, -9688870, 10799743, -16571957,
- 40450, -4431835, 4862400, 1133},
- },
- {
- {-32856209, -7873957, -5422389, 14860950, -16319031, 7956142,
- 7258061, 311861, -30594991, -7379421},
- {-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763,
- 16527196, 18278453, 15405622},
- {-4381906, 8508652, -19898366, -3674424, -5984453, 15149970,
- -13313598, 843523, -21875062, 13626197},
- },
- {
- {2281448, -13487055, -10915418, -2609910, 1879358, 16164207,
- -10783882, 3953792, 13340839, 15928663},
- {31727126, -7179855, -18437503, -8283652, 2875793, -16390330,
- -25269894, -7014826, -23452306, 5964753},
- {4100420, -5959452, -17179337, 6017714, -18705837, 12227141,
- -26684835, 11344144, 2538215, -7570755},
- },
- {
- {-9433605, 6123113, 11159803, -2156608, 30016280, 14966241,
- -20474983, 1485421, -629256, -15958862},
- {-26804558, 4260919, 11851389, 9658551, -32017107, 16367492,
- -20205425, -13191288, 11659922, -11115118},
- {26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568,
- -10170080, 33100372, -1306171},
- },
- {
- {15121113, -5201871, -10389905, 15427821, -27509937, -15992507,
- 21670947, 4486675, -5931810, -14466380},
- {16166486, -9483733, -11104130, 6023908, -31926798, -1364923,
- 2340060, -16254968, -10735770, -10039824},
- {28042865, -3557089, -12126526, 12259706, -3717498, -6945899,
- 6766453, -8689599, 18036436, 5803270},
- },
- },
- {
- {
- {-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391,
- 4598332, -6159431, -14117438},
- {-31031306, -14256194, 17332029, -2383520, 31312682, -5967183,
- 696309, 50292, -20095739, 11763584},
- {-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117,
- -12613632, -19773211, -10713562},
- },
- {
- {30464590, -11262872, -4127476, -12734478, 19835327, -7105613,
- -24396175, 2075773, -17020157, 992471},
- {18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841,
- 8080033, -11574335, -10601610},
- {19598397, 10334610, 12555054, 2555664, 18821899, -10339780,
- 21873263, 16014234, 26224780, 16452269},
- },
- {
- {-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804,
- -7618186, -20533829, 3698650},
- {14187449, 3448569, -10636236, -10810935, -22663880, -3433596,
- 7268410, -10890444, 27394301, 12015369},
- {19695761, 16087646, 28032085, 12999827, 6817792, 11427614,
- 20244189, -1312777, -13259127, -3402461},
- },
- {
- {30860103, 12735208, -1888245, -4699734, -16974906, 2256940,
- -8166013, 12298312, -8550524, -10393462},
- {-5719826, -11245325, -1910649, 15569035, 26642876, -7587760,
- -5789354, -15118654, -4976164, 12651793},
- {-2848395, 9953421, 11531313, -5282879, 26895123, -12697089,
- -13118820, -16517902, 9768698, -2533218},
- },
- {
- {-24719459, 1894651, -287698, -4704085, 15348719, -8156530,
- 32767513, 12765450, 4940095, 10678226},
- {18860224, 15980149, -18987240, -1562570, -26233012, -11071856,
- -7843882, 13944024, -24372348, 16582019},
- {-15504260, 4970268, -29893044, 4175593, -20993212, -2199756,
- -11704054, 15444560, -11003761, 7989037},
- },
- {
- {31490452, 5568061, -2412803, 2182383, -32336847, 4531686,
- -32078269, 6200206, -19686113, -14800171},
- {-17308668, -15879940, -31522777, -2831, -32887382, 16375549,
- 8680158, -16371713, 28550068, -6857132},
- {-28126887, -5688091, 16837845, -1820458, -6850681, 12700016,
- -30039981, 4364038, 1155602, 5988841},
- },
- {
- {21890435, -13272907, -12624011, 12154349, -7831873, 15300496,
- 23148983, -4470481, 24618407, 8283181},
- {-33136107, -10512751, 9975416, 6841041, -31559793, 16356536,
- 3070187, -7025928, 1466169, 10740210},
- {-1509399, -15488185, -13503385, -10655916, 32799044, 909394,
- -13938903, -5779719, -32164649, -15327040},
- },
- {
- {3960823, -14267803, -28026090, -15918051, -19404858, 13146868,
- 15567327, 951507, -3260321, -573935},
- {24740841, 5052253, -30094131, 8961361, 25877428, 6165135,
- -24368180, 14397372, -7380369, -6144105},
- {-28888365, 3510803, -28103278, -1158478, -11238128, -10631454,
- -15441463, -14453128, -1625486, -6494814},
- },
- },
- {
- {
- {793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843,
- -4885251, -9906200, -621852},
- {5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374,
- 1468826, -6171428, -15186581},
- {-4859255, -3779343, -2917758, -6748019, 7778750, 11688288,
- -30404353, -9871238, -1558923, -9863646},
- },
- {
- {10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958,
- 14783338, -30581476, -15757844},
- {10566929, 12612572, -31944212, 11118703, -12633376, 12362879,
- 21752402, 8822496, 24003793, 14264025},
- {27713862, -7355973, -11008240, 9227530, 27050101, 2504721,
- 23886875, -13117525, 13958495, -5732453},
- },
- {
- {-23481610, 4867226, -27247128, 3900521, 29838369, -8212291,
- -31889399, -10041781, 7340521, -15410068},
- {4646514, -8011124, -22766023, -11532654, 23184553, 8566613,
- 31366726, -1381061, -15066784, -10375192},
- {-17270517, 12723032, -16993061, 14878794, 21619651, -6197576,
- 27584817, 3093888, -8843694, 3849921},
- },
- {
- {-9064912, 2103172, 25561640, -15125738, -5239824, 9582958,
- 32477045, -9017955, 5002294, -15550259},
- {-12057553, -11177906, 21115585, -13365155, 8808712, -12030708,
- 16489530, 13378448, -25845716, 12741426},
- {-5946367, 10645103, -30911586, 15390284, -3286982, -7118677,
- 24306472, 15852464, 28834118, -7646072},
- },
- {
- {-17335748, -9107057, -24531279, 9434953, -8472084, -583362,
- -13090771, 455841, 20461858, 5491305},
- {13669248, -16095482, -12481974, -10203039, -14569770, -11893198,
- -24995986, 11293807, -28588204, -9421832},
- {28497928, 6272777, -33022994, 14470570, 8906179, -1225630,
- 18504674, -14165166, 29867745, -8795943},
- },
- {
- {-16207023, 13517196, -27799630, -13697798, 24009064, -6373891,
- -6367600, -13175392, 22853429, -4012011},
- {24191378, 16712145, -13931797, 15217831, 14542237, 1646131,
- 18603514, -11037887, 12876623, -2112447},
- {17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753,
- 608397, 16031844, 3723494},
- },
- {
- {-28632773, 12763728, -20446446, 7577504, 33001348, -13017745,
- 17558842, -7872890, 23896954, -4314245},
- {-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064,
- 7229064, -9919646, -8826859},
- {28816045, 298879, -28165016, -15920938, 19000928, -1665890,
- -12680833, -2949325, -18051778, -2082915},
- },
- {
- {16000882, -344896, 3493092, -11447198, -29504595, -13159789,
- 12577740, 16041268, -19715240, 7847707},
- {10151868, 10572098, 27312476, 7922682, 14825339, 4723128,
- -32855931, -6519018, -10020567, 3852848},
- {-11430470, 15697596, -21121557, -4420647, 5386314, 15063598,
- 16514493, -15932110, 29330899, -15076224},
- },
- },
- {
- {
- {-25499735, -4378794, -15222908, -6901211, 16615731, 2051784,
- 3303702, 15490, -27548796, 12314391},
- {15683520, -6003043, 18109120, -9980648, 15337968, -5997823,
- -16717435, 15921866, 16103996, -3731215},
- {-23169824, -10781249, 13588192, -1628807, -3798557, -1074929,
- -19273607, 5402699, -29815713, -9841101},
- },
- {
- {23190676, 2384583, -32714340, 3462154, -29903655, -1529132,
- -11266856, 8911517, -25205859, 2739713},
- {21374101, -3554250, -33524649, 9874411, 15377179, 11831242,
- -33529904, 6134907, 4931255, 11987849},
- {-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539,
- 13861388, -30076310, 10117930},
- },
- {
- {-29501170, -10744872, -26163768, 13051539, -25625564, 5089643,
- -6325503, 6704079, 12890019, 15728940},
- {-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376,
- -10428139, 12885167, 8311031},
- {-17516482, 5352194, 10384213, -13811658, 7506451, 13453191,
- 26423267, 4384730, 1888765, -5435404},
- },
- {
- {-25817338, -3107312, -13494599, -3182506, 30896459, -13921729,
- -32251644, -12707869, -19464434, -3340243},
- {-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245,
- 14845197, 17151279, -9854116},
- {-24830458, -12733720, -15165978, 10367250, -29530908, -265356,
- 22825805, -7087279, -16866484, 16176525},
- },
- {
- {-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182,
- -10363426, -28746253, -10197509},
- {-10626600, -4486402, -13320562, -5125317, 3432136, -6393229,
- 23632037, -1940610, 32808310, 1099883},
- {15030977, 5768825, -27451236, -2887299, -6427378, -15361371,
- -15277896, -6809350, 2051441, -15225865},
- },
- {
- {-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398,
- -14154188, -22686354, 16633660},
- {4577086, -16752288, 13249841, -15304328, 19958763, -14537274,
- 18559670, -10759549, 8402478, -9864273},
- {-28406330, -1051581, -26790155, -907698, -17212414, -11030789,
- 9453451, -14980072, 17983010, 9967138},
- },
- {
- {-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990,
- 7806337, 17507396, 3651560},
- {-10420457, -4118111, 14584639, 15971087, -15768321, 8861010,
- 26556809, -5574557, -18553322, -11357135},
- {2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121,
- 8459447, -5605463, -7621941},
- },
- {
- {-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813,
- -849066, 17258084, -7977739},
- {18164541, -10595176, -17154882, -1542417, 19237078, -9745295,
- 23357533, -15217008, 26908270, 12150756},
- {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168,
- -5537701, -32302074, 16215819},
- },
- },
- {
- {
- {-6898905, 9824394, -12304779, -4401089, -31397141, -6276835,
- 32574489, 12532905, -7503072, -8675347},
- {-27343522, -16515468, -27151524, -10722951, 946346, 16291093,
- 254968, 7168080, 21676107, -1943028},
- {21260961, -8424752, -16831886, -11920822, -23677961, 3968121,
- -3651949, -6215466, -3556191, -7913075},
- },
- {
- {16544754, 13250366, -16804428, 15546242, -4583003, 12757258,
- -2462308, -8680336, -18907032, -9662799},
- {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564,
- 26820651, 16690659, 25459437, -4564609},
- {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224,
- 9142795, -2391602, -6432418, -1644817},
- },
- {
- {-23104652, 6253476, 16964147, -3768872, -25113972, -12296437,
- -27457225, -16344658, 6335692, 7249989},
- {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693,
- -30272269, 2682242, 25993170, -12478523},
- {4364628, 5930691, 32304656, -10044554, -8054781, 15091131,
- 22857016, -10598955, 31820368, 15075278},
- },
- {
- {31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788,
- -9650886, -17970238, 12833045},
- {19073683, 14851414, -24403169, -11860168, 7625278, 11091125,
- -19619190, 2074449, -9413939, 14905377},
- {24483667, -11935567, -2518866, -11547418, -1553130, 15355506,
- -25282080, 9253129, 27628530, -7555480},
- },
- {
- {17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324,
- -9157582, -14110875, 15297016},
- {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417,
- -11864220, 8683221, 2921426},
- {18606791, 11874196, 27155355, -5281482, -24031742, 6265446,
- -25178240, -1278924, 4674690, 13890525},
- },
- {
- {13609624, 13069022, -27372361, -13055908, 24360586, 9592974,
- 14977157, 9835105, 4389687, 288396},
- {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062,
- 8317628, 23388070, 16052080},
- {12720016, 11937594, -31970060, -5028689, 26900120, 8561328,
- -20155687, -11632979, -14754271, -10812892},
- },
- {
- {15961858, 14150409, 26716931, -665832, -22794328, 13603569,
- 11829573, 7467844, -28822128, 929275},
- {11038231, -11582396, -27310482, -7316562, -10498527, -16307831,
- -23479533, -9371869, -21393143, 2465074},
- {20017163, -4323226, 27915242, 1529148, 12396362, 15675764,
- 13817261, -9658066, 2463391, -4622140},
- },
- {
- {-16358878, -12663911, -12065183, 4996454, -1256422, 1073572,
- 9583558, 12851107, 4003896, 12673717},
- {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325,
- 14741514, -9103726, 7903886, 2348101},
- {24536016, -16515207, 12715592, -3862155, 1511293, 10047386,
- -3842346, -7129159, -28377538, 10048127},
- },
- },
- {
- {
- {-12622226, -6204820, 30718825, 2591312, -10617028, 12192840,
- 18873298, -7297090, -32297756, 15221632},
- {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409,
- -21343950, 2095755, 29769758, 6593415},
- {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345,
- -6118678, 30958054, 8292160},
- },
- {
- {31429822, -13959116, 29173532, 15632448, 12174511, -2760094,
- 32808831, 3977186, 26143136, -3148876},
- {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633,
- -1674433, -3758243, -2304625},
- {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029,
- -1612713, -1535569, -16664475, 8194478},
- },
- {
- {27338066, -7507420, -7414224, 10140405, -19026427, -6589889,
- 27277191, 8855376, 28572286, 3005164},
- {26287124, 4821776, 25476601, -4145903, -3764513, -15788984,
- -18008582, 1182479, -26094821, -13079595},
- {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192,
- -21876275, -13982627, 32208683, -1198248},
- },
- {
- {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505,
- -27315504, -10497842, -27672585, -11539858},
- {15941029, -9405932, -21367050, 8062055, 31876073, -238629,
- -15278393, -1444429, 15397331, -4130193},
- {8934485, -13485467, -23286397, -13423241, -32446090, 14047986,
- 31170398, -1441021, -27505566, 15087184},
- },
- {
- {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776,
- -15502406, 11461896, 16788528, -5868942},
- {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433,
- -3770287, -10323320, 31322514, -11615635},
- {21426655, -5650218, -13648287, -5347537, -28812189, -4920970,
- -18275391, -14621414, 13040862, -12112948},
- },
- {
- {11293895, 12478086, -27136401, 15083750, -29307421, 14748872,
- 14555558, -13417103, 1613711, 4896935},
- {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460,
- 2825960, -4897045, -23971776, -11267415},
- {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618,
- 20615400, 12405433, -23753030, -8436416},
- },
- {
- {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801,
- 4378436, 2432030, 23097949, -566018},
- {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264,
- 10103221, -18512313, 2424778},
- {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678,
- 1344109, -3642553, 12412659},
- },
- {
- {-24001791, 7690286, 14929416, -168257, -32210835, -13412986,
- 24162697, -15326504, -3141501, 11179385},
- {18289522, -14724954, 8056945, 16430056, -21729724, 7842514,
- -6001441, -1486897, -18684645, -11443503},
- {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959,
- 13403813, 11052904, 5219329},
- },
- },
- {
- {
- {20678546, -8375738, -32671898, 8849123, -5009758, 14574752,
- 31186971, -3973730, 9014762, -8579056},
- {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600,
- -33102500, 9160280, 8473550, -3256838},
- {24900749, 14435722, 17209120, -15292541, -22592275, 9878983,
- -7689309, -16335821, -24568481, 11788948},
- },
- {
- {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904,
- -20037437, 10410733, -24568470, -1458691},
- {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911,
- 11871841, -12505194, -18513325, 8464118},
- {-23400612, 8348507, -14585951, -861714, -3950205, -6373419,
- 14325289, 8628612, 33313881, -8370517},
- },
- {
- {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838,
- -24805667, -10236854, -8940735, -5818269},
- {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245,
- 15989197, -12838188, 28358192, -4253904},
- {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267,
- -16637684, 4072016, -5351664, 5596589},
- },
- {
- {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565,
- 29266239, 2557221, 1768301, 15373193},
- {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902,
- -4504991, -24660491, 3442910},
- {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093,
- 22597931, 7176455, -18585478, 13365930},
- },
- {
- {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107,
- -8570186, -9689599, -3031667},
- {25008904, -10771599, -4305031, -9638010, 16265036, 15721635,
- 683793, -11823784, 15723479, -15163481},
- {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514,
- 11879682, 5400171, 519526, -1235876},
- },
- {
- {22258397, -16332233, -7869817, 14613016, -22520255, -2950923,
- -20353881, 7315967, 16648397, 7605640},
- {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212,
- 23994942, -5281555, -9468848, 4763278},
- {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390,
- 31088447, -7764523, -11356529, 728112},
- },
- {
- {26047220, -11751471, -6900323, -16521798, 24092068, 9158119,
- -4273545, -12555558, -29365436, -5498272},
- {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007,
- 12327945, 10750447, 10014012},
- {-10312768, 3936952, 9156313, -8897683, 16498692, -994647,
- -27481051, -666732, 3424691, 7540221},
- },
- {
- {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422,
- -16317219, -9244265, 15258046},
- {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406,
- 2711395, 1062915, -5136345},
- {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411,
- -6066489, 12194497, 32960380, 1459310},
- },
- },
- {
- {
- {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197,
- -6101885, 18638003, -11174937},
- {31395534, 15098109, 26581030, 8030562, -16527914, -5007134,
- 9012486, -7584354, -6643087, -5442636},
- {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222,
- 9677543, -32294889, -6456008},
- },
- {
- {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579,
- -7839692, -7852844, -8138429},
- {-15236356, -15433509, 7766470, 746860, 26346930, -10221762,
- -27333451, 10754588, -9431476, 5203576},
- {31834314, 14135496, -770007, 5159118, 20917671, -16768096,
- -7467973, -7337524, 31809243, 7347066},
- },
- {
- {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881,
- 19797970, -12211255, 15192876, -2087490},
- {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091,
- 10609330, 12694420, 33473243, -13382104},
- {33184999, 11180355, 15832085, -11385430, -1633671, 225884,
- 15089336, -11023903, -6135662, 14480053},
- },
- {
- {31308717, -5619998, 31030840, -1897099, 15674547, -6582883,
- 5496208, 13685227, 27595050, 8737275},
- {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022,
- -31008351, -12610604, 26498114, 66511},
- {22644454, -8761729, -16671776, 4884562, -3105614, -13559366,
- 30540766, -4286747, -13327787, -7515095},
- },
- {
- {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506,
- 8205540, 13585437, -17127465, 15115439},
- {23711543, -672915, 31206561, -8362711, 6164647, -9709987,
- -33535882, -1426096, 8236921, 16492939},
- {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270,
- 19574902, 10071562, 6708380, -6222424},
- },
- {
- {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017,
- 9328700, 29955601, -11678310},
- {3096359, 9271816, -21620864, -15521844, -14847996, -7592937,
- -25892142, -12635595, -9917575, 6216608},
- {-32615849, 338663, -25195611, 2510422, -29213566, -13820213,
- 24822830, -6146567, -26767480, 7525079},
- },
- {
- {-23066649, -13985623, 16133487, -7896178, -3389565, 778788,
- -910336, -2782495, -19386633, 11994101},
- {21691500, -13624626, -641331, -14367021, 3285881, -3483596,
- -25064666, 9718258, -7477437, 13381418},
- {18445390, -4202236, 14979846, 11622458, -1727110, -3582980,
- 23111648, -6375247, 28535282, 15779576},
- },
- {
- {30098053, 3089662, -9234387, 16662135, -21306940, 11308411,
- -14068454, 12021730, 9955285, -16303356},
- {9734894, -14576830, -7473633, -9138735, 2060392, 11313496,
- -18426029, 9924399, 20194861, 13380996},
- {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792,
- -1984914, 15707771, 26342023, 10146099},
- },
- },
- {
- {
- {-26016874, -219943, 21339191, -41388, 19745256, -2878700,
- -29637280, 2227040, 21612326, -545728},
- {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714,
- 25764461, 12243797, -20856566, 11649658},
- {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944,
- 6114064, 33514190, 2333242},
- },
- {
- {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134,
- -6679750, -12670638, 24350578, -13450001},
- {-4116307, -11271533, -23886186, 4843615, -30088339, 690623,
- -31536088, -10406836, 8317860, 12352766},
- {18200138, -14475911, -33087759, -2696619, -23702521, -9102511,
- -23552096, -2287550, 20712163, 6719373},
- },
- {
- {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530,
- -3763210, 26224235, -3297458},
- {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420,
- 21728352, 9493610, 18620611, -16428628},
- {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965,
- -5269471, -9725556, -30701573, -16479657},
- },
- {
- {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940,
- 12248509, -5240639, 13735342, 1934062},
- {25089769, 6742589, 17081145, -13406266, 21909293, -16067981,
- -15136294, -3765346, -21277997, 5473616},
- {31883677, -7961101, 1083432, -11572403, 22828471, 13290673,
- -7125085, 12469656, 29111212, -5451014},
- },
- {
- {24244947, -15050407, -26262976, 2791540, -14997599, 16666678,
- 24367466, 6388839, -10295587, 452383},
- {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269,
- -24236251, -5915248, 15766062, 8407814},
- {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495,
- -8917023, -4388953, -8067909, 2276718},
- },
- {
- {30157918, 12924066, -17712050, 9245753, 19895028, 3368142,
- -23827587, 5096219, 22740376, -7303417},
- {2041139, -14256350, 7783687, 13876377, -25946985, -13352459,
- 24051124, 13742383, -15637599, 13295222},
- {33338237, -8505733, 12532113, 7977527, 9106186, -1715251,
- -17720195, -4612972, -4451357, -14669444},
- },
- {
- {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651,
- -2469266, -4141880, 7770569, 9620597},
- {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528,
- -1694323, -33502340, -14767970},
- {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801,
- 1220118, 30494170, -11440799},
- },
- {
- {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666,
- -26739026, 926050, -1684339, -13333647},
- {13908495, -3549272, 30919928, -6273825, -21521863, 7989039,
- 9021034, 9078865, 3353509, 4033511},
- {-29663431, -15113610, 32259991, -344482, 24295849, -12912123,
- 23161163, 8839127, 27485041, 7356032},
- },
- },
- {
- {
- {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142,
- 2625015, 28431036, -16771834},
- {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183,
- -22545972, 14150565, 15970762, 4099461},
- {29262576, 16756590, 26350592, -8793563, 8529671, -11208050,
- 13617293, -9937143, 11465739, 8317062},
- },
- {
- {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222,
- 14898637, 3848455, 20969334, -5157516},
- {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114,
- -21610826, -3649888, 11177095, 14989547},
- {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771,
- 13515641, 2581286, -28487508, 9930240},
- },
- {
- {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081,
- 18345767, -13403753, 16291481, -5314038},
- {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774,
- 6957617, 4368891, 9788741},
- {16660756, 7281060, -10830758, 12911820, 20108584, -8101676,
- -21722536, -8613148, 16250552, -11111103},
- },
- {
- {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584,
- 10604807, -30190403, 4782747},
- {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590,
- -9981571, 4383045, 22546403, 437323},
- {31665577, -12180464, -16186830, 1491339, -18368625, 3294682,
- 27343084, 2786261, -30633590, -14097016},
- },
- {
- {-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
- -19690631, 2355319, -19284671, -6114373},
- {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
- 18952177, 15496498, -29380133, 11754228},
- {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
- 7141596, 11724556, 22761615, -10134141},
- },
- {
- {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
- -28741185, -12227393, 32851222, 11717399},
- {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
- 31474879, 3483633, -1193175, -4030831},
- {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
- 33142652, 6546660, -19985279, -3948376},
- },
- {
- {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
- -8537131, -12833048, -30772034, -15486313},
- {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
- -31135347, -16049879, 10928917, 3011958},
- {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
- -30831056, -12805180, 18008031, 10258577},
- },
- {
- {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
- -1853465, 1367120, 25127874, 6671743},
- {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
- 21382910, 11042292, 25838796, 4642684},
- {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
- 30468147, -13900640, 18423289, 4177476},
- },
- },
-};
-
-static uint8_t negative(signed char b) {
- uint32_t x = b;
- x >>= 31; // 1: yes; 0: no
- return x;
-}
-
-static void table_select(ge_precomp *t, int pos, signed char b) {
- ge_precomp minust;
- uint8_t bnegative = negative(b);
- uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
-
- ge_precomp_0(t);
- cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
- cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
- cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
- cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
- cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
- cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
- cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
- cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
- fe_copy(minust.yplusx, t->yminusx);
- fe_copy(minust.yminusx, t->yplusx);
- fe_neg(minust.xy2d, t->xy2d);
- cmov(t, &minust, bnegative);
-}
-
-// h = a * B
-// where a = a[0]+256*a[1]+...+256^31 a[31]
-// B is the Ed25519 base point (x,4/5) with x positive.
-//
-// Preconditions:
-// a[31] <= 127
-void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
- signed char e[64];
- signed char carry;
- ge_p1p1 r;
- ge_p2 s;
- ge_precomp t;
- int i;
-
- for (i = 0; i < 32; ++i) {
- e[2 * i + 0] = (a[i] >> 0) & 15;
- e[2 * i + 1] = (a[i] >> 4) & 15;
- }
- // each e[i] is between 0 and 15
- // e[63] is between 0 and 7
-
- carry = 0;
- for (i = 0; i < 63; ++i) {
- e[i] += carry;
- carry = e[i] + 8;
- carry >>= 4;
- e[i] -= carry << 4;
- }
- e[63] += carry;
- // each e[i] is between -8 and 8
-
- ge_p3_0(h);
- for (i = 1; i < 64; i += 2) {
- table_select(&t, i / 2, e[i]);
- ge_madd(&r, h, &t);
- x25519_ge_p1p1_to_p3(h, &r);
- }
-
- ge_p3_dbl(&r, h);
- x25519_ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- x25519_ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- x25519_ge_p1p1_to_p2(&s, &r);
- ge_p2_dbl(&r, &s);
- x25519_ge_p1p1_to_p3(h, &r);
-
- for (i = 0; i < 64; i += 2) {
- table_select(&t, i / 2, e[i]);
- ge_madd(&r, h, &t);
- x25519_ge_p1p1_to_p3(h, &r);
- }
-}
-
-#endif
-
-static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
- fe_cmov(t->YplusX, u->YplusX, b);
- fe_cmov(t->YminusX, u->YminusX, b);
- fe_cmov(t->Z, u->Z, b);
- fe_cmov(t->T2d, u->T2d, b);
-}
-
-// r = scalar * A.
-// where a = a[0]+256*a[1]+...+256^31 a[31].
-void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) {
- ge_p2 Ai_p2[8];
- ge_cached Ai[16];
- ge_p1p1 t;
-
- ge_cached_0(&Ai[0]);
- x25519_ge_p3_to_cached(&Ai[1], A);
- ge_p3_to_p2(&Ai_p2[1], A);
-
- unsigned i;
- for (i = 2; i < 16; i += 2) {
- ge_p2_dbl(&t, &Ai_p2[i / 2]);
- ge_p1p1_to_cached(&Ai[i], &t);
- if (i < 8) {
- x25519_ge_p1p1_to_p2(&Ai_p2[i], &t);
- }
- x25519_ge_add(&t, A, &Ai[i]);
- ge_p1p1_to_cached(&Ai[i + 1], &t);
- if (i < 7) {
- x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t);
- }
- }
-
- ge_p2_0(r);
- ge_p3 u;
-
- for (i = 0; i < 256; i += 4) {
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p2(r, &t);
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p2(r, &t);
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p2(r, &t);
- ge_p2_dbl(&t, r);
- x25519_ge_p1p1_to_p3(&u, &t);
-
- uint8_t index = scalar[31 - i/8];
- index >>= 4 - (i & 4);
- index &= 0xf;
-
- unsigned j;
- ge_cached selected;
- ge_cached_0(&selected);
- for (j = 0; j < 16; j++) {
- cmov_cached(&selected, &Ai[j], equal(j, index));
- }
-
- x25519_ge_add(&t, &u, &selected);
- x25519_ge_p1p1_to_p2(r, &t);
- }
-}
-
-static void slide(signed char *r, const uint8_t *a) {
- int i;
- int b;
- int k;
-
- for (i = 0; i < 256; ++i) {
- r[i] = 1 & (a[i >> 3] >> (i & 7));
- }
-
- for (i = 0; i < 256; ++i) {
- if (r[i]) {
- for (b = 1; b <= 6 && i + b < 256; ++b) {
- if (r[i + b]) {
- if (r[i] + (r[i + b] << b) <= 15) {
- r[i] += r[i + b] << b;
- r[i + b] = 0;
- } else if (r[i] - (r[i + b] << b) >= -15) {
- r[i] -= r[i + b] << b;
- for (k = i + b; k < 256; ++k) {
- if (!r[k]) {
- r[k] = 1;
- break;
- }
- r[k] = 0;
- }
- } else {
- break;
- }
- }
- }
- }
- }
-}
-
-static const ge_precomp Bi[8] = {
- {
- {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
- -11754271, -6079156, 2047605},
- {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378},
- {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
- 11864899, -24514362, -4438546},
- },
- {
- {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
- -14772189, 28944400, -1550024},
- {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
- -11775962, 7689662, 11199574},
- {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
- 10017326, -17749093, -9920357},
- },
- {
- {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
- 14515107, -15438304, 10819380},
- {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306},
- {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
- 13850243, -23678021, -15815942},
- },
- {
- {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766},
- {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
- 16520125, 30598449, 7715701},
- {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
- 1370708, 29794553, -1409300},
- },
- {
- {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
- -1361450, -13062696, 13821877},
- {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
- -7212327, 18853322, -14220951},
- {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
- -10431137, 2207753, -3209784},
- },
- {
- {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
- -663000, -31111463, -16132436},
- {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
- 15725684, 171356, 6466918},
- {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
- -14088058, -30714912, 16193877},
- },
- {
- {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
- 4729455, -18074513, 9256800},
- {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
- 9761698, -19827198, 630305},
- {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
- -15960994, -2449256, -14291300},
- },
- {
- {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
- 15033784, 25105118, -7894876},
- {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
- 1573892, -2625887, 2198790, -15804619},
- {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
- -16236442, -32461234, -12290683},
- },
-};
-
-// r = a * A + b * B
-// where a = a[0]+256*a[1]+...+256^31 a[31].
-// and b = b[0]+256*b[1]+...+256^31 b[31].
-// B is the Ed25519 base point (x,4/5) with x positive.
-static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
- const ge_p3 *A, const uint8_t *b) {
- signed char aslide[256];
- signed char bslide[256];
- ge_cached Ai[8]; // A,3A,5A,7A,9A,11A,13A,15A
- ge_p1p1 t;
- ge_p3 u;
- ge_p3 A2;
- int i;
-
- slide(aslide, a);
- slide(bslide, b);
-
- x25519_ge_p3_to_cached(&Ai[0], A);
- ge_p3_dbl(&t, A);
- x25519_ge_p1p1_to_p3(&A2, &t);
- x25519_ge_add(&t, &A2, &Ai[0]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[1], &u);
- x25519_ge_add(&t, &A2, &Ai[1]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[2], &u);
- x25519_ge_add(&t, &A2, &Ai[2]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[3], &u);
- x25519_ge_add(&t, &A2, &Ai[3]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[4], &u);
- x25519_ge_add(&t, &A2, &Ai[4]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[5], &u);
- x25519_ge_add(&t, &A2, &Ai[5]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[6], &u);
- x25519_ge_add(&t, &A2, &Ai[6]);
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_p3_to_cached(&Ai[7], &u);
-
- ge_p2_0(r);
-
- for (i = 255; i >= 0; --i) {
- if (aslide[i] || bslide[i]) {
- break;
- }
- }
-
- for (; i >= 0; --i) {
- ge_p2_dbl(&t, r);
-
- if (aslide[i] > 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
- } else if (aslide[i] < 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
- }
-
- if (bslide[i] > 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- ge_madd(&t, &u, &Bi[bslide[i] / 2]);
- } else if (bslide[i] < 0) {
- x25519_ge_p1p1_to_p3(&u, &t);
- ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
- }
-
- x25519_ge_p1p1_to_p2(r, &t);
- }
-}
-
-// The set of scalars is \Z/l
-// where l = 2^252 + 27742317777372353535851937790883648493.
-
-// Input:
-// s[0]+256*s[1]+...+256^63*s[63] = s
-//
-// Output:
-// s[0]+256*s[1]+...+256^31*s[31] = s mod l
-// where l = 2^252 + 27742317777372353535851937790883648493.
-// Overwrites s in place.
-void x25519_sc_reduce(uint8_t *s) {
- int64_t s0 = 2097151 & load_3(s);
- int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
- int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
- int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
- int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
- int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
- int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
- int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
- int64_t s8 = 2097151 & load_3(s + 21);
- int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
- int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
- int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
- int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
- int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
- int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
- int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
- int64_t s16 = 2097151 & load_3(s + 42);
- int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
- int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
- int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
- int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
- int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
- int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
- int64_t s23 = (load_4(s + 60) >> 3);
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-// Input:
-// a[0]+256*a[1]+...+256^31*a[31] = a
-// b[0]+256*b[1]+...+256^31*b[31] = b
-// c[0]+256*c[1]+...+256^31*c[31] = c
-//
-// Output:
-// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
-// where l = 2^252 + 27742317777372353535851937790883648493.
-static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
- const uint8_t *c) {
- int64_t a0 = 2097151 & load_3(a);
- int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
- int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
- int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
- int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
- int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
- int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
- int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
- int64_t a8 = 2097151 & load_3(a + 21);
- int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
- int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
- int64_t a11 = (load_4(a + 28) >> 7);
- int64_t b0 = 2097151 & load_3(b);
- int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
- int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
- int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
- int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
- int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
- int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
- int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
- int64_t b8 = 2097151 & load_3(b + 21);
- int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
- int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
- int64_t b11 = (load_4(b + 28) >> 7);
- int64_t c0 = 2097151 & load_3(c);
- int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
- int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
- int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
- int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
- int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
- int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
- int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
- int64_t c8 = 2097151 & load_3(c + 21);
- int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
- int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
- int64_t c11 = (load_4(c + 28) >> 7);
- int64_t s0;
- int64_t s1;
- int64_t s2;
- int64_t s3;
- int64_t s4;
- int64_t s5;
- int64_t s6;
- int64_t s7;
- int64_t s8;
- int64_t s9;
- int64_t s10;
- int64_t s11;
- int64_t s12;
- int64_t s13;
- int64_t s14;
- int64_t s15;
- int64_t s16;
- int64_t s17;
- int64_t s18;
- int64_t s19;
- int64_t s20;
- int64_t s21;
- int64_t s22;
- int64_t s23;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
- int64_t carry10;
- int64_t carry11;
- int64_t carry12;
- int64_t carry13;
- int64_t carry14;
- int64_t carry15;
- int64_t carry16;
- int64_t carry17;
- int64_t carry18;
- int64_t carry19;
- int64_t carry20;
- int64_t carry21;
- int64_t carry22;
-
- s0 = c0 + a0 * b0;
- s1 = c1 + a0 * b1 + a1 * b0;
- s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
- s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
- s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
- s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
- s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
- s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
- a6 * b1 + a7 * b0;
- s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
- a6 * b2 + a7 * b1 + a8 * b0;
- s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
- a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
- s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
- a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
- s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
- a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
- s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
- a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
- s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
- a9 * b4 + a10 * b3 + a11 * b2;
- s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
- a10 * b4 + a11 * b3;
- s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
- a11 * b4;
- s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
- s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
- s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
- s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
- s20 = a9 * b11 + a10 * b10 + a11 * b9;
- s21 = a10 * b11 + a11 * b10;
- s22 = a11 * b11;
- s23 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
- carry18 = (s18 + (1 << 20)) >> 21;
- s19 += carry18;
- s18 -= carry18 << 21;
- carry20 = (s20 + (1 << 20)) >> 21;
- s21 += carry20;
- s20 -= carry20 << 21;
- carry22 = (s22 + (1 << 20)) >> 21;
- s23 += carry22;
- s22 -= carry22 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
- carry17 = (s17 + (1 << 20)) >> 21;
- s18 += carry17;
- s17 -= carry17 << 21;
- carry19 = (s19 + (1 << 20)) >> 21;
- s20 += carry19;
- s19 -= carry19 << 21;
- carry21 = (s21 + (1 << 20)) >> 21;
- s22 += carry21;
- s21 -= carry21 << 21;
-
- s11 += s23 * 666643;
- s12 += s23 * 470296;
- s13 += s23 * 654183;
- s14 -= s23 * 997805;
- s15 += s23 * 136657;
- s16 -= s23 * 683901;
- s23 = 0;
-
- s10 += s22 * 666643;
- s11 += s22 * 470296;
- s12 += s22 * 654183;
- s13 -= s22 * 997805;
- s14 += s22 * 136657;
- s15 -= s22 * 683901;
- s22 = 0;
-
- s9 += s21 * 666643;
- s10 += s21 * 470296;
- s11 += s21 * 654183;
- s12 -= s21 * 997805;
- s13 += s21 * 136657;
- s14 -= s21 * 683901;
- s21 = 0;
-
- s8 += s20 * 666643;
- s9 += s20 * 470296;
- s10 += s20 * 654183;
- s11 -= s20 * 997805;
- s12 += s20 * 136657;
- s13 -= s20 * 683901;
- s20 = 0;
-
- s7 += s19 * 666643;
- s8 += s19 * 470296;
- s9 += s19 * 654183;
- s10 -= s19 * 997805;
- s11 += s19 * 136657;
- s12 -= s19 * 683901;
- s19 = 0;
-
- s6 += s18 * 666643;
- s7 += s18 * 470296;
- s8 += s18 * 654183;
- s9 -= s18 * 997805;
- s10 += s18 * 136657;
- s11 -= s18 * 683901;
- s18 = 0;
-
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry12 = (s12 + (1 << 20)) >> 21;
- s13 += carry12;
- s12 -= carry12 << 21;
- carry14 = (s14 + (1 << 20)) >> 21;
- s15 += carry14;
- s14 -= carry14 << 21;
- carry16 = (s16 + (1 << 20)) >> 21;
- s17 += carry16;
- s16 -= carry16 << 21;
-
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
- carry13 = (s13 + (1 << 20)) >> 21;
- s14 += carry13;
- s13 -= carry13 << 21;
- carry15 = (s15 + (1 << 20)) >> 21;
- s16 += carry15;
- s15 -= carry15 << 21;
-
- s5 += s17 * 666643;
- s6 += s17 * 470296;
- s7 += s17 * 654183;
- s8 -= s17 * 997805;
- s9 += s17 * 136657;
- s10 -= s17 * 683901;
- s17 = 0;
-
- s4 += s16 * 666643;
- s5 += s16 * 470296;
- s6 += s16 * 654183;
- s7 -= s16 * 997805;
- s8 += s16 * 136657;
- s9 -= s16 * 683901;
- s16 = 0;
-
- s3 += s15 * 666643;
- s4 += s15 * 470296;
- s5 += s15 * 654183;
- s6 -= s15 * 997805;
- s7 += s15 * 136657;
- s8 -= s15 * 683901;
- s15 = 0;
-
- s2 += s14 * 666643;
- s3 += s14 * 470296;
- s4 += s14 * 654183;
- s5 -= s14 * 997805;
- s6 += s14 * 136657;
- s7 -= s14 * 683901;
- s14 = 0;
-
- s1 += s13 * 666643;
- s2 += s13 * 470296;
- s3 += s13 * 654183;
- s4 -= s13 * 997805;
- s5 += s13 * 136657;
- s6 -= s13 * 683901;
- s13 = 0;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = (s0 + (1 << 20)) >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry2 = (s2 + (1 << 20)) >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry4 = (s4 + (1 << 20)) >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry6 = (s6 + (1 << 20)) >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry8 = (s8 + (1 << 20)) >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry10 = (s10 + (1 << 20)) >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- carry1 = (s1 + (1 << 20)) >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry3 = (s3 + (1 << 20)) >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry5 = (s5 + (1 << 20)) >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry7 = (s7 + (1 << 20)) >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry9 = (s9 + (1 << 20)) >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry11 = (s11 + (1 << 20)) >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
- carry11 = s11 >> 21;
- s12 += carry11;
- s11 -= carry11 << 21;
-
- s0 += s12 * 666643;
- s1 += s12 * 470296;
- s2 += s12 * 654183;
- s3 -= s12 * 997805;
- s4 += s12 * 136657;
- s5 -= s12 * 683901;
- s12 = 0;
-
- carry0 = s0 >> 21;
- s1 += carry0;
- s0 -= carry0 << 21;
- carry1 = s1 >> 21;
- s2 += carry1;
- s1 -= carry1 << 21;
- carry2 = s2 >> 21;
- s3 += carry2;
- s2 -= carry2 << 21;
- carry3 = s3 >> 21;
- s4 += carry3;
- s3 -= carry3 << 21;
- carry4 = s4 >> 21;
- s5 += carry4;
- s4 -= carry4 << 21;
- carry5 = s5 >> 21;
- s6 += carry5;
- s5 -= carry5 << 21;
- carry6 = s6 >> 21;
- s7 += carry6;
- s6 -= carry6 << 21;
- carry7 = s7 >> 21;
- s8 += carry7;
- s7 -= carry7 << 21;
- carry8 = s8 >> 21;
- s9 += carry8;
- s8 -= carry8 << 21;
- carry9 = s9 >> 21;
- s10 += carry9;
- s9 -= carry9 << 21;
- carry10 = s10 >> 21;
- s11 += carry10;
- s10 -= carry10 << 21;
-
- s[0] = s0 >> 0;
- s[1] = s0 >> 8;
- s[2] = (s0 >> 16) | (s1 << 5);
- s[3] = s1 >> 3;
- s[4] = s1 >> 11;
- s[5] = (s1 >> 19) | (s2 << 2);
- s[6] = s2 >> 6;
- s[7] = (s2 >> 14) | (s3 << 7);
- s[8] = s3 >> 1;
- s[9] = s3 >> 9;
- s[10] = (s3 >> 17) | (s4 << 4);
- s[11] = s4 >> 4;
- s[12] = s4 >> 12;
- s[13] = (s4 >> 20) | (s5 << 1);
- s[14] = s5 >> 7;
- s[15] = (s5 >> 15) | (s6 << 6);
- s[16] = s6 >> 2;
- s[17] = s6 >> 10;
- s[18] = (s6 >> 18) | (s7 << 3);
- s[19] = s7 >> 5;
- s[20] = s7 >> 13;
- s[21] = s8 >> 0;
- s[22] = s8 >> 8;
- s[23] = (s8 >> 16) | (s9 << 5);
- s[24] = s9 >> 3;
- s[25] = s9 >> 11;
- s[26] = (s9 >> 19) | (s10 << 2);
- s[27] = s10 >> 6;
- s[28] = (s10 >> 14) | (s11 << 7);
- s[29] = s11 >> 1;
- s[30] = s11 >> 9;
- s[31] = s11 >> 17;
-}
-
-void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
- uint8_t seed[32];
- RAND_bytes(seed, 32);
- ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
-}
-
-int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
- const uint8_t private_key[64]) {
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(private_key, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, az + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t nonce[SHA512_DIGEST_LENGTH];
- SHA512_Final(nonce, &hash_ctx);
-
- x25519_sc_reduce(nonce);
- ge_p3 R;
- x25519_ge_scalarmult_base(&R, nonce);
- ge_p3_tobytes(out_sig, &R);
-
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, out_sig, 32);
- SHA512_Update(&hash_ctx, private_key + 32, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t hram[SHA512_DIGEST_LENGTH];
- SHA512_Final(hram, &hash_ctx);
-
- x25519_sc_reduce(hram);
- sc_muladd(out_sig + 32, hram, az, nonce);
-
- return 1;
-}
-
-int ED25519_verify(const uint8_t *message, size_t message_len,
- const uint8_t signature[64], const uint8_t public_key[32]) {
- ge_p3 A;
- if ((signature[63] & 224) != 0 ||
- x25519_ge_frombytes_vartime(&A, public_key) != 0) {
- return 0;
- }
-
- fe_neg(A.X, A.X);
- fe_neg(A.T, A.T);
-
- uint8_t pkcopy[32];
- OPENSSL_memcpy(pkcopy, public_key, 32);
- uint8_t rcopy[32];
- OPENSSL_memcpy(rcopy, signature, 32);
- uint8_t scopy[32];
- OPENSSL_memcpy(scopy, signature + 32, 32);
-
- SHA512_CTX hash_ctx;
- SHA512_Init(&hash_ctx);
- SHA512_Update(&hash_ctx, signature, 32);
- SHA512_Update(&hash_ctx, public_key, 32);
- SHA512_Update(&hash_ctx, message, message_len);
- uint8_t h[SHA512_DIGEST_LENGTH];
- SHA512_Final(h, &hash_ctx);
-
- x25519_sc_reduce(h);
-
- ge_p2 R;
- ge_double_scalarmult_vartime(&R, h, &A, scopy);
-
- uint8_t rcheck[32];
- x25519_ge_tobytes(rcheck, &R);
-
- return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
-}
-
-void ED25519_keypair_from_seed(uint8_t out_public_key[32],
- uint8_t out_private_key[64],
- const uint8_t seed[32]) {
- uint8_t az[SHA512_DIGEST_LENGTH];
- SHA512(seed, 32, az);
-
- az[0] &= 248;
- az[31] &= 63;
- az[31] |= 64;
-
- ge_p3 A;
- x25519_ge_scalarmult_base(&A, az);
- ge_p3_tobytes(out_public_key, &A);
-
- OPENSSL_memcpy(out_private_key, seed, 32);
- OPENSSL_memcpy(out_private_key + 32, out_public_key, 32);
-}
-
-
-#if defined(BORINGSSL_X25519_X86_64)
-
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
- x25519_x86_64(out, scalar, point);
-}
-
-#else
-
-// Replace (f,g) with (g,f) if b == 1;
-// replace (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-static void fe_cswap(fe f, fe g, unsigned int b) {
- b = 0-b;
- unsigned i;
- for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
- x &= b;
- f[i] ^= x;
- g[i] ^= x;
- }
-}
-
-// h = f * 121666
-// Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-static void fe_mul121666(fe h, fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int64_t h0 = f0 * (int64_t) 121666;
- int64_t h1 = f1 * (int64_t) 121666;
- int64_t h2 = f2 * (int64_t) 121666;
- int64_t h3 = f3 * (int64_t) 121666;
- int64_t h4 = f4 * (int64_t) 121666;
- int64_t h5 = f5 * (int64_t) 121666;
- int64_t h6 = f6 * (int64_t) 121666;
- int64_t h7 = f7 * (int64_t) 121666;
- int64_t h8 = f8 * (int64_t) 121666;
- int64_t h9 = f9 * (int64_t) 121666;
- int64_t carry0;
- int64_t carry1;
- int64_t carry2;
- int64_t carry3;
- int64_t carry4;
- int64_t carry5;
- int64_t carry6;
- int64_t carry7;
- int64_t carry8;
- int64_t carry9;
-
- carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
- carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
- carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
- carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
- carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
-
- carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
- carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
- carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
- carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
- carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
-
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-static void x25519_scalar_mult_generic(uint8_t out[32],
- const uint8_t scalar[32],
- const uint8_t point[32]) {
- fe x1, x2, z2, x3, z3, tmp0, tmp1;
-
- uint8_t e[32];
- OPENSSL_memcpy(e, scalar, 32);
- e[0] &= 248;
- e[31] &= 127;
- e[31] |= 64;
- fe_frombytes(x1, point);
- fe_1(x2);
- fe_0(z2);
- fe_copy(x3, x1);
- fe_1(z3);
-
- unsigned swap = 0;
- int pos;
- for (pos = 254; pos >= 0; --pos) {
- unsigned b = 1 & (e[pos / 8] >> (pos & 7));
- swap ^= b;
- fe_cswap(x2, x3, swap);
- fe_cswap(z2, z3, swap);
- swap = b;
- fe_sub(tmp0, x3, z3);
- fe_sub(tmp1, x2, z2);
- fe_add(x2, x2, z2);
- fe_add(z2, x3, z3);
- fe_mul(z3, tmp0, x2);
- fe_mul(z2, z2, tmp1);
- fe_sq(tmp0, tmp1);
- fe_sq(tmp1, x2);
- fe_add(x3, z3, z2);
- fe_sub(z2, z3, z2);
- fe_mul(x2, tmp1, tmp0);
- fe_sub(tmp1, tmp1, tmp0);
- fe_sq(z2, z2);
- fe_mul121666(z3, tmp1);
- fe_sq(x3, x3);
- fe_add(tmp0, tmp0, z3);
- fe_mul(z3, x1, z2);
- fe_mul(z2, tmp1, tmp0);
- }
- fe_cswap(x2, x3, swap);
- fe_cswap(z2, z3, swap);
-
- fe_invert(z2, z2);
- fe_mul(x2, x2, z2);
- fe_tobytes(out, x2);
-}
-
-static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]) {
-#if defined(BORINGSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- x25519_NEON(out, scalar, point);
- return;
- }
-#endif
-
- x25519_scalar_mult_generic(out, scalar, point);
-}
-
-#endif // BORINGSSL_X25519_X86_64
-
-
-void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
- RAND_bytes(out_private_key, 32);
-
- // All X25519 implementations should decode scalars correctly (see
- // https://tools.ietf.org/html/rfc7748#section-5). However, if an
- // implementation doesn't then it might interoperate with random keys a
- // fraction of the time because they'll, randomly, happen to be correctly
- // formed.
- //
- // Thus we do the opposite of the masking here to make sure that our private
- // keys are never correctly masked and so, hopefully, any incorrect
- // implementations are deterministically broken.
- //
- // This does not affect security because, although we're throwing away
- // entropy, a valid implementation of scalarmult should throw away the exact
- // same bits anyway.
- out_private_key[0] |= 7;
- out_private_key[31] &= 63;
- out_private_key[31] |= 128;
-
- X25519_public_from_private(out_public_value, out_private_key);
-}
-
-int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
- const uint8_t peer_public_value[32]) {
- static const uint8_t kZeros[32] = {0};
- x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
- // The all-zero output results when the input is a point of small order.
- return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
-}
-
-#if defined(BORINGSSL_X25519_X86_64)
-
-// When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with
-// the Montgomery ladder because it's faster. Otherwise it's done using the
-// Ed25519 tables.
-
-void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
-}
-
-#else
-
-void X25519_public_from_private(uint8_t out_public_value[32],
- const uint8_t private_key[32]) {
-#if defined(BORINGSSL_X25519_NEON)
- if (CRYPTO_is_NEON_capable()) {
- static const uint8_t kMongomeryBasePoint[32] = {9};
- x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
- return;
- }
-#endif
-
- uint8_t e[32];
- OPENSSL_memcpy(e, private_key, 32);
- e[0] &= 248;
- e[31] &= 127;
- e[31] |= 64;
-
- ge_p3 A;
- x25519_ge_scalarmult_base(&A, e);
-
- // We only need the u-coordinate of the curve25519 point. The map is
- // u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y).
- fe zplusy, zminusy, zminusy_inv;
- fe_add(zplusy, A.Z, A.Y);
- fe_sub(zminusy, A.Z, A.Y);
- fe_invert(zminusy_inv, zminusy);
- fe_mul(zplusy, zplusy, zminusy_inv);
- fe_tobytes(out_public_value, zplusy);
-}
-
-#endif // BORINGSSL_X25519_X86_64
diff --git a/src/crypto/curve25519/internal.h b/src/crypto/curve25519/internal.h
deleted file mode 100644
index 9487a6c..0000000
--- a/src/crypto/curve25519/internal.h
+++ /dev/null
@@ -1,109 +0,0 @@
-/* Copyright (c) 2015, Google Inc.
- *
- * Permission to use, copy, modify, and/or distribute this software for any
- * purpose with or without fee is hereby granted, provided that the above
- * copyright notice and this permission notice appear in all copies.
- *
- * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
- * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
- * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
- * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
- * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
- * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
- * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
-
-#ifndef OPENSSL_HEADER_CURVE25519_INTERNAL_H
-#define OPENSSL_HEADER_CURVE25519_INTERNAL_H
-
-#if defined(__cplusplus)
-extern "C" {
-#endif
-
-
-#if defined(OPENSSL_X86_64) && !defined(OPENSSL_SMALL) && \
- !defined(OPENSSL_WINDOWS) && !defined(OPENSSL_NO_ASM)
-#define BORINGSSL_X25519_X86_64
-
-void x25519_x86_64(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]);
-#endif
-
-
-#if defined(OPENSSL_ARM) && !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_APPLE)
-#define BORINGSSL_X25519_NEON
-
-// x25519_NEON is defined in asm/x25519-arm.S.
-void x25519_NEON(uint8_t out[32], const uint8_t scalar[32],
- const uint8_t point[32]);
-#endif
-
-// fe means field element. Here the field is \Z/(2^255-19). An element t,
-// entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
-// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
-// context.
-typedef int32_t fe[10];
-
-/* ge means group element.
-
- * Here the group is the set of pairs (x,y) of field elements (see fe.h)
- * satisfying -x^2 + y^2 = 1 + d x^2y^2
- * where d = -121665/121666.
- *
- * Representations:
- * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
- * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
- * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
- * ge_precomp (Duif): (y+x,y-x,2dxy) */
-
-typedef struct {
- fe X;
- fe Y;
- fe Z;
-} ge_p2;
-
-typedef struct {
- fe X;
- fe Y;
- fe Z;
- fe T;
-} ge_p3;
-
-typedef struct {
- fe X;
- fe Y;
- fe Z;
- fe T;
-} ge_p1p1;
-
-typedef struct {
- fe yplusx;
- fe yminusx;
- fe xy2d;
-} ge_precomp;
-
-typedef struct {
- fe YplusX;
- fe YminusX;
- fe Z;
- fe T2d;
-} ge_cached;
-
-void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h);
-int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s);
-void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p);
-void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p);
-void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p);
-void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
-void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
-void x25519_ge_scalarmult_small_precomp(
- ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]);
-void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]);
-void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A);
-void x25519_sc_reduce(uint8_t *s);
-
-
-#if defined(__cplusplus)
-} // extern C
-#endif
-
-#endif // OPENSSL_HEADER_CURVE25519_INTERNAL_H
diff --git a/src/crypto/curve25519/spake25519.c b/src/crypto/curve25519/spake25519.c
index 8ebedf9..e0ff9ba 100644
--- a/src/crypto/curve25519/spake25519.c
+++ b/src/crypto/curve25519/spake25519.c
@@ -14,6 +14,7 @@
#include <openssl/curve25519.h>
+#include <assert.h>
#include <string.h>
#include <openssl/bytestring.h>
@@ -21,8 +22,8 @@
#include <openssl/rand.h>
#include <openssl/sha.h>
-#include "internal.h"
#include "../internal.h"
+#include "../../third_party/fiat/internal.h"
// The following precomputation tables are for the following
@@ -43,14 +44,14 @@
// see curve25519.c in this directory.
//
// Exact copies of the source code are kept in bug 27296743.
-//
-// import hashlib
-// import ed25519 as E # http://ed25519.cr.yp.to/python/ed25519.py
-//
-// SEED_N = 'edwards25519 point generation seed (N)'
-// SEED_M = 'edwards25519 point generation seed (M)'
/*
+import hashlib
+import ed25519 as E # http://ed25519.cr.yp.to/python/ed25519.py
+
+SEED_N = 'edwards25519 point generation seed (N)'
+SEED_M = 'edwards25519 point generation seed (M)'
+
def genpoint(seed):
v = hashlib.sha256(seed).digest()
it = 1
@@ -72,10 +73,10 @@
def gentable(P):
t = []
for i in range(1,16):
- k = (i >> 3 & 1) * (1 << 192) + \
- (i >> 2 & 1) * (1 << 128) + \
- (i >> 1 & 1) * (1 << 64) + \
- (i & 1)
+ k = ((i >> 3 & 1) * (1 << 192) +
+ (i >> 2 & 1) * (1 << 128) +
+ (i >> 1 & 1) * (1 << 64) +
+ (i & 1))
t.append(E.scalarmult(P, k))
return ''.join(E.encodeint(x) + E.encodeint(y) for (x,y) in t)
@@ -267,25 +268,6 @@
0xa6, 0x76, 0x81, 0x28, 0xb2, 0x65, 0xe8, 0x47, 0x14, 0xc6, 0x39, 0x06,
};
-enum spake2_state_t {
- spake2_state_init = 0,
- spake2_state_msg_generated,
- spake2_state_key_generated,
-};
-
-struct spake2_ctx_st {
- uint8_t private_key[32];
- uint8_t my_msg[32];
- uint8_t password_scalar[32];
- uint8_t password_hash[SHA512_DIGEST_LENGTH];
- uint8_t *my_name;
- size_t my_name_len;
- uint8_t *their_name;
- size_t their_name_len;
- enum spake2_role_t my_role;
- enum spake2_state_t state;
-};
-
SPAKE2_CTX *SPAKE2_CTX_new(enum spake2_role_t my_role,
const uint8_t *my_name, size_t my_name_len,
const uint8_t *their_name, size_t their_name_len) {
@@ -332,6 +314,48 @@
}
}
+typedef union {
+ uint8_t bytes[32];
+ uint32_t words[8];
+} scalar;
+
+// kOrder is the order of the prime-order subgroup of curve25519 in
+// little-endian order.
+static const scalar kOrder = {{0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
+ 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10}};
+
+// scalar_cmov copies |src| to |dest| if |mask| is all ones.
+static void scalar_cmov(scalar *dest, const scalar *src, crypto_word_t mask) {
+ for (size_t i = 0; i < 8; i++) {
+ dest->words[i] =
+ constant_time_select_w(mask, src->words[i], dest->words[i]);
+ }
+}
+
+// scalar_double sets |s| to |2×s|.
+static void scalar_double(scalar *s) {
+ uint32_t carry = 0;
+
+ for (size_t i = 0; i < 8; i++) {
+ const uint32_t carry_out = s->words[i] >> 31;
+ s->words[i] = (s->words[i] << 1) | carry;
+ carry = carry_out;
+ }
+}
+
+// scalar_add sets |dest| to |dest| plus |src|.
+static void scalar_add(scalar *dest, const scalar *src) {
+ uint32_t carry = 0;
+
+ for (size_t i = 0; i < 8; i++) {
+ uint64_t tmp = ((uint64_t)dest->words[i] + src->words[i]) + carry;
+ dest->words[i] = (uint32_t)tmp;
+ carry = (uint32_t)(tmp >> 32);
+ }
+}
+
int SPAKE2_generate_msg(SPAKE2_CTX *ctx, uint8_t *out, size_t *out_len,
size_t max_out_len, const uint8_t *password,
size_t password_len) {
@@ -359,13 +383,61 @@
SHA512(password, password_len, password_tmp);
OPENSSL_memcpy(ctx->password_hash, password_tmp, sizeof(ctx->password_hash));
x25519_sc_reduce(password_tmp);
- OPENSSL_memcpy(ctx->password_scalar, password_tmp, sizeof(ctx->password_scalar));
+
+ // Due to a copy-paste error, the call to |left_shift_3| was omitted after
+ // the |x25519_sc_reduce|, just above. This meant that |ctx->password_scalar|
+ // was not a multiple of eight to clear the cofactor and thus three bits of
+ // the password hash would leak. In order to fix this in a unilateral way,
+ // points of small order are added to the mask point such that it is in the
+ // prime-order subgroup. Since the ephemeral scalar is a multiple of eight,
+ // these points will cancel out when calculating the shared secret.
+ //
+ // Adding points of small order is the same as adding multiples of the prime
+ // order to the password scalar. Since that's faster, that is what is done
+ // below. The prime order (kOrder) is a large prime, thus odd, thus the LSB
+ // is one. So adding it will flip the LSB. Adding twice it will flip the next
+ // bit and so one for all the bottom three bits.
+
+ scalar password_scalar;
+ OPENSSL_memcpy(&password_scalar, password_tmp, sizeof(password_scalar));
+
+ // |password_scalar| is the result of |x25519_sc_reduce| and thus is, at
+ // most, $l-1$ (where $l$ is |kOrder|, the order of the prime-order subgroup
+ // of Ed25519). In the following, we may add $l + 2×l + 4×l$ for a max value
+ // of $8×l-1$. That is < 2**256, as required.
+
+ if (!ctx->disable_password_scalar_hack) {
+ scalar order = kOrder;
+ scalar tmp;
+
+ OPENSSL_memset(&tmp, 0, sizeof(tmp));
+ scalar_cmov(&tmp, &order,
+ constant_time_eq_w(password_scalar.bytes[0] & 1, 1));
+ scalar_add(&password_scalar, &tmp);
+
+ scalar_double(&order);
+ OPENSSL_memset(&tmp, 0, sizeof(tmp));
+ scalar_cmov(&tmp, &order,
+ constant_time_eq_w(password_scalar.bytes[0] & 2, 2));
+ scalar_add(&password_scalar, &tmp);
+
+ scalar_double(&order);
+ OPENSSL_memset(&tmp, 0, sizeof(tmp));
+ scalar_cmov(&tmp, &order,
+ constant_time_eq_w(password_scalar.bytes[0] & 4, 4));
+ scalar_add(&password_scalar, &tmp);
+
+ assert((password_scalar.bytes[0] & 7) == 0);
+ }
+
+ OPENSSL_memcpy(ctx->password_scalar, password_scalar.bytes,
+ sizeof(ctx->password_scalar));
ge_p3 mask;
x25519_ge_scalarmult_small_precomp(&mask, ctx->password_scalar,
- ctx->my_role == spake2_role_alice
- ? kSpakeMSmallPrecomp
- : kSpakeNSmallPrecomp);
+ ctx->my_role == spake2_role_alice
+ ? kSpakeMSmallPrecomp
+ : kSpakeNSmallPrecomp);
// P* = P + mask.
ge_cached mask_cached;
diff --git a/src/crypto/curve25519/spake25519_test.cc b/src/crypto/curve25519/spake25519_test.cc
index cdf4ff5..71c9771 100644
--- a/src/crypto/curve25519/spake25519_test.cc
+++ b/src/crypto/curve25519/spake25519_test.cc
@@ -23,6 +23,7 @@
#include <gtest/gtest.h>
#include "../internal.h"
+#include "../../third_party/fiat/internal.h"
// TODO(agl): add tests with fixed vectors once SPAKE2 is nailed down.
@@ -46,6 +47,13 @@
return false;
}
+ if (alice_disable_password_scalar_hack) {
+ alice->disable_password_scalar_hack = 1;
+ }
+ if (bob_disable_password_scalar_hack) {
+ bob->disable_password_scalar_hack = 1;
+ }
+
uint8_t alice_msg[SPAKE2_MAX_MSG_SIZE];
uint8_t bob_msg[SPAKE2_MAX_MSG_SIZE];
size_t alice_msg_len, bob_msg_len;
@@ -90,6 +98,8 @@
std::string bob_password = "password";
std::pair<std::string, std::string> alice_names = {"alice", "bob"};
std::pair<std::string, std::string> bob_names = {"bob", "alice"};
+ bool alice_disable_password_scalar_hack = false;
+ bool bob_disable_password_scalar_hack = false;
int alice_corrupt_msg_bit = -1;
private:
@@ -104,6 +114,24 @@
}
}
+TEST(SPAKE25519Test, OldAlice) {
+ for (unsigned i = 0; i < 20; i++) {
+ SPAKE2Run spake2;
+ spake2.alice_disable_password_scalar_hack = true;
+ ASSERT_TRUE(spake2.Run());
+ EXPECT_TRUE(spake2.key_matches());
+ }
+}
+
+TEST(SPAKE25519Test, OldBob) {
+ for (unsigned i = 0; i < 20; i++) {
+ SPAKE2Run spake2;
+ spake2.bob_disable_password_scalar_hack = true;
+ ASSERT_TRUE(spake2.Run());
+ EXPECT_TRUE(spake2.key_matches());
+ }
+}
+
TEST(SPAKE25519Test, WrongPassword) {
SPAKE2Run spake2;
spake2.bob_password = "wrong password";
diff --git a/src/crypto/curve25519/x25519-x86_64.c b/src/crypto/curve25519/x25519-x86_64.c
index d677b52..41db0bd 100644
--- a/src/crypto/curve25519/x25519-x86_64.c
+++ b/src/crypto/curve25519/x25519-x86_64.c
@@ -24,7 +24,7 @@
#include <string.h>
#include "../internal.h"
-#include "internal.h"
+#include "../../third_party/fiat/internal.h"
#if defined(BORINGSSL_X25519_X86_64)
diff --git a/src/crypto/curve25519/x25519_test.cc b/src/crypto/curve25519/x25519_test.cc
index 903892f..3e0a27e 100644
--- a/src/crypto/curve25519/x25519_test.cc
+++ b/src/crypto/curve25519/x25519_test.cc
@@ -105,3 +105,22 @@
EXPECT_EQ(Bytes(kExpected), Bytes(scalar));
}
+
+TEST(X25519Test, DISABLED_IteratedLarge) {
+ // Taken from https://tools.ietf.org/html/rfc7748#section-5.2.
+ uint8_t scalar[32] = {9}, point[32] = {9}, out[32];
+
+ for (unsigned i = 0; i < 1000000; i++) {
+ EXPECT_TRUE(X25519(out, scalar, point));
+ OPENSSL_memcpy(point, scalar, sizeof(point));
+ OPENSSL_memcpy(scalar, out, sizeof(scalar));
+ }
+
+ static const uint8_t kExpected[32] = {
+ 0x7c, 0x39, 0x11, 0xe0, 0xab, 0x25, 0x86, 0xfd, 0x86, 0x44, 0x97,
+ 0x29, 0x7e, 0x57, 0x5e, 0x6f, 0x3b, 0xc6, 0x01, 0xc0, 0x88, 0x3c,
+ 0x30, 0xdf, 0x5f, 0x4d, 0xd2, 0xd2, 0x4f, 0x66, 0x54, 0x24,
+ };
+
+ EXPECT_EQ(Bytes(kExpected), Bytes(scalar));
+}
diff --git a/src/crypto/fipsmodule/bn/asm/x86_64-mont5.pl b/src/crypto/fipsmodule/bn/asm/x86_64-mont5.pl
index dfb8b37..69b8e01 100755
--- a/src/crypto/fipsmodule/bn/asm/x86_64-mont5.pl
+++ b/src/crypto/fipsmodule/bn/asm/x86_64-mont5.pl
@@ -3190,11 +3190,19 @@
.align 32
.Lsqrx8x_break:
- sub 16+8(%rsp),%r8 # consume last carry
+ xor $zero,$zero
+ sub 16+8(%rsp),%rbx # mov 16(%rsp),%cf
+ adcx $zero,%r8
mov 24+8(%rsp),$carry # initial $tptr, borrow $carry
+ adcx $zero,%r9
mov 0*8($aptr),%rdx # a[8], modulo-scheduled
- xor %ebp,%ebp # xor $zero,$zero
+ adc \$0,%r10
mov %r8,0*8($tptr)
+ adc \$0,%r11
+ adc \$0,%r12
+ adc \$0,%r13
+ adc \$0,%r14
+ adc \$0,%r15
cmp $carry,$tptr # cf=0, of=0
je .Lsqrx8x_outer_loop
diff --git a/src/crypto/fipsmodule/bn/bn_tests.txt b/src/crypto/fipsmodule/bn/bn_tests.txt
index c53eb23..f809e7e 100644
--- a/src/crypto/fipsmodule/bn/bn_tests.txt
+++ b/src/crypto/fipsmodule/bn/bn_tests.txt
@@ -9897,6 +9897,12 @@
A = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00000000000000ffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffff00000000
M = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00000000000000ffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffff
+# Regression test for CVE-2017-3736.
+ModSquare = fe06fe0b06160c09
+A = fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8f8f8f800000000000010000000006c000000000000000000000000000000000000000000000000000000000000000000000000000000000000fffffffffffff8f8f8f800000000000010000000006c000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffff00000000ffffffffffffffffffffffffffff00fcfdfc
+# A in Montgomery form is 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
+M = fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8f8f8f800000000000010000000006c000000000000000000000000000000000000000000000000000000000000000000000000000000000000fffffffffffff8f8f8f800000000000010000000006c000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffff00000000ffffffffffffffffffffffffffffffffffff
+
# ModExp tests.
#
diff --git a/src/crypto/fipsmodule/bn/exponentiation.c b/src/crypto/fipsmodule/bn/exponentiation.c
index b6b7fa9..e2dfb34 100644
--- a/src/crypto/fipsmodule/bn/exponentiation.c
+++ b/src/crypto/fipsmodule/bn/exponentiation.c
@@ -733,12 +733,14 @@
return ret;
}
-// BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
+
+// |BN_mod_exp_mont_consttime| stores the precomputed powers in a specific
// layout so that accessing any of these table values shows the same access
// pattern as far as cache lines are concerned. The following functions are
// used to transfer a BIGNUM from/to that table.
-static int copy_to_prebuf(const BIGNUM *b, int top, unsigned char *buf, int idx,
- int window) {
+
+static void copy_to_prebuf(const BIGNUM *b, int top, unsigned char *buf,
+ int idx, int window) {
int i, j;
const int width = 1 << window;
BN_ULONG *table = (BN_ULONG *) buf;
@@ -750,8 +752,6 @@
for (i = 0, j = idx; i < top; i++, j += width) {
table[j] = b->d[i];
}
-
- return 1;
}
static int copy_from_prebuf(BIGNUM *b, int top, unsigned char *buf, int idx,
@@ -1103,26 +1103,27 @@
} else
#endif
{
- if (!copy_to_prebuf(&tmp, top, powerbuf, 0, window) ||
- !copy_to_prebuf(&am, top, powerbuf, 1, window)) {
- goto err;
- }
+ copy_to_prebuf(&tmp, top, powerbuf, 0, window);
+ copy_to_prebuf(&am, top, powerbuf, 1, window);
// If the window size is greater than 1, then calculate
// val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
// (even powers could instead be computed as (a^(i/2))^2
// to use the slight performance advantage of sqr over mul).
if (window > 1) {
- if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx) ||
- !copy_to_prebuf(&tmp, top, powerbuf, 2, window)) {
+ if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) {
goto err;
}
+
+ copy_to_prebuf(&tmp, top, powerbuf, 2, window);
+
for (i = 3; i < numPowers; i++) {
// Calculate a^i = a^(i-1) * a
- if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx) ||
- !copy_to_prebuf(&tmp, top, powerbuf, i, window)) {
+ if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) {
goto err;
}
+
+ copy_to_prebuf(&tmp, top, powerbuf, i, window);
}
}
diff --git a/src/crypto/fipsmodule/cipher/cipher.c b/src/crypto/fipsmodule/cipher/cipher.c
index 7b00c3f..f3d4057 100644
--- a/src/crypto/fipsmodule/cipher/cipher.c
+++ b/src/crypto/fipsmodule/cipher/cipher.c
@@ -611,3 +611,5 @@
int EVP_add_cipher_alias(const char *a, const char *b) {
return 1;
}
+
+void EVP_CIPHER_CTX_set_flags(const EVP_CIPHER_CTX *ctx, uint32_t flags) {}
diff --git a/src/crypto/fipsmodule/rsa/rsa_impl.c b/src/crypto/fipsmodule/rsa/rsa_impl.c
index b89eccb..adbb69f 100644
--- a/src/crypto/fipsmodule/rsa/rsa_impl.c
+++ b/src/crypto/fipsmodule/rsa/rsa_impl.c
@@ -807,11 +807,16 @@
return 0;
}
- // Ensure the bound on |tries| does not overflow.
- if (bits >= INT_MAX/5) {
+ // See FIPS 186-4 appendix B.3.3, steps 4 and 5. Note |bits| here is nlen/2.
+
+ // Use the limit from steps 4.7 and 5.8 for most values of |e|. When |e| is 3,
+ // the 186-4 limit is too low, so we use a higher one. Note this case is not
+ // reachable from |RSA_generate_key_fips|.
+ if (bits >= INT_MAX/32) {
OPENSSL_PUT_ERROR(RSA, RSA_R_MODULUS_TOO_LARGE);
return 0;
}
+ int limit = BN_is_word(e, 3) ? bits * 32 : bits * 5;
int ret = 0, tries = 0, rand_tries = 0;
BN_CTX_start(ctx);
@@ -820,8 +825,6 @@
goto err;
}
- // See FIPS 186-4 appendix B.3.3, steps 4 and 5. Note |bits| here is
- // nlen/2.
for (;;) {
// Generate a random number of length |bits| where the bottom bit is set
// (steps 4.2, 4.3, 5.2 and 5.3) and the top bit is set (implied by the
@@ -890,7 +893,7 @@
// If we've tried too many times to find a prime, abort (steps 4.7 and
// 5.8).
tries++;
- if (tries >= bits * 5) {
+ if (tries >= limit) {
OPENSSL_PUT_ERROR(RSA, RSA_R_TOO_MANY_ITERATIONS);
goto err;
}
diff --git a/src/include/openssl/bio.h b/src/include/openssl/bio.h
index b397696..f87167e 100644
--- a/src/include/openssl/bio.h
+++ b/src/include/openssl/bio.h
@@ -622,7 +622,9 @@
// Use the |BIO_meth_set_*| functions below to initialize the |BIO_METHOD|. The
// function implementations may use |BIO_set_data| and |BIO_get_data| to add
// method-specific state to associated |BIO|s. Additionally, |BIO_set_init| must
-// be called after an associated |BIO| is fully initialized.
+// be called after an associated |BIO| is fully initialized. State set via
+// |BIO_set_data| may be released by configuring a destructor with
+// |BIO_meth_set_destroy|.
OPENSSL_EXPORT BIO_METHOD *BIO_meth_new(int type, const char *name);
// BIO_meth_free releases memory associated with |method|.
@@ -640,7 +642,8 @@
int (*destroy)(BIO *));
// BIO_meth_set_write sets the implementation of |BIO_write| for |method| and
-// returns one.
+// returns one. |BIO_METHOD|s which implement |BIO_write| should also implement
+// |BIO_CTRL_FLUSH|. (See |BIO_meth_set_ctrl|.)
OPENSSL_EXPORT int BIO_meth_set_write(BIO_METHOD *method,
int (*write)(BIO *, const char *, int));
diff --git a/src/include/openssl/cipher.h b/src/include/openssl/cipher.h
index 5c380a1..643bf04 100644
--- a/src/include/openssl/cipher.h
+++ b/src/include/openssl/cipher.h
@@ -417,6 +417,16 @@
// EVP_aes_128_cfb128 is only available in decrepit.
OPENSSL_EXPORT const EVP_CIPHER *EVP_aes_128_cfb128(void);
+// The following flags do nothing and are included only to make it easier to
+// compile code with BoringSSL.
+#define EVP_CIPH_CCM_MODE 0
+#define EVP_CIPH_WRAP_MODE 0
+#define EVP_CIPHER_CTX_FLAG_WRAP_ALLOW 0
+
+// EVP_CIPHER_CTX_set_flags does nothing.
+OPENSSL_EXPORT void EVP_CIPHER_CTX_set_flags(const EVP_CIPHER_CTX *ctx,
+ uint32_t flags);
+
// Private functions.
diff --git a/src/include/openssl/conf.h b/src/include/openssl/conf.h
index ebf6dc4..4ffce37 100644
--- a/src/include/openssl/conf.h
+++ b/src/include/openssl/conf.h
@@ -141,13 +141,9 @@
#define CONF_MFLAGS_DEFAULT_SECTION 0
#define CONF_MFLAGS_IGNORE_MISSING_FILE 0
-typedef struct conf_must_be_null_st CONF_MUST_BE_NULL;
-
-// CONF_modules_load_file returns one. |filename| was originally a string, with
-// NULL indicating the default. BoringSSL does not support configuration files,
-// so this stub emulates the "default" no-op file but intentionally breaks
-// compilation of consumers actively attempting to use this subsystem.
-OPENSSL_EXPORT int CONF_modules_load_file(CONF_MUST_BE_NULL *filename,
+// CONF_modules_load_file returns one. BoringSSL is defined to have no config
+// file options, thus loading from |filename| always succeeds by doing nothing.
+OPENSSL_EXPORT int CONF_modules_load_file(const char *filename,
const char *appname,
unsigned long flags);
@@ -155,7 +151,7 @@
OPENSSL_EXPORT void CONF_modules_free(void);
// OPENSSL_config does nothing.
-OPENSSL_EXPORT void OPENSSL_config(CONF_MUST_BE_NULL *config_name);
+OPENSSL_EXPORT void OPENSSL_config(const char *config_name);
// OPENSSL_no_config does nothing.
OPENSSL_EXPORT void OPENSSL_no_config(void);
diff --git a/src/include/openssl/ssl.h b/src/include/openssl/ssl.h
index a2d3ce7..3540a25 100644
--- a/src/include/openssl/ssl.h
+++ b/src/include/openssl/ssl.h
@@ -592,6 +592,7 @@
#define DTLS1_2_VERSION 0xfefd
#define TLS1_3_DRAFT_VERSION 0x7f12
+#define TLS1_3_DRAFT21_VERSION 0x7f15
#define TLS1_3_EXPERIMENT_VERSION 0x7e01
#define TLS1_3_EXPERIMENT2_VERSION 0x7e02
#define TLS1_3_EXPERIMENT3_VERSION 0x7e03
@@ -977,6 +978,25 @@
// before TLS 1.2.
#define SSL_SIGN_RSA_PKCS1_MD5_SHA1 0xff01
+// SSL_get_signature_algorithm_name returns a human-readable name for |sigalg|,
+// or NULL if unknown. If |include_curve| is one, the curve for ECDSA algorithms
+// is included as in TLS 1.3. Otherwise, it is excluded as in TLS 1.2.
+OPENSSL_EXPORT const char *SSL_get_signature_algorithm_name(uint16_t sigalg,
+ int include_curve);
+
+// SSL_get_signature_algorithm_key_type returns the key type associated with
+// |sigalg| as an |EVP_PKEY_*| constant or |EVP_PKEY_NONE| if unknown.
+OPENSSL_EXPORT int SSL_get_signature_algorithm_key_type(uint16_t sigalg);
+
+// SSL_get_signature_algorithm_digest returns the digest function associated
+// with |sigalg| or |NULL| if |sigalg| has no prehash (Ed25519) or is unknown.
+OPENSSL_EXPORT const EVP_MD *SSL_get_signature_algorithm_digest(
+ uint16_t sigalg);
+
+// SSL_is_signature_algorithm_rsa_pss returns one if |sigalg| is an RSA-PSS
+// signature algorithm and zero otherwise.
+OPENSSL_EXPORT int SSL_is_signature_algorithm_rsa_pss(uint16_t sigalg);
+
// SSL_CTX_set_signing_algorithm_prefs configures |ctx| to use |prefs| as the
// preference list when signing with |ctx|'s private key. It returns one on
// success and zero on error. |prefs| should not include the internal-only value
@@ -3234,6 +3254,7 @@
tls13_experiment = 1,
tls13_experiment2 = 2,
tls13_experiment3 = 3,
+ tls13_draft21 = 4,
};
// SSL_CTX_set_tls13_variant sets which variant of TLS 1.3 we negotiate. On the
diff --git a/src/include/openssl/ssl3.h b/src/include/openssl/ssl3.h
index 6754cec..ae0be88 100644
--- a/src/include/openssl/ssl3.h
+++ b/src/include/openssl/ssl3.h
@@ -299,6 +299,7 @@
#define SSL3_MT_CLIENT_HELLO 1
#define SSL3_MT_SERVER_HELLO 2
#define SSL3_MT_NEW_SESSION_TICKET 4
+#define SSL3_MT_END_OF_EARLY_DATA 5
#define SSL3_MT_HELLO_RETRY_REQUEST 6
#define SSL3_MT_ENCRYPTED_EXTENSIONS 8
#define SSL3_MT_CERTIFICATE 11
@@ -313,6 +314,7 @@
#define SSL3_MT_KEY_UPDATE 24
#define SSL3_MT_NEXT_PROTO 67
#define SSL3_MT_CHANNEL_ID 203
+#define SSL3_MT_MESSAGE_HASH 254
#define DTLS1_MT_HELLO_VERIFY_REQUEST 3
// The following are legacy aliases for consumers which use
diff --git a/src/include/openssl/tls1.h b/src/include/openssl/tls1.h
index 8eafe4c..f62ee1f 100644
--- a/src/include/openssl/tls1.h
+++ b/src/include/openssl/tls1.h
@@ -214,6 +214,7 @@
#define TLSEXT_TYPE_cookie 44
#define TLSEXT_TYPE_psk_key_exchange_modes 45
#define TLSEXT_TYPE_ticket_early_data_info 46
+#define TLSEXT_TYPE_certificate_authorities 47
// ExtensionType value from RFC5746
#define TLSEXT_TYPE_renegotiate 0xff01
@@ -600,22 +601,6 @@
#define TLS_CT_ECDSA_FIXED_ECDH 66
#define TLS_MD_MAX_CONST_SIZE 20
-#define TLS_MD_CLIENT_FINISH_CONST "client finished"
-#define TLS_MD_CLIENT_FINISH_CONST_SIZE 15
-#define TLS_MD_SERVER_FINISH_CONST "server finished"
-#define TLS_MD_SERVER_FINISH_CONST_SIZE 15
-#define TLS_MD_KEY_EXPANSION_CONST "key expansion"
-#define TLS_MD_KEY_EXPANSION_CONST_SIZE 13
-#define TLS_MD_CLIENT_WRITE_KEY_CONST "client write key"
-#define TLS_MD_CLIENT_WRITE_KEY_CONST_SIZE 16
-#define TLS_MD_SERVER_WRITE_KEY_CONST "server write key"
-#define TLS_MD_SERVER_WRITE_KEY_CONST_SIZE 16
-#define TLS_MD_IV_BLOCK_CONST "IV block"
-#define TLS_MD_IV_BLOCK_CONST_SIZE 8
-#define TLS_MD_MASTER_SECRET_CONST "master secret"
-#define TLS_MD_MASTER_SECRET_CONST_SIZE 13
-#define TLS_MD_EXTENDED_MASTER_SECRET_CONST "extended master secret"
-#define TLS_MD_EXTENDED_MASTER_SECRET_CONST_SIZE 22
#ifdef __cplusplus
diff --git a/src/ssl/dtls_method.cc b/src/ssl/dtls_method.cc
index 91a955f..d0416ad 100644
--- a/src/ssl/dtls_method.cc
+++ b/src/ssl/dtls_method.cc
@@ -68,10 +68,6 @@
using namespace bssl;
-static bool dtls1_supports_cipher(const SSL_CIPHER *cipher) {
- return cipher->algorithm_enc != SSL_eNULL;
-}
-
static void dtls1_on_handshake_complete(SSL *ssl) {
// Stop the reply timer left by the last flight we sent.
dtls1_stop_timer(ssl);
@@ -121,7 +117,6 @@
dtls1_open_app_data,
dtls1_write_app_data,
dtls1_dispatch_alert,
- dtls1_supports_cipher,
dtls1_init_message,
dtls1_finish_message,
dtls1_add_message,
diff --git a/src/ssl/handshake_client.cc b/src/ssl/handshake_client.cc
index ff8ebd8..f907939 100644
--- a/src/ssl/handshake_client.cc
+++ b/src/ssl/handshake_client.cc
@@ -500,9 +500,8 @@
return ssl_hs_ok;
}
- if (!tls13_init_early_key_schedule(hs) ||
- !tls13_advance_key_schedule(hs, ssl->session->master_key,
- ssl->session->master_key_length) ||
+ if (!tls13_init_early_key_schedule(hs, ssl->session->master_key,
+ ssl->session->master_key_length) ||
!tls13_derive_early_secrets(hs) ||
!tls13_set_traffic_key(ssl, evp_aead_seal, hs->early_traffic_secret,
hs->hash_len)) {
@@ -1360,8 +1359,8 @@
return ssl_hs_error;
}
- hs->new_session->master_key_length = tls1_generate_master_secret(
- hs, hs->new_session->master_key, pms.data(), pms.size());
+ hs->new_session->master_key_length =
+ tls1_generate_master_secret(hs, hs->new_session->master_key, pms);
if (hs->new_session->master_key_length == 0) {
return ssl_hs_error;
}
diff --git a/src/ssl/handshake_server.cc b/src/ssl/handshake_server.cc
index d346875..bb565e9 100644
--- a/src/ssl/handshake_server.cc
+++ b/src/ssl/handshake_server.cc
@@ -1243,8 +1243,7 @@
// Compute the master secret.
hs->new_session->master_key_length = tls1_generate_master_secret(
- hs, hs->new_session->master_key, premaster_secret.data(),
- premaster_secret.size());
+ hs, hs->new_session->master_key, premaster_secret);
if (hs->new_session->master_key_length == 0) {
return ssl_hs_error;
}
diff --git a/src/ssl/internal.h b/src/ssl/internal.h
index 7e1801a..55bece9 100644
--- a/src/ssl/internal.h
+++ b/src/ssl/internal.h
@@ -392,6 +392,10 @@
// call this function before the version is determined.
uint16_t ssl_protocol_version(const SSL *ssl);
+// ssl_is_draft21 returns whether the version corresponds to a draft21 TLS 1.3
+// variant.
+bool ssl_is_draft21(uint16_t version);
+
// ssl_is_resumption_experiment returns whether the version corresponds to a
// TLS 1.3 resumption experiment.
bool ssl_is_resumption_experiment(uint16_t version);
@@ -490,14 +494,12 @@
const EVP_MD *ssl_get_handshake_digest(uint16_t version,
const SSL_CIPHER *cipher);
-// ssl_create_cipher_list evaluates |rule_str| according to the ciphers in
-// |ssl_method|. It sets |*out_cipher_list| to a newly-allocated
-// |ssl_cipher_preference_list_st| containing the result. It returns true on
-// success and false on failure. If |strict| is true, nonsense will be
-// rejected. If false, nonsense will be silently ignored. An empty result is
-// considered an error regardless of |strict|.
+// ssl_create_cipher_list evaluates |rule_str|. It sets |*out_cipher_list| to a
+// newly-allocated |ssl_cipher_preference_list_st| containing the result. It
+// returns true on success and false on failure. If |strict| is true, nonsense
+// will be rejected. If false, nonsense will be silently ignored. An empty
+// result is considered an error regardless of |strict|.
bool ssl_create_cipher_list(
- const SSL_PROTOCOL_METHOD *ssl_method,
struct ssl_cipher_preference_list_st **out_cipher_list,
const char *rule_str, bool strict);
@@ -545,6 +547,16 @@
// to call this function after the handshake buffer is released.
bool InitHash(uint16_t version, const SSL_CIPHER *cipher);
+ // UpdateForHelloRetryRequest resets the rolling hash with the
+ // HelloRetryRequest construction. It returns true on success and false on
+ // failure. It is an error to call this function before the handshake buffer
+ // is released.
+ bool UpdateForHelloRetryRequest();
+
+ // CopyHashContext copies the hash context into |ctx| and returns true on
+ // success.
+ bool CopyHashContext(EVP_MD_CTX *ctx);
+
Span<const uint8_t> buffer() {
return MakeConstSpan(reinterpret_cast<const uint8_t *>(buffer_->data),
buffer_->length);
@@ -596,14 +608,12 @@
ScopedEVP_MD_CTX md5_;
};
-// tls1_prf computes the PRF function for |ssl|. It writes |out_len| bytes to
-// |out|, using |secret| as the secret and |label| as the label. |seed1| and
-// |seed2| are concatenated to form the seed parameter. It returns one on
-// success and zero on failure.
-int tls1_prf(const EVP_MD *digest, uint8_t *out, size_t out_len,
- const uint8_t *secret, size_t secret_len, const char *label,
- size_t label_len, const uint8_t *seed1, size_t seed1_len,
- const uint8_t *seed2, size_t seed2_len);
+// tls1_prf computes the PRF function for |ssl|. It fills |out|, using |secret|
+// as the secret and |label| as the label. |seed1| and |seed2| are concatenated
+// to form the seed parameter. It returns true on success and false on failure.
+bool tls1_prf(const EVP_MD *digest, Span<uint8_t> out,
+ Span<const uint8_t> secret, Span<const char> label,
+ Span<const uint8_t> seed1, Span<const uint8_t> seed2);
// Encryption layer.
@@ -1161,6 +1171,9 @@
uint8_t *out_alert,
CBS *cbs);
+// ssl_has_client_CAs returns there are configured CAs.
+bool ssl_has_client_CAs(SSL *ssl);
+
// ssl_add_client_CA_list adds the configured CA list to |cbb| in the format
// used by a TLS CertificateRequest message. It returns one on success and zero
// on error.
@@ -1181,14 +1194,16 @@
// TLS 1.3 key derivation.
// tls13_init_key_schedule initializes the handshake hash and key derivation
-// state. The cipher suite and PRF hash must have been selected at this point.
-// It returns one on success and zero on error.
-int tls13_init_key_schedule(SSL_HANDSHAKE *hs);
+// state, and incorporates the PSK. The cipher suite and PRF hash must have been
+// selected at this point. It returns one on success and zero on error.
+int tls13_init_key_schedule(SSL_HANDSHAKE *hs, const uint8_t *psk,
+ size_t psk_len);
// tls13_init_early_key_schedule initializes the handshake hash and key
-// derivation state from the resumption secret to derive the early secrets. It
-// returns one on success and zero on error.
-int tls13_init_early_key_schedule(SSL_HANDSHAKE *hs);
+// derivation state from the resumption secret and incorporates the PSK to
+// derive the early secrets. It returns one on success and zero on error.
+int tls13_init_early_key_schedule(SSL_HANDSHAKE *hs, const uint8_t *psk,
+ size_t psk_len);
// tls13_advance_key_schedule incorporates |in| into the key schedule with
// HKDF-Extract. It returns one on success and zero on error.
@@ -1235,6 +1250,11 @@
int tls13_finished_mac(SSL_HANDSHAKE *hs, uint8_t *out,
size_t *out_len, int is_server);
+// tls13_derive_session_psk calculates the PSK for this session based on the
+// resumption master secret and |nonce|. It returns true on success, and false
+// on failure.
+bool tls13_derive_session_psk(SSL_SESSION *session, Span<const uint8_t> nonce);
+
// tls13_write_psk_binder calculates the PSK binder value and replaces the last
// bytes of |msg| with the resulting value. It returns 1 on success, and 0 on
// failure.
@@ -1773,8 +1793,6 @@
int (*write_app_data)(SSL *ssl, bool *out_needs_handshake, const uint8_t *buf,
int len);
int (*dispatch_alert)(SSL *ssl);
- // supports_cipher returns whether |cipher| is supported by this protocol.
- bool (*supports_cipher)(const SSL_CIPHER *cipher);
// init_message begins a new handshake message of type |type|. |cbb| is the
// root CBB to be passed into |finish_message|. |*body| is set to a child CBB
// the caller should write to. It returns true on success and false on error.
@@ -2803,7 +2821,7 @@
int tls1_change_cipher_state(SSL_HANDSHAKE *hs, evp_aead_direction_t direction);
int tls1_generate_master_secret(SSL_HANDSHAKE *hs, uint8_t *out,
- const uint8_t *premaster, size_t premaster_len);
+ Span<const uint8_t> premaster);
// tls1_get_grouplist returns the locally-configured group preference list.
Span<const uint16_t> tls1_get_grouplist(const SSL *ssl);
@@ -2865,8 +2883,8 @@
// tls1_write_channel_id generates a Channel ID message and puts the output in
// |cbb|. |ssl->tlsext_channel_id_private| must already be set before calling.
-// This function returns one on success and zero on error.
-int tls1_write_channel_id(SSL_HANDSHAKE *hs, CBB *cbb);
+// This function returns true on success and false on error.
+bool tls1_write_channel_id(SSL_HANDSHAKE *hs, CBB *cbb);
// tls1_channel_id_hash computes the hash to be signed by Channel ID and writes
// it to |out|, which must contain at least |EVP_MAX_MD_SIZE| bytes. It returns
diff --git a/src/ssl/s3_pkt.cc b/src/ssl/s3_pkt.cc
index 285abb3..e6518ba 100644
--- a/src/ssl/s3_pkt.cc
+++ b/src/ssl/s3_pkt.cc
@@ -306,7 +306,7 @@
if (type == SSL3_RT_HANDSHAKE) {
// If reading 0-RTT data, reject handshake data. 0-RTT data is terminated
// by an alert.
- if (is_early_data_read) {
+ if (!ssl_is_draft21(ssl->version) && is_early_data_read) {
OPENSSL_PUT_ERROR(SSL, SSL_R_UNEXPECTED_RECORD);
*out_alert = SSL_AD_UNEXPECTED_MESSAGE;
return ssl_open_record_error;
@@ -335,7 +335,8 @@
// Handle the end_of_early_data alert.
static const uint8_t kEndOfEarlyData[2] = {SSL3_AL_WARNING,
TLS1_AD_END_OF_EARLY_DATA};
- if (is_early_data_read && type == SSL3_RT_ALERT && body == kEndOfEarlyData) {
+ if (!ssl_is_draft21(ssl->version) && is_early_data_read &&
+ type == SSL3_RT_ALERT && body == kEndOfEarlyData) {
// Stop accepting early data.
ssl->s3->hs->can_early_read = false;
return ssl_open_record_discard;
diff --git a/src/ssl/ssl_cert.cc b/src/ssl/ssl_cert.cc
index cd586a0..9a3eef3 100644
--- a/src/ssl/ssl_cert.cc
+++ b/src/ssl/ssl_cert.cc
@@ -704,6 +704,17 @@
return ret;
}
+bool ssl_has_client_CAs(SSL *ssl) {
+ STACK_OF(CRYPTO_BUFFER) *names = ssl->client_CA;
+ if (names == NULL) {
+ names = ssl->ctx->client_CA;
+ }
+ if (names == NULL) {
+ return false;
+ }
+ return sk_CRYPTO_BUFFER_num(names) > 0;
+}
+
int ssl_add_client_CA_list(SSL *ssl, CBB *cbb) {
CBB child, name_cbb;
if (!CBB_add_u16_length_prefixed(cbb, &child)) {
diff --git a/src/ssl/ssl_cipher.cc b/src/ssl/ssl_cipher.cc
index 0c02389..87dc7cd 100644
--- a/src/ssl/ssl_cipher.cc
+++ b/src/ssl/ssl_cipher.cc
@@ -578,7 +578,7 @@
static const CIPHER_ALIAS kCipherAliases[] = {
// "ALL" doesn't include eNULL. It must be explicitly enabled.
- {"ALL", ~0u, ~0u, ~SSL_eNULL, ~0u, 0},
+ {"ALL", ~0u, ~0u, ~0u, ~0u, 0},
// The "COMPLEMENTOFDEFAULT" rule is omitted. It matches nothing.
@@ -594,7 +594,7 @@
{"kPSK", SSL_kPSK, ~0u, ~0u, ~0u, 0},
// server authentication aliases
- {"aRSA", ~0u, SSL_aRSA, ~SSL_eNULL, ~0u, 0},
+ {"aRSA", ~0u, SSL_aRSA, ~0u, ~0u, 0},
{"aECDSA", ~0u, SSL_aECDSA, ~0u, ~0u, 0},
{"ECDSA", ~0u, SSL_aECDSA, ~0u, ~0u, 0},
{"aPSK", ~0u, SSL_aPSK, ~0u, ~0u, 0},
@@ -602,7 +602,7 @@
// aliases combining key exchange and server authentication
{"ECDHE", SSL_kECDHE, ~0u, ~0u, ~0u, 0},
{"EECDH", SSL_kECDHE, ~0u, ~0u, ~0u, 0},
- {"RSA", SSL_kRSA, SSL_aRSA, ~SSL_eNULL, ~0u, 0},
+ {"RSA", SSL_kRSA, SSL_aRSA, ~0u, ~0u, 0},
{"PSK", SSL_kPSK, SSL_aPSK, ~0u, ~0u, 0},
// symmetric encryption aliases
@@ -614,20 +614,20 @@
{"CHACHA20", ~0u, ~0u, SSL_CHACHA20POLY1305, ~0u, 0},
// MAC aliases
- {"SHA1", ~0u, ~0u, ~SSL_eNULL, SSL_SHA1, 0},
- {"SHA", ~0u, ~0u, ~SSL_eNULL, SSL_SHA1, 0},
+ {"SHA1", ~0u, ~0u, ~0u, SSL_SHA1, 0},
+ {"SHA", ~0u, ~0u, ~0u, SSL_SHA1, 0},
{"SHA256", ~0u, ~0u, ~0u, SSL_SHA256, 0},
{"SHA384", ~0u, ~0u, ~0u, SSL_SHA384, 0},
// Legacy protocol minimum version aliases. "TLSv1" is intentionally the
// same as "SSLv3".
- {"SSLv3", ~0u, ~0u, ~SSL_eNULL, ~0u, SSL3_VERSION},
- {"TLSv1", ~0u, ~0u, ~SSL_eNULL, ~0u, SSL3_VERSION},
- {"TLSv1.2", ~0u, ~0u, ~SSL_eNULL, ~0u, TLS1_2_VERSION},
+ {"SSLv3", ~0u, ~0u, ~0u, ~0u, SSL3_VERSION},
+ {"TLSv1", ~0u, ~0u, ~0u, ~0u, SSL3_VERSION},
+ {"TLSv1.2", ~0u, ~0u, ~0u, ~0u, TLS1_2_VERSION},
// Legacy strength classes.
- {"HIGH", ~0u, ~0u, ~SSL_eNULL, ~0u, 0},
- {"FIPS", ~0u, ~0u, ~SSL_eNULL, ~0u, 0},
+ {"HIGH", ~0u, ~0u, ~0u, ~0u, 0},
+ {"FIPS", ~0u, ~0u, ~0u, ~0u, 0},
};
static const size_t kCipherAliasesLen = OPENSSL_ARRAY_SIZE(kCipherAliases);
@@ -811,19 +811,14 @@
*head = curr;
}
-static void ssl_cipher_collect_ciphers(const SSL_PROTOCOL_METHOD *ssl_method,
- CIPHER_ORDER *co_list,
+static void ssl_cipher_collect_ciphers(CIPHER_ORDER *co_list,
CIPHER_ORDER **head_p,
CIPHER_ORDER **tail_p) {
- // The set of ciphers is static, but some subset may be unsupported by
- // |ssl_method|, so the list may be smaller.
size_t co_list_num = 0;
- for (size_t i = 0; i < kCiphersLen; i++) {
- const SSL_CIPHER *cipher = &kCiphers[i];
- if (ssl_method->supports_cipher(cipher) &&
- // TLS 1.3 ciphers do not participate in this mechanism.
- cipher->algorithm_mkey != SSL_kGENERIC) {
- co_list[co_list_num].cipher = cipher;
+ for (const SSL_CIPHER &cipher : kCiphers) {
+ // TLS 1.3 ciphers do not participate in this mechanism.
+ if (cipher.algorithm_mkey != SSL_kGENERIC) {
+ co_list[co_list_num].cipher = &cipher;
co_list[co_list_num].next = NULL;
co_list[co_list_num].prev = NULL;
co_list[co_list_num].active = false;
@@ -923,7 +918,9 @@
!(alg_auth & cp->algorithm_auth) ||
!(alg_enc & cp->algorithm_enc) ||
!(alg_mac & cp->algorithm_mac) ||
- (min_version != 0 && SSL_CIPHER_get_min_version(cp) != min_version)) {
+ (min_version != 0 && SSL_CIPHER_get_min_version(cp) != min_version) ||
+ // The NULL cipher must be selected explicitly.
+ cp->algorithm_enc == SSL_eNULL) {
continue;
}
}
@@ -1023,8 +1020,7 @@
return true;
}
-static bool ssl_cipher_process_rulestr(const SSL_PROTOCOL_METHOD *ssl_method,
- const char *rule_str,
+static bool ssl_cipher_process_rulestr(const char *rule_str,
CIPHER_ORDER **head_p,
CIPHER_ORDER **tail_p, bool strict) {
uint32_t alg_mkey, alg_auth, alg_enc, alg_mac;
@@ -1206,7 +1202,6 @@
}
bool ssl_create_cipher_list(
- const SSL_PROTOCOL_METHOD *ssl_method,
struct ssl_cipher_preference_list_st **out_cipher_list,
const char *rule_str, bool strict) {
STACK_OF(SSL_CIPHER) *cipherstack = NULL;
@@ -1229,7 +1224,7 @@
return false;
}
- ssl_cipher_collect_ciphers(ssl_method, co_list, &head, &tail);
+ ssl_cipher_collect_ciphers(co_list, &head, &tail);
// Now arrange all ciphers by preference:
// TODO(davidben): Compute this order once and copy it.
@@ -1288,8 +1283,8 @@
// using the (possibly available) additional rules.
const char *rule_p = rule_str;
if (strncmp(rule_str, "DEFAULT", 7) == 0) {
- if (!ssl_cipher_process_rulestr(ssl_method, SSL_DEFAULT_CIPHER_LIST, &head,
- &tail, strict)) {
+ if (!ssl_cipher_process_rulestr(SSL_DEFAULT_CIPHER_LIST, &head, &tail,
+ strict)) {
goto err;
}
rule_p += 7;
@@ -1299,7 +1294,7 @@
}
if (*rule_p != '\0' &&
- !ssl_cipher_process_rulestr(ssl_method, rule_p, &head, &tail, strict)) {
+ !ssl_cipher_process_rulestr(rule_p, &head, &tail, strict)) {
goto err;
}
diff --git a/src/ssl/ssl_key_share.cc b/src/ssl/ssl_key_share.cc
index 52ff85d..a5ae578 100644
--- a/src/ssl/ssl_key_share.cc
+++ b/src/ssl/ssl_key_share.cc
@@ -171,13 +171,13 @@
CONSTEXPR_ARRAY struct {
int nid;
uint16_t group_id;
- const char name[8];
+ const char name[8], alias[11];
} kNamedGroups[] = {
- {NID_secp224r1, SSL_CURVE_SECP224R1, "P-224"},
- {NID_X9_62_prime256v1, SSL_CURVE_SECP256R1, "P-256"},
- {NID_secp384r1, SSL_CURVE_SECP384R1, "P-384"},
- {NID_secp521r1, SSL_CURVE_SECP521R1, "P-521"},
- {NID_X25519, SSL_CURVE_X25519, "X25519"},
+ {NID_secp224r1, SSL_CURVE_SECP224R1, "P-224", "secp224r1"},
+ {NID_X9_62_prime256v1, SSL_CURVE_SECP256R1, "P-256", "prime256v1"},
+ {NID_secp384r1, SSL_CURVE_SECP384R1, "P-384", "secp384r1"},
+ {NID_secp521r1, SSL_CURVE_SECP521R1, "P-521", "secp521r1"},
+ {NID_X25519, SSL_CURVE_X25519, "X25519", "x25519"},
};
} // namespace
@@ -227,6 +227,11 @@
*out_group_id = group.group_id;
return 1;
}
+ if (len == strlen(group.alias) &&
+ !strncmp(group.alias, name, len)) {
+ *out_group_id = group.group_id;
+ return 1;
+ }
}
return 0;
}
diff --git a/src/ssl/ssl_lib.cc b/src/ssl/ssl_lib.cc
index 2fc6ffd..122313f 100644
--- a/src/ssl/ssl_lib.cc
+++ b/src/ssl/ssl_lib.cc
@@ -986,6 +986,13 @@
// Process any buffered post-handshake messages.
SSLMessage msg;
if (ssl->method->get_message(ssl, &msg)) {
+ // If we received an interrupt in early read (EndOfEarlyData), loop again
+ // for the handshake to process it.
+ if (SSL_in_init(ssl)) {
+ ssl->s3->hs->can_early_read = false;
+ continue;
+ }
+
// Handle the post-handshake message and try again.
if (!ssl_do_post_handshake(ssl, msg)) {
ssl_set_read_error(ssl);
@@ -1827,23 +1834,19 @@
}
int SSL_CTX_set_cipher_list(SSL_CTX *ctx, const char *str) {
- return ssl_create_cipher_list(ctx->method, &ctx->cipher_list, str,
- false /* not strict */);
+ return ssl_create_cipher_list(&ctx->cipher_list, str, false /* not strict */);
}
int SSL_CTX_set_strict_cipher_list(SSL_CTX *ctx, const char *str) {
- return ssl_create_cipher_list(ctx->method, &ctx->cipher_list, str,
- true /* strict */);
+ return ssl_create_cipher_list(&ctx->cipher_list, str, true /* strict */);
}
int SSL_set_cipher_list(SSL *ssl, const char *str) {
- return ssl_create_cipher_list(ssl->ctx->method, &ssl->cipher_list, str,
- false /* not strict */);
+ return ssl_create_cipher_list(&ssl->cipher_list, str, false /* not strict */);
}
int SSL_set_strict_cipher_list(SSL *ssl, const char *str) {
- return ssl_create_cipher_list(ssl->ctx->method, &ssl->cipher_list, str,
- true /* strict */);
+ return ssl_create_cipher_list(&ssl->cipher_list, str, true /* strict */);
}
const char *SSL_get_servername(const SSL *ssl, const int type) {
diff --git a/src/ssl/ssl_privkey.cc b/src/ssl/ssl_privkey.cc
index b00613d..e9990af 100644
--- a/src/ssl/ssl_privkey.cc
+++ b/src/ssl/ssl_privkey.cc
@@ -438,6 +438,58 @@
ctx->cert->key_method = key_method;
}
+const char *SSL_get_signature_algorithm_name(uint16_t sigalg,
+ int include_curve) {
+ switch (sigalg) {
+ case SSL_SIGN_RSA_PKCS1_MD5_SHA1:
+ return "rsa_pkcs1_md5_sha1";
+ case SSL_SIGN_RSA_PKCS1_SHA1:
+ return "rsa_pkcs1_sha1";
+ case SSL_SIGN_RSA_PKCS1_SHA256:
+ return "rsa_pkcs1_sha256";
+ case SSL_SIGN_RSA_PKCS1_SHA384:
+ return "rsa_pkcs1_sha384";
+ case SSL_SIGN_RSA_PKCS1_SHA512:
+ return "rsa_pkcs1_sha512";
+ case SSL_SIGN_ECDSA_SHA1:
+ return "ecdsa_sha1";
+ case SSL_SIGN_ECDSA_SECP256R1_SHA256:
+ return include_curve ? "ecdsa_secp256r1_sha256" : "ecdsa_sha256";
+ case SSL_SIGN_ECDSA_SECP384R1_SHA384:
+ return include_curve ? "ecdsa_secp384r1_sha384" : "ecdsa_sha384";
+ case SSL_SIGN_ECDSA_SECP521R1_SHA512:
+ return include_curve ? "ecdsa_secp521r1_sha512" : "ecdsa_sha512";
+ case SSL_SIGN_RSA_PSS_SHA256:
+ return "rsa_pss_sha256";
+ case SSL_SIGN_RSA_PSS_SHA384:
+ return "rsa_pss_sha384";
+ case SSL_SIGN_RSA_PSS_SHA512:
+ return "rsa_pss_sha512";
+ case SSL_SIGN_ED25519:
+ return "ed25519";
+ default:
+ return NULL;
+ }
+}
+
+int SSL_get_signature_algorithm_key_type(uint16_t sigalg) {
+ const SSL_SIGNATURE_ALGORITHM *alg = get_signature_algorithm(sigalg);
+ return alg != nullptr ? alg->pkey_type : EVP_PKEY_NONE;
+}
+
+const EVP_MD *SSL_get_signature_algorithm_digest(uint16_t sigalg) {
+ const SSL_SIGNATURE_ALGORITHM *alg = get_signature_algorithm(sigalg);
+ if (alg == nullptr || alg->digest_func == nullptr) {
+ return nullptr;
+ }
+ return alg->digest_func();
+}
+
+int SSL_is_signature_algorithm_rsa_pss(uint16_t sigalg) {
+ const SSL_SIGNATURE_ALGORITHM *alg = get_signature_algorithm(sigalg);
+ return alg != nullptr && alg->is_rsa_pss;
+}
+
static int set_algorithm_prefs(uint16_t **out_prefs, size_t *out_num_prefs,
const uint16_t *prefs, size_t num_prefs) {
OPENSSL_free(*out_prefs);
diff --git a/src/ssl/ssl_test.cc b/src/ssl/ssl_test.cc
index ab50a57..8288878 100644
--- a/src/ssl/ssl_test.cc
+++ b/src/ssl/ssl_test.cc
@@ -379,6 +379,15 @@
SSL_CURVE_X25519,
},
},
+ {
+ "prime256v1:secp384r1:secp521r1:x25519",
+ {
+ SSL_CURVE_SECP256R1,
+ SSL_CURVE_SECP384R1,
+ SSL_CURVE_SECP521R1,
+ SSL_CURVE_X25519,
+ },
+ },
};
static const char *kBadCurvesLists[] = {
@@ -3813,6 +3822,31 @@
EXPECT_EQ(1, SSL_shutdown(client.get()));
}
+TEST(SSLTest, SignatureAlgorithmProperties) {
+ EXPECT_EQ(EVP_PKEY_NONE, SSL_get_signature_algorithm_key_type(0x1234));
+ EXPECT_EQ(nullptr, SSL_get_signature_algorithm_digest(0x1234));
+ EXPECT_FALSE(SSL_is_signature_algorithm_rsa_pss(0x1234));
+
+ EXPECT_EQ(EVP_PKEY_RSA,
+ SSL_get_signature_algorithm_key_type(SSL_SIGN_RSA_PKCS1_MD5_SHA1));
+ EXPECT_EQ(EVP_md5_sha1(),
+ SSL_get_signature_algorithm_digest(SSL_SIGN_RSA_PKCS1_MD5_SHA1));
+ EXPECT_FALSE(SSL_is_signature_algorithm_rsa_pss(SSL_SIGN_RSA_PKCS1_MD5_SHA1));
+
+ EXPECT_EQ(EVP_PKEY_EC, SSL_get_signature_algorithm_key_type(
+ SSL_SIGN_ECDSA_SECP256R1_SHA256));
+ EXPECT_EQ(EVP_sha256(), SSL_get_signature_algorithm_digest(
+ SSL_SIGN_ECDSA_SECP256R1_SHA256));
+ EXPECT_FALSE(
+ SSL_is_signature_algorithm_rsa_pss(SSL_SIGN_ECDSA_SECP256R1_SHA256));
+
+ EXPECT_EQ(EVP_PKEY_RSA,
+ SSL_get_signature_algorithm_key_type(SSL_SIGN_RSA_PSS_SHA384));
+ EXPECT_EQ(EVP_sha384(),
+ SSL_get_signature_algorithm_digest(SSL_SIGN_RSA_PSS_SHA384));
+ EXPECT_TRUE(SSL_is_signature_algorithm_rsa_pss(SSL_SIGN_RSA_PSS_SHA384));
+}
+
// TODO(davidben): Convert this file to GTest properly.
TEST(SSLTest, AllTests) {
if (!TestSSL_SESSIONEncoding(kOpenSSLSession) ||
diff --git a/src/ssl/ssl_transcript.cc b/src/ssl/ssl_transcript.cc
index ab9822f..2033dfd 100644
--- a/src/ssl/ssl_transcript.cc
+++ b/src/ssl/ssl_transcript.cc
@@ -209,6 +209,30 @@
return EVP_MD_CTX_md(hash_.get());
}
+bool SSLTranscript::UpdateForHelloRetryRequest() {
+ if (buffer_) {
+ buffer_->length = 0;
+ }
+
+ uint8_t old_hash[EVP_MAX_MD_SIZE];
+ size_t hash_len;
+ if (!GetHash(old_hash, &hash_len)) {
+ return false;
+ }
+ const uint8_t header[4] = {SSL3_MT_MESSAGE_HASH, 0, 0,
+ static_cast<uint8_t>(hash_len)};
+ if (!EVP_DigestInit_ex(hash_.get(), Digest(), nullptr) ||
+ !Update(header) ||
+ !Update(MakeConstSpan(old_hash, hash_len))) {
+ return false;
+ }
+ return true;
+}
+
+bool SSLTranscript::CopyHashContext(EVP_MD_CTX *ctx) {
+ return EVP_MD_CTX_copy_ex(ctx, hash_.get());
+}
+
bool SSLTranscript::Update(Span<const uint8_t> in) {
// Depending on the state of the handshake, either the handshake buffer may be
// active, the rolling hash, or both.
@@ -348,12 +372,11 @@
// its own.
assert(!buffer_);
- const char *label = TLS_MD_CLIENT_FINISH_CONST;
- size_t label_len = TLS_MD_SERVER_FINISH_CONST_SIZE;
- if (from_server) {
- label = TLS_MD_SERVER_FINISH_CONST;
- label_len = TLS_MD_SERVER_FINISH_CONST_SIZE;
- }
+ static const char kClientLabel[] = "client finished";
+ static const char kServerLabel[] = "server finished";
+ auto label = from_server
+ ? MakeConstSpan(kServerLabel, sizeof(kServerLabel) - 1)
+ : MakeConstSpan(kClientLabel, sizeof(kClientLabel) - 1);
uint8_t digests[EVP_MAX_MD_SIZE];
size_t digests_len;
@@ -362,9 +385,9 @@
}
static const size_t kFinishedLen = 12;
- if (!tls1_prf(Digest(), out, kFinishedLen, session->master_key,
- session->master_key_length, label, label_len, digests,
- digests_len, NULL, 0)) {
+ if (!tls1_prf(Digest(), MakeSpan(out, kFinishedLen),
+ MakeConstSpan(session->master_key, session->master_key_length),
+ label, MakeConstSpan(digests, digests_len), {})) {
return false;
}
diff --git a/src/ssl/ssl_versions.cc b/src/ssl/ssl_versions.cc
index ccae6ef..1f30b41 100644
--- a/src/ssl/ssl_versions.cc
+++ b/src/ssl/ssl_versions.cc
@@ -35,6 +35,7 @@
return true;
case TLS1_3_DRAFT_VERSION:
+ case TLS1_3_DRAFT21_VERSION:
case TLS1_3_EXPERIMENT_VERSION:
case TLS1_3_EXPERIMENT2_VERSION:
case TLS1_3_EXPERIMENT3_VERSION:
@@ -63,6 +64,7 @@
TLS1_3_EXPERIMENT2_VERSION,
TLS1_3_EXPERIMENT_VERSION,
TLS1_3_DRAFT_VERSION,
+ TLS1_3_DRAFT21_VERSION,
TLS1_2_VERSION,
TLS1_1_VERSION,
TLS1_VERSION,
@@ -106,6 +108,7 @@
static const char *ssl_version_to_string(uint16_t version) {
switch (version) {
case TLS1_3_DRAFT_VERSION:
+ case TLS1_3_DRAFT21_VERSION:
case TLS1_3_EXPERIMENT_VERSION:
case TLS1_3_EXPERIMENT2_VERSION:
case TLS1_3_EXPERIMENT3_VERSION:
@@ -138,6 +141,7 @@
switch (version) {
// Report TLS 1.3 draft versions as TLS 1.3 in the public API.
case TLS1_3_DRAFT_VERSION:
+ case TLS1_3_DRAFT21_VERSION:
case TLS1_3_EXPERIMENT_VERSION:
case TLS1_3_EXPERIMENT2_VERSION:
case TLS1_3_EXPERIMENT3_VERSION:
@@ -152,6 +156,7 @@
// used in context where that does not matter.
static bool api_version_to_wire(uint16_t *out, uint16_t version) {
if (version == TLS1_3_DRAFT_VERSION ||
+ version == TLS1_3_DRAFT21_VERSION ||
version == TLS1_3_EXPERIMENT_VERSION ||
version == TLS1_3_EXPERIMENT2_VERSION ||
version == TLS1_3_EXPERIMENT3_VERSION) {
@@ -301,34 +306,42 @@
bool ssl_supports_version(SSL_HANDSHAKE *hs, uint16_t version) {
SSL *const ssl = hs->ssl;
- // As a client, only allow the configured TLS 1.3 variant. As a server,
- // support all TLS 1.3 variants as long as tls13_variant is set to a
- // non-default value.
- if (ssl->server) {
- if (ssl->tls13_variant == tls13_default &&
- (version == TLS1_3_EXPERIMENT_VERSION ||
- version == TLS1_3_EXPERIMENT2_VERSION ||
- version == TLS1_3_EXPERIMENT3_VERSION)) {
- return false;
- }
- } else {
- if ((ssl->tls13_variant != tls13_experiment &&
- version == TLS1_3_EXPERIMENT_VERSION) ||
- (ssl->tls13_variant != tls13_experiment2 &&
- version == TLS1_3_EXPERIMENT2_VERSION) ||
- (ssl->tls13_variant != tls13_experiment3 &&
- version == TLS1_3_EXPERIMENT3_VERSION) ||
- (ssl->tls13_variant != tls13_default &&
- version == TLS1_3_DRAFT_VERSION)) {
- return false;
- }
+ uint16_t protocol_version;
+ if (!method_supports_version(ssl->method, version) ||
+ !ssl_protocol_version_from_wire(&protocol_version, version) ||
+ hs->min_version > protocol_version ||
+ protocol_version > hs->max_version) {
+ return false;
}
- uint16_t protocol_version;
- return method_supports_version(ssl->method, version) &&
- ssl_protocol_version_from_wire(&protocol_version, version) &&
- hs->min_version <= protocol_version &&
- protocol_version <= hs->max_version;
+ // TLS 1.3 variants must additionally match |tls13_variant|.
+ if (protocol_version != TLS1_3_VERSION ||
+ (ssl->tls13_variant == tls13_experiment &&
+ version == TLS1_3_EXPERIMENT_VERSION) ||
+ (ssl->tls13_variant == tls13_experiment2 &&
+ version == TLS1_3_EXPERIMENT2_VERSION) ||
+ (ssl->tls13_variant == tls13_experiment3 &&
+ version == TLS1_3_EXPERIMENT3_VERSION) ||
+ (ssl->tls13_variant == tls13_draft21 &&
+ version == TLS1_3_DRAFT21_VERSION) ||
+ (ssl->tls13_variant == tls13_default &&
+ version == TLS1_3_DRAFT_VERSION)) {
+ return true;
+ }
+
+ // The server, when not configured at |tls13_default|, should additionally
+ // enable all variants, except draft-21 which is implemented solely for QUIC
+ // interop testing and will not be deployed. Currently, this is to implement
+ // the draft-18 vs. experiments field trials. In the future, this will be to
+ // transition cleanly to a future draft-22 which hopefully includes the
+ // deployability fixes.
+ if (ssl->server &&
+ ssl->tls13_variant != tls13_default &&
+ version != TLS1_3_DRAFT21_VERSION) {
+ return true;
+ }
+
+ return false;
}
bool ssl_add_supported_versions(SSL_HANDSHAKE *hs, CBB *cbb) {
@@ -375,6 +388,10 @@
return false;
}
+bool ssl_is_draft21(uint16_t version) {
+ return version == TLS1_3_DRAFT21_VERSION;
+}
+
bool ssl_is_resumption_experiment(uint16_t version) {
return version == TLS1_3_EXPERIMENT_VERSION ||
version == TLS1_3_EXPERIMENT2_VERSION ||
diff --git a/src/ssl/t1_enc.cc b/src/ssl/t1_enc.cc
index 1298a10..2a09987 100644
--- a/src/ssl/t1_enc.cc
+++ b/src/ssl/t1_enc.cc
@@ -155,26 +155,26 @@
namespace bssl {
// tls1_P_hash computes the TLS P_<hash> function as described in RFC 5246,
-// section 5. It XORs |out_len| bytes to |out|, using |md| as the hash and
-// |secret| as the secret. |seed1| through |seed3| are concatenated to form the
-// seed parameter. It returns one on success and zero on failure.
-static int tls1_P_hash(uint8_t *out, size_t out_len, const EVP_MD *md,
- const uint8_t *secret, size_t secret_len,
- const uint8_t *seed1, size_t seed1_len,
- const uint8_t *seed2, size_t seed2_len,
- const uint8_t *seed3, size_t seed3_len) {
+// section 5. It XORs |out.size()| bytes to |out|, using |md| as the hash and
+// |secret| as the secret. |label|, |seed1|, and |seed2| are concatenated to
+// form the seed parameter. It returns true on success and false on failure.
+static bool tls1_P_hash(Span<uint8_t> out, const EVP_MD *md,
+ Span<const uint8_t> secret, Span<const char> label,
+ Span<const uint8_t> seed1, Span<const uint8_t> seed2) {
ScopedHMAC_CTX ctx, ctx_tmp, ctx_init;
uint8_t A1[EVP_MAX_MD_SIZE];
unsigned A1_len;
- int ret = 0;
+ bool ret = false;
size_t chunk = EVP_MD_size(md);
- if (!HMAC_Init_ex(ctx_init.get(), secret, secret_len, md, NULL) ||
+ if (!HMAC_Init_ex(ctx_init.get(), secret.data(), secret.size(), md,
+ nullptr) ||
!HMAC_CTX_copy_ex(ctx.get(), ctx_init.get()) ||
- !HMAC_Update(ctx.get(), seed1, seed1_len) ||
- !HMAC_Update(ctx.get(), seed2, seed2_len) ||
- !HMAC_Update(ctx.get(), seed3, seed3_len) ||
+ !HMAC_Update(ctx.get(), reinterpret_cast<const uint8_t *>(label.data()),
+ label.size()) ||
+ !HMAC_Update(ctx.get(), seed1.data(), seed1.size()) ||
+ !HMAC_Update(ctx.get(), seed2.data(), seed2.size()) ||
!HMAC_Final(ctx.get(), A1, &A1_len)) {
goto err;
}
@@ -185,27 +185,26 @@
if (!HMAC_CTX_copy_ex(ctx.get(), ctx_init.get()) ||
!HMAC_Update(ctx.get(), A1, A1_len) ||
// Save a copy of |ctx| to compute the next A1 value below.
- (out_len > chunk && !HMAC_CTX_copy_ex(ctx_tmp.get(), ctx.get())) ||
- !HMAC_Update(ctx.get(), seed1, seed1_len) ||
- !HMAC_Update(ctx.get(), seed2, seed2_len) ||
- !HMAC_Update(ctx.get(), seed3, seed3_len) ||
+ (out.size() > chunk && !HMAC_CTX_copy_ex(ctx_tmp.get(), ctx.get())) ||
+ !HMAC_Update(ctx.get(), reinterpret_cast<const uint8_t *>(label.data()),
+ label.size()) ||
+ !HMAC_Update(ctx.get(), seed1.data(), seed1.size()) ||
+ !HMAC_Update(ctx.get(), seed2.data(), seed2.size()) ||
!HMAC_Final(ctx.get(), hmac, &len)) {
goto err;
}
assert(len == chunk);
// XOR the result into |out|.
- if (len > out_len) {
- len = out_len;
+ if (len > out.size()) {
+ len = out.size();
}
- unsigned i;
- for (i = 0; i < len; i++) {
+ for (unsigned i = 0; i < len; i++) {
out[i] ^= hmac[i];
}
- out += len;
- out_len -= len;
+ out = out.subspan(len);
- if (out_len == 0) {
+ if (out.empty()) {
break;
}
@@ -215,105 +214,86 @@
}
}
- ret = 1;
+ ret = true;
err:
OPENSSL_cleanse(A1, sizeof(A1));
return ret;
}
-int tls1_prf(const EVP_MD *digest, uint8_t *out, size_t out_len,
- const uint8_t *secret, size_t secret_len, const char *label,
- size_t label_len, const uint8_t *seed1, size_t seed1_len,
- const uint8_t *seed2, size_t seed2_len) {
- if (out_len == 0) {
- return 1;
+bool tls1_prf(const EVP_MD *digest, Span<uint8_t> out,
+ Span<const uint8_t> secret, Span<const char> label,
+ Span<const uint8_t> seed1, Span<const uint8_t> seed2) {
+ if (out.empty()) {
+ return true;
}
- OPENSSL_memset(out, 0, out_len);
+ OPENSSL_memset(out.data(), 0, out.size());
if (digest == EVP_md5_sha1()) {
- // If using the MD5/SHA1 PRF, |secret| is partitioned between SHA-1 and
- // MD5, MD5 first.
- size_t secret_half = secret_len - (secret_len / 2);
- if (!tls1_P_hash(out, out_len, EVP_md5(), secret, secret_half,
- (const uint8_t *)label, label_len, seed1, seed1_len, seed2,
- seed2_len)) {
- return 0;
+ // If using the MD5/SHA1 PRF, |secret| is partitioned between MD5 and SHA-1.
+ size_t secret_half = secret.size() - (secret.size() / 2);
+ if (!tls1_P_hash(out, EVP_md5(), secret.subspan(0, secret_half), label,
+ seed1, seed2)) {
+ return false;
}
- // Note that, if |secret_len| is odd, the two halves share a byte.
- secret = secret + (secret_len - secret_half);
- secret_len = secret_half;
-
+ // Note that, if |secret.size()| is odd, the two halves share a byte.
+ secret = secret.subspan(secret.size() - secret_half);
digest = EVP_sha1();
}
- if (!tls1_P_hash(out, out_len, digest, secret, secret_len,
- (const uint8_t *)label, label_len, seed1, seed1_len, seed2,
- seed2_len)) {
- return 0;
- }
-
- return 1;
+ return tls1_P_hash(out, digest, secret, label, seed1, seed2);
}
-static int ssl3_prf(uint8_t *out, size_t out_len, const uint8_t *secret,
- size_t secret_len, const char *label, size_t label_len,
- const uint8_t *seed1, size_t seed1_len,
- const uint8_t *seed2, size_t seed2_len) {
+static bool ssl3_prf(Span<uint8_t> out, Span<const uint8_t> secret,
+ Span<const char> label, Span<const uint8_t> seed1,
+ Span<const uint8_t> seed2) {
ScopedEVP_MD_CTX md5;
ScopedEVP_MD_CTX sha1;
uint8_t buf[16], smd[SHA_DIGEST_LENGTH];
uint8_t c = 'A';
- size_t i, j, k;
-
- k = 0;
- for (i = 0; i < out_len; i += MD5_DIGEST_LENGTH) {
+ size_t k = 0;
+ while (!out.empty()) {
k++;
if (k > sizeof(buf)) {
// bug: 'buf' is too small for this ciphersuite
OPENSSL_PUT_ERROR(SSL, ERR_R_INTERNAL_ERROR);
- return 0;
+ return false;
}
- for (j = 0; j < k; j++) {
+ for (size_t j = 0; j < k; j++) {
buf[j] = c;
}
c++;
if (!EVP_DigestInit_ex(sha1.get(), EVP_sha1(), NULL)) {
OPENSSL_PUT_ERROR(SSL, ERR_LIB_EVP);
- return 0;
+ return false;
}
EVP_DigestUpdate(sha1.get(), buf, k);
- EVP_DigestUpdate(sha1.get(), secret, secret_len);
+ EVP_DigestUpdate(sha1.get(), secret.data(), secret.size());
// |label| is ignored for SSLv3.
- if (seed1_len) {
- EVP_DigestUpdate(sha1.get(), seed1, seed1_len);
- }
- if (seed2_len) {
- EVP_DigestUpdate(sha1.get(), seed2, seed2_len);
- }
+ EVP_DigestUpdate(sha1.get(), seed1.data(), seed1.size());
+ EVP_DigestUpdate(sha1.get(), seed2.data(), seed2.size());
EVP_DigestFinal_ex(sha1.get(), smd, NULL);
if (!EVP_DigestInit_ex(md5.get(), EVP_md5(), NULL)) {
OPENSSL_PUT_ERROR(SSL, ERR_LIB_EVP);
- return 0;
+ return false;
}
- EVP_DigestUpdate(md5.get(), secret, secret_len);
+ EVP_DigestUpdate(md5.get(), secret.data(), secret.size());
EVP_DigestUpdate(md5.get(), smd, SHA_DIGEST_LENGTH);
- if (i + MD5_DIGEST_LENGTH > out_len) {
+ if (out.size() < MD5_DIGEST_LENGTH) {
EVP_DigestFinal_ex(md5.get(), smd, NULL);
- OPENSSL_memcpy(out, smd, out_len - i);
- } else {
- EVP_DigestFinal_ex(md5.get(), out, NULL);
+ OPENSSL_memcpy(out.data(), smd, out.size());
+ break;
}
-
- out += MD5_DIGEST_LENGTH;
+ EVP_DigestFinal_ex(md5.get(), out.data(), NULL);
+ out = out.subspan(MD5_DIGEST_LENGTH);
}
OPENSSL_cleanse(smd, SHA_DIGEST_LENGTH);
- return 1;
+ return true;
}
static bool get_key_block_lengths(const SSL *ssl, size_t *out_mac_secret_len,
@@ -405,33 +385,33 @@
}
int tls1_generate_master_secret(SSL_HANDSHAKE *hs, uint8_t *out,
- const uint8_t *premaster,
- size_t premaster_len) {
+ Span<const uint8_t> premaster) {
+ static const char kMasterSecretLabel[] = "master secret";
+ static const char kExtendedMasterSecretLabel[] = "extended master secret";
+
const SSL *ssl = hs->ssl;
+ auto out_span = MakeSpan(out, SSL3_MASTER_SECRET_SIZE);
if (hs->extended_master_secret) {
+ auto label = MakeConstSpan(kExtendedMasterSecretLabel,
+ sizeof(kExtendedMasterSecretLabel) - 1);
uint8_t digests[EVP_MAX_MD_SIZE];
size_t digests_len;
if (!hs->transcript.GetHash(digests, &digests_len) ||
- !tls1_prf(hs->transcript.Digest(), out, SSL3_MASTER_SECRET_SIZE,
- premaster, premaster_len, TLS_MD_EXTENDED_MASTER_SECRET_CONST,
- TLS_MD_EXTENDED_MASTER_SECRET_CONST_SIZE, digests,
- digests_len, NULL, 0)) {
+ !tls1_prf(hs->transcript.Digest(), out_span, premaster, label,
+ MakeConstSpan(digests, digests_len), {})) {
return 0;
}
} else {
+ auto label =
+ MakeConstSpan(kMasterSecretLabel, sizeof(kMasterSecretLabel) - 1);
if (ssl_protocol_version(ssl) == SSL3_VERSION) {
- if (!ssl3_prf(out, SSL3_MASTER_SECRET_SIZE, premaster, premaster_len,
- TLS_MD_MASTER_SECRET_CONST, TLS_MD_MASTER_SECRET_CONST_SIZE,
- ssl->s3->client_random, SSL3_RANDOM_SIZE,
- ssl->s3->server_random, SSL3_RANDOM_SIZE)) {
+ if (!ssl3_prf(out_span, premaster, label, ssl->s3->client_random,
+ ssl->s3->server_random)) {
return 0;
}
} else {
- if (!tls1_prf(hs->transcript.Digest(), out, SSL3_MASTER_SECRET_SIZE,
- premaster, premaster_len, TLS_MD_MASTER_SECRET_CONST,
- TLS_MD_MASTER_SECRET_CONST_SIZE, ssl->s3->client_random,
- SSL3_RANDOM_SIZE, ssl->s3->server_random,
- SSL3_RANDOM_SIZE)) {
+ if (!tls1_prf(hs->transcript.Digest(), out_span, premaster, label,
+ ssl->s3->client_random, ssl->s3->server_random)) {
return 0;
}
}
@@ -457,18 +437,20 @@
int SSL_generate_key_block(const SSL *ssl, uint8_t *out, size_t out_len) {
const SSL_SESSION *session = SSL_get_session(ssl);
+ auto out_span = MakeSpan(out, out_len);
+ auto master_key =
+ MakeConstSpan(session->master_key, session->master_key_length);
+ static const char kLabel[] = "key expansion";
+ auto label = MakeConstSpan(kLabel, sizeof(kLabel) - 1);
+
if (ssl_protocol_version(ssl) == SSL3_VERSION) {
- return ssl3_prf(out, out_len, session->master_key,
- session->master_key_length, TLS_MD_KEY_EXPANSION_CONST,
- TLS_MD_KEY_EXPANSION_CONST_SIZE, ssl->s3->server_random,
- SSL3_RANDOM_SIZE, ssl->s3->client_random, SSL3_RANDOM_SIZE);
+ return ssl3_prf(out_span, master_key, label, ssl->s3->server_random,
+ ssl->s3->client_random);
}
const EVP_MD *digest = ssl_session_get_digest(session);
- return tls1_prf(digest, out, out_len, session->master_key,
- session->master_key_length, TLS_MD_KEY_EXPANSION_CONST,
- TLS_MD_KEY_EXPANSION_CONST_SIZE, ssl->s3->server_random,
- SSL3_RANDOM_SIZE, ssl->s3->client_random, SSL3_RANDOM_SIZE);
+ return tls1_prf(digest, out_span, master_key, label, ssl->s3->server_random,
+ ssl->s3->client_random);
}
int SSL_export_keying_material(SSL *ssl, uint8_t *out, size_t out_len,
@@ -497,26 +479,25 @@
}
seed_len += 2 + context_len;
}
- uint8_t *seed = (uint8_t *)OPENSSL_malloc(seed_len);
- if (seed == NULL) {
+ Array<uint8_t> seed;
+ if (!seed.Init(seed_len)) {
OPENSSL_PUT_ERROR(SSL, ERR_R_MALLOC_FAILURE);
return 0;
}
- OPENSSL_memcpy(seed, ssl->s3->client_random, SSL3_RANDOM_SIZE);
- OPENSSL_memcpy(seed + SSL3_RANDOM_SIZE, ssl->s3->server_random,
+ OPENSSL_memcpy(seed.data(), ssl->s3->client_random, SSL3_RANDOM_SIZE);
+ OPENSSL_memcpy(seed.data() + SSL3_RANDOM_SIZE, ssl->s3->server_random,
SSL3_RANDOM_SIZE);
if (use_context) {
- seed[2 * SSL3_RANDOM_SIZE] = (uint8_t)(context_len >> 8);
- seed[2 * SSL3_RANDOM_SIZE + 1] = (uint8_t)context_len;
- OPENSSL_memcpy(seed + 2 * SSL3_RANDOM_SIZE + 2, context, context_len);
+ seed[2 * SSL3_RANDOM_SIZE] = static_cast<uint8_t>(context_len >> 8);
+ seed[2 * SSL3_RANDOM_SIZE + 1] = static_cast<uint8_t>(context_len);
+ OPENSSL_memcpy(seed.data() + 2 * SSL3_RANDOM_SIZE + 2, context, context_len);
}
const SSL_SESSION *session = SSL_get_session(ssl);
const EVP_MD *digest = ssl_session_get_digest(session);
- int ret = tls1_prf(digest, out, out_len, session->master_key,
- session->master_key_length, label, label_len, seed,
- seed_len, NULL, 0);
- OPENSSL_free(seed);
- return ret;
+ return tls1_prf(
+ digest, MakeSpan(out, out_len),
+ MakeConstSpan(session->master_key, session->master_key_length),
+ MakeConstSpan(label, label_len), seed, {});
}
diff --git a/src/ssl/t1_lib.cc b/src/ssl/t1_lib.cc
index 31b51c9..a7bfec4 100644
--- a/src/ssl/t1_lib.cc
+++ b/src/ssl/t1_lib.cc
@@ -1800,11 +1800,21 @@
static bool ext_pre_shared_key_add_clienthello(SSL_HANDSHAKE *hs, CBB *out) {
SSL *const ssl = hs->ssl;
+ hs->needs_psk_binder = false;
if (hs->max_version < TLS1_3_VERSION || ssl->session == NULL ||
ssl_session_protocol_version(ssl->session) < TLS1_3_VERSION) {
return true;
}
+ // Per draft-ietf-tls-tls13-21 section 4.1.4, skip offering the session if the
+ // selected cipher in HelloRetryRequest does not match. This avoids performing
+ // the transcript hash transformation for multiple hashes.
+ if (hs->received_hello_retry_request &&
+ ssl_is_draft21(ssl->version) &&
+ ssl->session->cipher->algorithm_prf != hs->new_cipher->algorithm_prf) {
+ return true;
+ }
+
struct OPENSSL_timeval now;
ssl_get_current_time(ssl, &now);
uint32_t ticket_age = 1000 * (now.tv_sec - ssl->session->time);
@@ -3265,54 +3275,45 @@
return 1;
}
-int tls1_write_channel_id(SSL_HANDSHAKE *hs, CBB *cbb) {
+bool tls1_write_channel_id(SSL_HANDSHAKE *hs, CBB *cbb) {
SSL *const ssl = hs->ssl;
uint8_t digest[EVP_MAX_MD_SIZE];
size_t digest_len;
if (!tls1_channel_id_hash(hs, digest, &digest_len)) {
- return 0;
+ return false;
}
EC_KEY *ec_key = EVP_PKEY_get0_EC_KEY(ssl->tlsext_channel_id_private);
- if (ec_key == NULL) {
+ if (ec_key == nullptr) {
OPENSSL_PUT_ERROR(SSL, ERR_R_INTERNAL_ERROR);
- return 0;
+ return false;
}
- int ret = 0;
- BIGNUM *x = BN_new();
- BIGNUM *y = BN_new();
- ECDSA_SIG *sig = NULL;
- if (x == NULL || y == NULL ||
+ UniquePtr<BIGNUM> x(BN_new()), y(BN_new());
+ if (!x || !y ||
!EC_POINT_get_affine_coordinates_GFp(EC_KEY_get0_group(ec_key),
EC_KEY_get0_public_key(ec_key),
- x, y, NULL)) {
- goto err;
+ x.get(), y.get(), nullptr)) {
+ return false;
}
- sig = ECDSA_do_sign(digest, digest_len, ec_key);
- if (sig == NULL) {
- goto err;
+ UniquePtr<ECDSA_SIG> sig(ECDSA_do_sign(digest, digest_len, ec_key));
+ if (!sig) {
+ return false;
}
CBB child;
if (!CBB_add_u16(cbb, TLSEXT_TYPE_channel_id) ||
!CBB_add_u16_length_prefixed(cbb, &child) ||
- !BN_bn2cbb_padded(&child, 32, x) ||
- !BN_bn2cbb_padded(&child, 32, y) ||
+ !BN_bn2cbb_padded(&child, 32, x.get()) ||
+ !BN_bn2cbb_padded(&child, 32, y.get()) ||
!BN_bn2cbb_padded(&child, 32, sig->r) ||
!BN_bn2cbb_padded(&child, 32, sig->s) ||
!CBB_flush(cbb)) {
- goto err;
+ return false;
}
- ret = 1;
-
-err:
- BN_free(x);
- BN_free(y);
- ECDSA_SIG_free(sig);
- return ret;
+ return true;
}
int tls1_channel_id_hash(SSL_HANDSHAKE *hs, uint8_t *out, size_t *out_len) {
diff --git a/src/ssl/test/bssl_shim.cc b/src/ssl/test/bssl_shim.cc
index d439cb5..7eca21d 100644
--- a/src/ssl/test/bssl_shim.cc
+++ b/src/ssl/test/bssl_shim.cc
@@ -1278,6 +1278,9 @@
if (!config->use_client_ca_list.empty()) {
if (config->use_client_ca_list == "<NULL>") {
SSL_CTX_set_client_CA_list(ssl_ctx.get(), nullptr);
+ } else if (config->use_client_ca_list == "<EMPTY>") {
+ bssl::UniquePtr<STACK_OF(X509_NAME)> names;
+ SSL_CTX_set_client_CA_list(ssl_ctx.get(), names.release());
} else {
bssl::UniquePtr<STACK_OF(X509_NAME)> names =
DecodeHexX509Names(config->use_client_ca_list);
@@ -2396,14 +2399,13 @@
}
if (expect_new_session) {
- bool got_early_data_info =
+ bool got_early_data =
GetTestState(ssl)->new_session->ticket_max_early_data != 0;
- if (config->expect_early_data_info != got_early_data_info) {
- fprintf(
- stderr,
- "new session did%s include ticket_early_data_info, but we expected "
- "the opposite\n",
- got_early_data_info ? "" : " not");
+ if (config->expect_ticket_supports_early_data != got_early_data) {
+ fprintf(stderr,
+ "new session did%s support early data, but we expected the "
+ "opposite\n",
+ got_early_data ? "" : " not");
return false;
}
}
diff --git a/src/ssl/test/runner/cipher_suites.go b/src/ssl/test/runner/cipher_suites.go
index 2681e71..f4c5900 100644
--- a/src/ssl/test/runner/cipher_suites.go
+++ b/src/ssl/test/runner/cipher_suites.go
@@ -11,7 +11,6 @@
"crypto/des"
"crypto/hmac"
"crypto/md5"
- "crypto/rc4"
"crypto/sha1"
"crypto/sha256"
"crypto/sha512"
@@ -62,9 +61,6 @@
// suiteSHA384 indicates that the cipher suite uses SHA384 as the
// handshake hash.
suiteSHA384
- // suiteNoDTLS indicates that the cipher suite cannot be used
- // in DTLS.
- suiteNoDTLS
// suitePSK indicates that the cipher suite authenticates with
// a pre-shared key rather than a server private key.
suitePSK
@@ -99,8 +95,6 @@
}
var cipherSuites = []*cipherSuite{
- // Ciphersuite order is chosen so that ECDHE comes before plain RSA
- // and RC4 comes before AES (because of the Lucky13 attack).
{TLS_CHACHA20_POLY1305_SHA256, 32, 0, ivLenChaCha20Poly1305, nil, suiteTLS13, nil, nil, aeadCHACHA20POLY1305},
{TLS_AES_128_GCM_SHA256, 16, 0, ivLenAESGCM, nil, suiteTLS13, nil, nil, aeadAESGCM},
{TLS_AES_256_GCM_SHA384, 32, 0, ivLenAESGCM, nil, suiteTLS13 | suiteSHA384, nil, nil, aeadAESGCM},
@@ -110,8 +104,6 @@
{TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256, 16, 0, ivLenAESGCM, ecdheECDSAKA, suiteECDHE | suiteECDSA | suiteTLS12, nil, nil, aeadAESGCM},
{TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384, 32, 0, ivLenAESGCM, ecdheRSAKA, suiteECDHE | suiteTLS12 | suiteSHA384, nil, nil, aeadAESGCM},
{TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384, 32, 0, ivLenAESGCM, ecdheECDSAKA, suiteECDHE | suiteECDSA | suiteTLS12 | suiteSHA384, nil, nil, aeadAESGCM},
- {TLS_ECDHE_RSA_WITH_RC4_128_SHA, 16, 20, noIV, ecdheRSAKA, suiteECDHE | suiteNoDTLS, cipherRC4, macSHA1, nil},
- {TLS_ECDHE_ECDSA_WITH_RC4_128_SHA, 16, 20, noIV, ecdheECDSAKA, suiteECDHE | suiteECDSA | suiteNoDTLS, cipherRC4, macSHA1, nil},
{TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256, 16, 32, ivLenAES, ecdheRSAKA, suiteECDHE | suiteTLS12, cipherAES, macSHA256, nil},
{TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256, 16, 32, ivLenAES, ecdheECDSAKA, suiteECDHE | suiteECDSA | suiteTLS12, cipherAES, macSHA256, nil},
{TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA, 16, 20, ivLenAES, ecdheRSAKA, suiteECDHE, cipherAES, macSHA1, nil},
@@ -122,8 +114,6 @@
{TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA, 32, 20, ivLenAES, ecdheECDSAKA, suiteECDHE | suiteECDSA, cipherAES, macSHA1, nil},
{TLS_RSA_WITH_AES_128_GCM_SHA256, 16, 0, ivLenAESGCM, rsaKA, suiteTLS12, nil, nil, aeadAESGCM},
{TLS_RSA_WITH_AES_256_GCM_SHA384, 32, 0, ivLenAESGCM, rsaKA, suiteTLS12 | suiteSHA384, nil, nil, aeadAESGCM},
- {TLS_RSA_WITH_RC4_128_SHA, 16, 20, noIV, rsaKA, suiteNoDTLS, cipherRC4, macSHA1, nil},
- {TLS_RSA_WITH_RC4_128_MD5, 16, 16, noIV, rsaKA, suiteNoDTLS, cipherRC4, macMD5, nil},
{TLS_RSA_WITH_AES_128_CBC_SHA256, 16, 32, ivLenAES, rsaKA, suiteTLS12, cipherAES, macSHA256, nil},
{TLS_RSA_WITH_AES_256_CBC_SHA256, 32, 32, ivLenAES, rsaKA, suiteTLS12, cipherAES, macSHA256, nil},
{TLS_RSA_WITH_AES_128_CBC_SHA, 16, 20, ivLenAES, rsaKA, 0, cipherAES, macSHA1, nil},
@@ -133,10 +123,9 @@
{TLS_ECDHE_PSK_WITH_CHACHA20_POLY1305_SHA256, 32, 0, ivLenChaCha20Poly1305, ecdhePSKKA, suiteECDHE | suitePSK | suiteTLS12, nil, nil, aeadCHACHA20POLY1305},
{TLS_ECDHE_PSK_WITH_AES_128_CBC_SHA, 16, 20, ivLenAES, ecdhePSKKA, suiteECDHE | suitePSK, cipherAES, macSHA1, nil},
{TLS_ECDHE_PSK_WITH_AES_256_CBC_SHA, 32, 20, ivLenAES, ecdhePSKKA, suiteECDHE | suitePSK, cipherAES, macSHA1, nil},
- {TLS_PSK_WITH_RC4_128_SHA, 16, 20, noIV, pskKA, suiteNoDTLS | suitePSK, cipherRC4, macSHA1, nil},
{TLS_PSK_WITH_AES_128_CBC_SHA, 16, 20, ivLenAES, pskKA, suitePSK, cipherAES, macSHA1, nil},
{TLS_PSK_WITH_AES_256_CBC_SHA, 32, 20, ivLenAES, pskKA, suitePSK, cipherAES, macSHA1, nil},
- {TLS_RSA_WITH_NULL_SHA, 0, 20, noIV, rsaKA, suiteNoDTLS, cipherNull, macSHA1, nil},
+ {TLS_RSA_WITH_NULL_SHA, 0, 20, noIV, rsaKA, 0, cipherNull, macSHA1, nil},
}
func noIV(vers uint16) int {
@@ -168,11 +157,6 @@
return nullCipher{}
}
-func cipherRC4(key, iv []byte, isRead bool) interface{} {
- cipher, _ := rc4.NewCipher(key)
- return cipher
-}
-
func cipher3DES(key, iv []byte, isRead bool) interface{} {
block, _ := des.NewTripleDESCipher(key)
if isRead {
@@ -448,22 +432,17 @@
// http://www.iana.org/assignments/tls-parameters/tls-parameters.xml
const (
TLS_RSA_WITH_NULL_SHA uint16 = 0x0002
- TLS_RSA_WITH_RC4_128_MD5 uint16 = 0x0004
- TLS_RSA_WITH_RC4_128_SHA uint16 = 0x0005
TLS_RSA_WITH_3DES_EDE_CBC_SHA uint16 = 0x000a
TLS_RSA_WITH_AES_128_CBC_SHA uint16 = 0x002f
TLS_RSA_WITH_AES_256_CBC_SHA uint16 = 0x0035
TLS_RSA_WITH_AES_128_CBC_SHA256 uint16 = 0x003c
TLS_RSA_WITH_AES_256_CBC_SHA256 uint16 = 0x003d
- TLS_PSK_WITH_RC4_128_SHA uint16 = 0x008a
TLS_PSK_WITH_AES_128_CBC_SHA uint16 = 0x008c
TLS_PSK_WITH_AES_256_CBC_SHA uint16 = 0x008d
TLS_RSA_WITH_AES_128_GCM_SHA256 uint16 = 0x009c
TLS_RSA_WITH_AES_256_GCM_SHA384 uint16 = 0x009d
- TLS_ECDHE_ECDSA_WITH_RC4_128_SHA uint16 = 0xc007
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA uint16 = 0xc009
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA uint16 = 0xc00a
- TLS_ECDHE_RSA_WITH_RC4_128_SHA uint16 = 0xc011
TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA uint16 = 0xc012
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA uint16 = 0xc013
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA uint16 = 0xc014
diff --git a/src/ssl/test/runner/common.go b/src/ssl/test/runner/common.go
index eee1337..9e0deef 100644
--- a/src/ssl/test/runner/common.go
+++ b/src/ssl/test/runner/common.go
@@ -34,6 +34,7 @@
// A draft version of TLS 1.3 that is sent over the wire for the current draft.
const (
tls13DraftVersion = 0x7f12
+ tls13Draft21Version = 0x7f15
tls13ExperimentVersion = 0x7e01
tls13Experiment2Version = 0x7e02
tls13Experiment3Version = 0x7e03
@@ -44,10 +45,12 @@
TLS13Experiment = 1
TLS13Experiment2 = 2
TLS13Experiment3 = 3
+ TLS13Draft21 = 4
)
var allTLSWireVersions = []uint16{
tls13DraftVersion,
+ tls13Draft21Version,
tls13Experiment3Version,
tls13Experiment2Version,
tls13ExperimentVersion,
@@ -91,6 +94,7 @@
typeServerHello uint8 = 2
typeHelloVerifyRequest uint8 = 3
typeNewSessionTicket uint8 = 4
+ typeEndOfEarlyData uint8 = 5 // draft-ietf-tls-tls13-21
typeHelloRetryRequest uint8 = 6 // draft-ietf-tls-tls13-16
typeEncryptedExtensions uint8 = 8 // draft-ietf-tls-tls13-16
typeCertificate uint8 = 11
@@ -104,6 +108,7 @@
typeKeyUpdate uint8 = 24 // draft-ietf-tls-tls13-16
typeNextProtocol uint8 = 67 // Not IANA assigned
typeChannelID uint8 = 203 // Not IANA assigned
+ typeMessageHash uint8 = 254 // draft-ietf-tls-tls13-21
)
// TLS compression types.
@@ -131,6 +136,7 @@
extensionCookie uint16 = 44 // draft-ietf-tls-tls13-16
extensionPSKKeyExchangeModes uint16 = 45 // draft-ietf-tls-tls13-18
extensionTicketEarlyDataInfo uint16 = 46 // draft-ietf-tls-tls13-18
+ extensionCertificateAuthorities uint16 = 47 // draft-ietf-tls-tls13-21
extensionCustom uint16 = 1234 // not IANA assigned
extensionNextProtoNeg uint16 = 13172 // not IANA assigned
extensionRenegotiationInfo uint16 = 0xff01
@@ -456,8 +462,7 @@
// MaxEarlyDataSize controls the maximum number of bytes that the
// server will accept in early data and advertise in a
// NewSessionTicketMsg. If 0, no early data will be accepted and
- // the TicketEarlyDataInfo extension in the NewSessionTicketMsg
- // will be omitted.
+ // the early_data extension in the NewSessionTicketMsg will be omitted.
MaxEarlyDataSize uint32
// SRTPProtectionProfiles, if not nil, is the list of SRTP
@@ -581,10 +586,14 @@
// message.
SkipFinished bool
- // SkipEndOfEarlyData causes the implementation to skip the
- // end_of_early_data alert.
+ // SkipEndOfEarlyData causes the implementation to skip
+ // end_of_early_data.
SkipEndOfEarlyData bool
+ // NonEmptyEndOfEarlyData causes the implementation to end an extra byte in the
+ // EndOfEarlyData.
+ NonEmptyEndOfEarlyData bool
+
// SkipCertificateVerify, if true causes peer to skip sending a
// CertificateVerify message after the Certificate message.
SkipCertificateVerify bool
@@ -755,6 +764,10 @@
// if a TLS 1.3 PSK is offered.
ExpectNoTLS13PSK bool
+ // ExpectNoTLS13PSKAfterHRR, if true, causes the server to fail the connection
+ // if a TLS 1.3 PSK is offered after HRR.
+ ExpectNoTLS13PSKAfterHRR bool
+
// RequireExtendedMasterSecret, if true, requires that the peer support
// the extended master secret option.
RequireExtendedMasterSecret bool
@@ -1054,13 +1067,13 @@
// receipt of a NewSessionTicket message.
ExpectNoNewSessionTicket bool
- // DuplicateTicketEarlyDataInfo causes an extra empty extension of
- // ticket_early_data_info to be sent in NewSessionTicket.
- DuplicateTicketEarlyDataInfo bool
+ // DuplicateTicketEarlyData causes an extra empty extension of early_data to
+ // be sent in NewSessionTicket.
+ DuplicateTicketEarlyData bool
- // ExpectTicketEarlyDataInfo, if true, means that the client will fail upon
- // absence of the ticket_early_data_info extension.
- ExpectTicketEarlyDataInfo bool
+ // ExpectTicketEarlyData, if true, means that the client will fail upon
+ // absence of the early_data extension.
+ ExpectTicketEarlyData bool
// ExpectTicketAge, if non-zero, is the expected age of the ticket that the
// server receives from the client.
@@ -1308,6 +1321,10 @@
// the specified curve in a HelloRetryRequest.
SendHelloRetryRequestCurve CurveID
+ // SendHelloRetryRequestCipherSuite, if non-zero, causes the server to send
+ // the specified cipher suite in a HelloRetryRequest.
+ SendHelloRetryRequestCipherSuite uint16
+
// SendHelloRetryRequestCookie, if not nil, contains a cookie to be
// sent by the server in HelloRetryRequest.
SendHelloRetryRequestCookie []byte
@@ -1345,6 +1362,14 @@
// a TLS 1.3 CertificateRequest.
SendRequestContext []byte
+ // OmitCertificateRequestAlgorithms, if true, omits the signature_algorithm
+ // extension in a TLS 1.3 CertificateRequest.
+ OmitCertificateRequestAlgorithms bool
+
+ // SendCustomCertificateRequest, if non-zero, send an additional custom
+ // extension in a TLS 1.3 CertificateRequest.
+ SendCustomCertificateRequest uint16
+
// SendSNIWarningAlert, if true, causes the server to send an
// unrecognized_name alert before the ServerHello.
SendSNIWarningAlert bool
@@ -1432,6 +1457,10 @@
// renegotiation handshakes.
RenegotiationCertificate *Certificate
+ // ExpectNoCertificateAuthoritiesExtension, if true, causes the client to
+ // reject CertificateRequest with the CertificateAuthorities extension.
+ ExpectNoCertificateAuthoritiesExtension bool
+
// UseLegacySigningAlgorithm, if non-zero, is the signature algorithm
// to use when signing in TLS 1.1 and earlier where algorithms are not
// negotiated.
@@ -1576,7 +1605,7 @@
switch vers {
case VersionSSL30, VersionTLS10, VersionTLS11, VersionTLS12:
return vers, true
- case tls13DraftVersion, tls13ExperimentVersion, tls13Experiment2Version, tls13Experiment3Version:
+ case tls13DraftVersion, tls13Draft21Version, tls13ExperimentVersion, tls13Experiment2Version, tls13Experiment3Version:
return VersionTLS13, true
}
}
@@ -1584,6 +1613,10 @@
return 0, false
}
+func isDraft21(vers uint16) bool {
+ return vers == tls13Draft21Version
+}
+
func isResumptionExperiment(vers uint16) bool {
return vers == tls13ExperimentVersion || vers == tls13Experiment2Version || vers == tls13Experiment3Version
}
@@ -1603,6 +1636,7 @@
if (c.TLS13Variant != TLS13Experiment && wireVers == tls13ExperimentVersion) ||
(c.TLS13Variant != TLS13Experiment2 && wireVers == tls13Experiment2Version) ||
(c.TLS13Variant != TLS13Experiment3 && wireVers == tls13Experiment3Version) ||
+ (c.TLS13Variant != TLS13Draft21 && wireVers == tls13Draft21Version) ||
(c.TLS13Variant != TLS13Default && wireVers == tls13DraftVersion) {
return 0, false
}
diff --git a/src/ssl/test/runner/conn.go b/src/ssl/test/runner/conn.go
index 71b52f2..6a2c59c 100644
--- a/src/ssl/test/runner/conn.go
+++ b/src/ssl/test/runner/conn.go
@@ -1274,7 +1274,8 @@
m = new(helloRetryRequestMsg)
case typeNewSessionTicket:
m = &newSessionTicketMsg{
- version: c.vers,
+ vers: c.wireVersion,
+ isDTLS: c.isDTLS,
}
case typeEncryptedExtensions:
m = new(encryptedExtensionsMsg)
@@ -1284,6 +1285,7 @@
}
case typeCertificateRequest:
m = &certificateRequestMsg{
+ vers: c.wireVersion,
hasSignatureAlgorithm: c.vers >= VersionTLS12,
hasRequestContext: c.vers >= VersionTLS13,
}
@@ -1309,6 +1311,8 @@
m = new(channelIDMsg)
case typeKeyUpdate:
m = new(keyUpdateMsg)
+ case typeEndOfEarlyData:
+ m = new(endOfEarlyDataMsg)
default:
return nil, c.in.setErrorLocked(c.sendAlert(alertUnexpectedMessage))
}
@@ -1469,8 +1473,8 @@
return errors.New("tls: no GREASE ticket extension found")
}
- if c.config.Bugs.ExpectTicketEarlyDataInfo && newSessionTicket.maxEarlyDataSize == 0 {
- return errors.New("tls: no ticket_early_data_info extension found")
+ if c.config.Bugs.ExpectTicketEarlyData && newSessionTicket.maxEarlyDataSize == 0 {
+ return errors.New("tls: no early_data ticket extension found")
}
if c.config.Bugs.ExpectNoNewSessionTicket {
@@ -1497,6 +1501,10 @@
earlyALPN: c.clientProtocol,
}
+ if isDraft21(c.wireVersion) {
+ session.masterSecret = deriveSessionPSK(cipherSuite, c.wireVersion, c.resumptionSecret, newSessionTicket.ticketNonce)
+ }
+
cacheKey := clientSessionCacheKey(c.conn.RemoteAddr(), c.config)
_, ok := c.config.ClientSessionCache.Get(cacheKey)
if !ok || !c.config.Bugs.UseFirstSessionTicket {
@@ -1537,7 +1545,7 @@
if c.config.Bugs.RejectUnsolicitedKeyUpdate {
return errors.New("tls: unexpected KeyUpdate message")
}
- if err := c.useInTrafficSecret(c.in.wireVersion, c.cipherSuite, updateTrafficSecret(c.cipherSuite.hash(), c.in.trafficSecret)); err != nil {
+ if err := c.useInTrafficSecret(c.in.wireVersion, c.cipherSuite, updateTrafficSecret(c.cipherSuite.hash(), c.wireVersion, c.in.trafficSecret)); err != nil {
return err
}
if keyUpdate.keyUpdateRequest == keyUpdateRequested {
@@ -1571,7 +1579,7 @@
return errors.New("tls: received invalid KeyUpdate message")
}
- return c.useInTrafficSecret(c.in.wireVersion, c.cipherSuite, updateTrafficSecret(c.cipherSuite.hash(), c.in.trafficSecret))
+ return c.useInTrafficSecret(c.in.wireVersion, c.cipherSuite, updateTrafficSecret(c.cipherSuite.hash(), c.wireVersion, c.in.trafficSecret))
}
func (c *Conn) Renegotiate() error {
@@ -1789,9 +1797,16 @@
}
if c.vers >= VersionTLS13 {
- // TODO(davidben): What should we do with useContext? See
- // https://github.com/tlswg/tls13-spec/issues/546
- return hkdfExpandLabel(c.cipherSuite.hash(), c.exporterSecret, label, context, length), nil
+ if isDraft21(c.wireVersion) {
+ hash := c.cipherSuite.hash()
+ exporterKeyingLabel := []byte("exporter")
+ contextHash := hash.New()
+ contextHash.Write(context)
+ exporterContext := hash.New().Sum(nil)
+ derivedSecret := hkdfExpandLabel(c.cipherSuite.hash(), c.wireVersion, c.exporterSecret, label, exporterContext, hash.Size())
+ return hkdfExpandLabel(c.cipherSuite.hash(), c.wireVersion, derivedSecret, exporterKeyingLabel, contextHash.Sum(nil), length), nil
+ }
+ return hkdfExpandLabel(c.cipherSuite.hash(), c.wireVersion, c.exporterSecret, label, context, length), nil
}
seedLen := len(c.clientRandom) + len(c.serverRandom)
@@ -1825,7 +1840,7 @@
return false
}
-func (c *Conn) SendNewSessionTicket() error {
+func (c *Conn) SendNewSessionTicket(nonce []byte) error {
if c.isClient || c.vers < VersionTLS13 {
return errors.New("tls: cannot send post-handshake NewSessionTicket")
}
@@ -1845,12 +1860,17 @@
// TODO(davidben): Allow configuring these values.
m := &newSessionTicketMsg{
- version: c.vers,
- ticketLifetime: uint32(24 * time.Hour / time.Second),
- duplicateEarlyDataInfo: c.config.Bugs.DuplicateTicketEarlyDataInfo,
- customExtension: c.config.Bugs.CustomTicketExtension,
- ticketAgeAdd: ticketAgeAdd,
- maxEarlyDataSize: c.config.MaxEarlyDataSize,
+ vers: c.wireVersion,
+ isDTLS: c.isDTLS,
+ ticketLifetime: uint32(24 * time.Hour / time.Second),
+ duplicateEarlyDataExtension: c.config.Bugs.DuplicateTicketEarlyData,
+ customExtension: c.config.Bugs.CustomTicketExtension,
+ ticketAgeAdd: ticketAgeAdd,
+ maxEarlyDataSize: c.config.MaxEarlyDataSize,
+ }
+
+ if isDraft21(c.wireVersion) {
+ m.ticketNonce = nonce
}
if c.config.Bugs.SendTicketLifetime != 0 {
@@ -1868,6 +1888,10 @@
earlyALPN: []byte(c.clientProtocol),
}
+ if isDraft21(c.wireVersion) {
+ state.masterSecret = deriveSessionPSK(c.cipherSuite, c.wireVersion, c.resumptionSecret, nonce)
+ }
+
if !c.config.Bugs.SendEmptySessionTicket {
var err error
m.ticket, err = c.encryptTicket(&state)
@@ -1901,7 +1925,7 @@
if err := c.flushHandshake(); err != nil {
return err
}
- c.useOutTrafficSecret(c.out.wireVersion, c.cipherSuite, updateTrafficSecret(c.cipherSuite.hash(), c.out.trafficSecret))
+ c.useOutTrafficSecret(c.out.wireVersion, c.cipherSuite, updateTrafficSecret(c.cipherSuite.hash(), c.wireVersion, c.out.trafficSecret))
return nil
}
diff --git a/src/ssl/test/runner/handshake_client.go b/src/ssl/test/runner/handshake_client.go
index 30105a5..ba34647 100644
--- a/src/ssl/test/runner/handshake_client.go
+++ b/src/ssl/test/runner/handshake_client.go
@@ -211,10 +211,6 @@
if maxVersion < VersionTLS12 && suite.flags&suiteTLS12 != 0 {
continue
}
- // Don't advertise non-DTLS cipher suites in DTLS.
- if c.isDTLS && suite.flags&suiteNoDTLS != 0 {
- continue
- }
hello.cipherSuites = append(hello.cipherSuites, suiteId)
continue NextCipherSuite
}
@@ -376,7 +372,14 @@
c.writeV2Record(helloBytes)
} else {
if len(hello.pskIdentities) > 0 {
- generatePSKBinders(hello, pskCipherSuite, session.masterSecret, []byte{}, c.config)
+ version := session.wireVersion
+ // We may have a pre-1.3 session if SendBothTickets is
+ // set. Fill in an arbitrary TLS 1.3 version to compute
+ // the binder.
+ if session.vers < VersionTLS13 {
+ version = tls13DraftVersion
+ }
+ generatePSKBinders(version, hello, pskCipherSuite, session.masterSecret, []byte{}, []byte{}, c.config)
}
helloBytes = hello.marshal()
@@ -407,10 +410,16 @@
// Derive early write keys and set Conn state to allow early writes.
if sendEarlyData {
- finishedHash := newFinishedHash(session.vers, pskCipherSuite)
+ finishedHash := newFinishedHash(session.wireVersion, c.isDTLS, pskCipherSuite)
finishedHash.addEntropy(session.masterSecret)
finishedHash.Write(helloBytes)
- earlyTrafficSecret := finishedHash.deriveSecret(earlyTrafficLabel)
+
+ earlyLabel := earlyTrafficLabel
+ if isDraft21(session.wireVersion) {
+ earlyLabel = earlyTrafficLabelDraft21
+ }
+
+ earlyTrafficSecret := finishedHash.deriveSecret(earlyLabel)
c.useOutTrafficSecret(session.wireVersion, pskCipherSuite, earlyTrafficSecret)
for _, earlyData := range c.config.Bugs.SendEarlyData {
if _, err := c.writeRecord(recordTypeApplicationData, earlyData); err != nil {
@@ -518,7 +527,7 @@
hello.raw = nil
if len(hello.pskIdentities) > 0 {
- generatePSKBinders(hello, pskCipherSuite, session.masterSecret, append(helloBytes, helloRetryRequest.marshal()...), c.config)
+ generatePSKBinders(c.wireVersion, hello, pskCipherSuite, session.masterSecret, helloBytes, helloRetryRequest.marshal(), c.config)
}
secondHelloBytes = hello.marshal()
@@ -588,13 +597,19 @@
serverHello: serverHello,
hello: hello,
suite: suite,
- finishedHash: newFinishedHash(c.vers, suite),
+ finishedHash: newFinishedHash(c.wireVersion, c.isDTLS, suite),
keyShares: keyShares,
session: session,
}
hs.writeHash(helloBytes, hs.c.sendHandshakeSeq-1)
if haveHelloRetryRequest {
+ if isDraft21(c.wireVersion) {
+ err = hs.finishedHash.UpdateForHelloRetryRequest()
+ if err != nil {
+ return err
+ }
+ }
hs.writeServerHash(helloRetryRequest.marshal())
hs.writeClientHash(secondHelloBytes)
}
@@ -739,8 +754,10 @@
if err != nil {
return err
}
+ hs.finishedHash.nextSecret()
hs.finishedHash.addEntropy(ecdheSecret)
} else {
+ hs.finishedHash.nextSecret()
hs.finishedHash.addEntropy(zeroSecret)
}
@@ -750,10 +767,17 @@
}
}
+ clientLabel := clientHandshakeTrafficLabel
+ serverLabel := serverHandshakeTrafficLabel
+ if isDraft21(c.wireVersion) {
+ clientLabel = clientHandshakeTrafficLabelDraft21
+ serverLabel = serverHandshakeTrafficLabelDraft21
+ }
+
// Derive handshake traffic keys and switch read key to handshake
// traffic key.
- clientHandshakeTrafficSecret := hs.finishedHash.deriveSecret(clientHandshakeTrafficLabel)
- serverHandshakeTrafficSecret := hs.finishedHash.deriveSecret(serverHandshakeTrafficLabel)
+ clientHandshakeTrafficSecret := hs.finishedHash.deriveSecret(clientLabel)
+ serverHandshakeTrafficSecret := hs.finishedHash.deriveSecret(serverLabel)
if err := c.useInTrafficSecret(c.wireVersion, hs.suite, serverHandshakeTrafficSecret); err != nil {
return err
}
@@ -795,6 +819,10 @@
return errors.New("tls: non-empty certificate request context sent in handshake")
}
+ if c.config.Bugs.ExpectNoCertificateAuthoritiesExtension && certReq.hasCAExtension {
+ return errors.New("tls: expected no certificate_authorities extension")
+ }
+
if c.config.Bugs.IgnorePeerSignatureAlgorithmPreferences {
certReq.signatureAlgorithms = c.config.signSignatureAlgorithms()
}
@@ -883,10 +911,21 @@
// The various secrets do not incorporate the client's final leg, so
// derive them now before updating the handshake context.
+ hs.finishedHash.nextSecret()
hs.finishedHash.addEntropy(zeroSecret)
- clientTrafficSecret := hs.finishedHash.deriveSecret(clientApplicationTrafficLabel)
- serverTrafficSecret := hs.finishedHash.deriveSecret(serverApplicationTrafficLabel)
- c.exporterSecret = hs.finishedHash.deriveSecret(exporterLabel)
+
+ clientLabel = clientApplicationTrafficLabel
+ serverLabel = serverApplicationTrafficLabel
+ exportLabel := exporterLabel
+ if isDraft21(c.wireVersion) {
+ clientLabel = clientApplicationTrafficLabelDraft21
+ serverLabel = serverApplicationTrafficLabelDraft21
+ exportLabel = exporterLabelDraft21
+ }
+
+ clientTrafficSecret := hs.finishedHash.deriveSecret(clientLabel)
+ serverTrafficSecret := hs.finishedHash.deriveSecret(serverLabel)
+ c.exporterSecret = hs.finishedHash.deriveSecret(exportLabel)
// Switch to application data keys on read. In particular, any alerts
// from the client certificate are read over these keys.
@@ -894,8 +933,8 @@
return err
}
- // If we're expecting 0.5-RTT messages from the server, read them
- // now.
+ // If we're expecting 0.5-RTT messages from the server, read them now.
+ var deferredTickets []*newSessionTicketMsg
if encryptedExtensions.extensions.hasEarlyData {
// BoringSSL will always send two tickets half-RTT when
// negotiating 0-RTT.
@@ -908,9 +947,8 @@
if !ok {
return errors.New("tls: expected half-RTT ticket")
}
- if err := c.processTLS13NewSessionTicket(newSessionTicket, hs.suite); err != nil {
- return err
- }
+ // Defer processing until the resumption secret is computed.
+ deferredTickets = append(deferredTickets, newSessionTicket)
}
for _, expectedMsg := range c.config.Bugs.ExpectHalfRTTData {
if err := c.readRecord(recordTypeApplicationData); err != nil {
@@ -926,12 +964,19 @@
// Send EndOfEarlyData and then switch write key to handshake
// traffic key.
- if c.out.cipher != nil && !c.config.Bugs.SkipEndOfEarlyData {
+ if encryptedExtensions.extensions.hasEarlyData && c.out.cipher != nil && !c.config.Bugs.SkipEndOfEarlyData {
if c.config.Bugs.SendStrayEarlyHandshake {
helloRequest := new(helloRequestMsg)
c.writeRecord(recordTypeHandshake, helloRequest.marshal())
}
- c.sendAlert(alertEndOfEarlyData)
+ if isDraft21(c.wireVersion) {
+ endOfEarlyData := new(endOfEarlyDataMsg)
+ endOfEarlyData.nonEmpty = c.config.Bugs.NonEmptyEndOfEarlyData
+ c.writeRecord(recordTypeHandshake, endOfEarlyData.marshal())
+ hs.writeClientHash(endOfEarlyData.marshal())
+ } else {
+ c.sendAlert(alertEndOfEarlyData)
+ }
}
if isResumptionClientCCSExperiment(c.wireVersion) {
@@ -1026,7 +1071,18 @@
// Switch to application data keys.
c.useOutTrafficSecret(c.wireVersion, hs.suite, clientTrafficSecret)
- c.resumptionSecret = hs.finishedHash.deriveSecret(resumptionLabel)
+ resumeLabel := resumptionLabel
+ if isDraft21(c.wireVersion) {
+ resumeLabel = resumptionLabelDraft21
+ }
+
+ c.resumptionSecret = hs.finishedHash.deriveSecret(resumeLabel)
+ for _, ticket := range deferredTickets {
+ if err := c.processTLS13NewSessionTicket(ticket, hs.suite); err != nil {
+ return err
+ }
+ }
+
return nil
}
@@ -1502,6 +1558,7 @@
// session ID or session ticket will be attached.
session := &ClientSessionState{
vers: c.vers,
+ wireVersion: c.wireVersion,
cipherSuite: hs.suite.id,
masterSecret: hs.masterSecret,
handshakeHash: hs.finishedHash.Sum(),
@@ -1735,7 +1792,7 @@
copy(b[len(b)-len(xb):], xb)
}
-func generatePSKBinders(hello *clientHelloMsg, pskCipherSuite *cipherSuite, psk, transcript []byte, config *Config) {
+func generatePSKBinders(version uint16, hello *clientHelloMsg, pskCipherSuite *cipherSuite, psk, firstClientHello, helloRetryRequest []byte, config *Config) {
if config.Bugs.SendNoPSKBinder {
return
}
@@ -1761,7 +1818,11 @@
helloBytes := hello.marshal()
binderSize := len(hello.pskBinders)*(binderLen+1) + 2
truncatedHello := helloBytes[:len(helloBytes)-binderSize]
- binder := computePSKBinder(psk, resumptionPSKBinderLabel, pskCipherSuite, transcript, truncatedHello)
+ binderLabel := resumptionPSKBinderLabel
+ if isDraft21(version) {
+ binderLabel = resumptionPSKBinderLabelDraft21
+ }
+ binder := computePSKBinder(psk, version, binderLabel, pskCipherSuite, firstClientHello, helloRetryRequest, truncatedHello)
if config.Bugs.SendShortPSKBinder {
binder = binder[:binderLen]
}
diff --git a/src/ssl/test/runner/handshake_messages.go b/src/ssl/test/runner/handshake_messages.go
index bf9cb7f..aa6b463 100644
--- a/src/ssl/test/runner/handshake_messages.go
+++ b/src/ssl/test/runner/handshake_messages.go
@@ -1406,6 +1406,7 @@
type helloRetryRequestMsg struct {
raw []byte
vers uint16
+ cipherSuite uint16
hasSelectedGroup bool
selectedGroup CurveID
cookie []byte
@@ -1422,6 +1423,9 @@
retryRequestMsg.addU8(typeHelloRetryRequest)
retryRequest := retryRequestMsg.addU24LengthPrefixed()
retryRequest.addU16(m.vers)
+ if isDraft21(m.vers) {
+ retryRequest.addU16(m.cipherSuite)
+ }
extensions := retryRequest.addU16LengthPrefixed()
count := 1
@@ -1456,8 +1460,13 @@
return false
}
m.vers = uint16(data[4])<<8 | uint16(data[5])
- extLen := int(data[6])<<8 | int(data[7])
- data = data[8:]
+ data = data[6:]
+ if isDraft21(m.vers) {
+ m.cipherSuite = uint16(data[0])<<8 | uint16(data[1])
+ data = data[2:]
+ }
+ extLen := int(data[0])<<8 | int(data[1])
+ data = data[2:]
if len(data) != extLen || len(data) == 0 {
return false
}
@@ -1870,7 +1879,8 @@
}
type certificateRequestMsg struct {
- raw []byte
+ raw []byte
+ vers uint16
// hasSignatureAlgorithm indicates whether this message includes a list
// of signature and hash functions. This change was introduced with TLS
// 1.2.
@@ -1884,6 +1894,8 @@
requestContext []byte
signatureAlgorithms []signatureAlgorithm
certificateAuthorities [][]byte
+ hasCAExtension bool
+ customExtension uint16
}
func (m *certificateRequestMsg) marshal() []byte {
@@ -1899,33 +1911,119 @@
if m.hasRequestContext {
requestContext := body.addU8LengthPrefixed()
requestContext.addBytes(m.requestContext)
+ extensions := newByteBuilder()
+ if isDraft21(m.vers) {
+ extensions = body.addU16LengthPrefixed()
+ if m.hasSignatureAlgorithm {
+ extensions.addU16(extensionSignatureAlgorithms)
+ signatureAlgorithms := extensions.addU16LengthPrefixed().addU16LengthPrefixed()
+ for _, sigAlg := range m.signatureAlgorithms {
+ signatureAlgorithms.addU16(uint16(sigAlg))
+ }
+ }
+ if len(m.certificateAuthorities) > 0 {
+ extensions.addU16(extensionCertificateAuthorities)
+ certificateAuthorities := extensions.addU16LengthPrefixed().addU16LengthPrefixed()
+ for _, ca := range m.certificateAuthorities {
+ caEntry := certificateAuthorities.addU16LengthPrefixed()
+ caEntry.addBytes(ca)
+ }
+ }
+ } else {
+ if m.hasSignatureAlgorithm {
+ signatureAlgorithms := body.addU16LengthPrefixed()
+ for _, sigAlg := range m.signatureAlgorithms {
+ signatureAlgorithms.addU16(uint16(sigAlg))
+ }
+ }
+
+ certificateAuthorities := body.addU16LengthPrefixed()
+ for _, ca := range m.certificateAuthorities {
+ caEntry := certificateAuthorities.addU16LengthPrefixed()
+ caEntry.addBytes(ca)
+ }
+ extensions = body.addU16LengthPrefixed()
+ }
+
+ if m.customExtension > 0 {
+ extensions.addU16(m.customExtension)
+ extensions.addU16LengthPrefixed()
+ }
} else {
certificateTypes := body.addU8LengthPrefixed()
certificateTypes.addBytes(m.certificateTypes)
- }
- if m.hasSignatureAlgorithm {
- signatureAlgorithms := body.addU16LengthPrefixed()
- for _, sigAlg := range m.signatureAlgorithms {
- signatureAlgorithms.addU16(uint16(sigAlg))
+ if m.hasSignatureAlgorithm {
+ signatureAlgorithms := body.addU16LengthPrefixed()
+ for _, sigAlg := range m.signatureAlgorithms {
+ signatureAlgorithms.addU16(uint16(sigAlg))
+ }
}
- }
- certificateAuthorities := body.addU16LengthPrefixed()
- for _, ca := range m.certificateAuthorities {
- caEntry := certificateAuthorities.addU16LengthPrefixed()
- caEntry.addBytes(ca)
- }
-
- if m.hasRequestContext {
- // Emit no certificate extensions.
- body.addU16(0)
+ certificateAuthorities := body.addU16LengthPrefixed()
+ for _, ca := range m.certificateAuthorities {
+ caEntry := certificateAuthorities.addU16LengthPrefixed()
+ caEntry.addBytes(ca)
+ }
}
m.raw = builder.finish()
return m.raw
}
+func parseSignatureAlgorithms(data []byte) ([]signatureAlgorithm, []byte, bool) {
+ if len(data) < 2 {
+ return nil, nil, false
+ }
+ sigAlgsLen := int(data[0])<<8 | int(data[1])
+ data = data[2:]
+ if sigAlgsLen&1 != 0 {
+ return nil, nil, false
+ }
+ if len(data) < int(sigAlgsLen) {
+ return nil, nil, false
+ }
+ numSigAlgs := sigAlgsLen / 2
+ signatureAlgorithms := make([]signatureAlgorithm, numSigAlgs)
+ for i := range signatureAlgorithms {
+ signatureAlgorithms[i] = signatureAlgorithm(data[0])<<8 | signatureAlgorithm(data[1])
+ data = data[2:]
+ }
+
+ return signatureAlgorithms, data, true
+}
+
+func parseCAs(data []byte) ([][]byte, []byte, bool) {
+ if len(data) < 2 {
+ return nil, nil, false
+ }
+ casLength := uint16(data[0])<<8 | uint16(data[1])
+ data = data[2:]
+ if len(data) < int(casLength) {
+ return nil, nil, false
+ }
+
+ cas := data[:casLength]
+ data = data[casLength:]
+
+ var certificateAuthorities [][]byte
+ for len(cas) > 0 {
+ if len(cas) < 2 {
+ return nil, nil, false
+ }
+ caLen := uint16(cas[0])<<8 | uint16(cas[1])
+ cas = cas[2:]
+
+ if len(cas) < int(caLen) {
+ return nil, nil, false
+ }
+
+ certificateAuthorities = append(certificateAuthorities, cas[:caLen])
+ cas = cas[caLen:]
+ }
+ return certificateAuthorities, data, true
+}
+
func (m *certificateRequestMsg) unmarshal(data []byte) bool {
m.raw = data
@@ -1942,6 +2040,70 @@
m.requestContext = make([]byte, contextLen)
copy(m.requestContext, data[1:])
data = data[1+contextLen:]
+ if isDraft21(m.vers) {
+ if len(data) < 2 {
+ return false
+ }
+ extensionsLen := int(data[0])<<8 | int(data[1])
+ if len(data) < 2+extensionsLen {
+ return false
+ }
+ extensions := data[2 : 2+extensionsLen]
+ data = data[2+extensionsLen:]
+ for len(extensions) != 0 {
+ if len(extensions) < 4 {
+ return false
+ }
+ extension := uint16(extensions[0])<<8 | uint16(extensions[1])
+ length := int(extensions[2])<<8 | int(extensions[3])
+ if len(extensions) < 4+length {
+ return false
+ }
+ contents := extensions[4 : 4+length]
+ extensions = extensions[4+length:]
+ switch extension {
+ case extensionSignatureAlgorithms:
+ sigAlgs, rest, ok := parseSignatureAlgorithms(contents)
+ if !ok || len(rest) != 0 {
+ return false
+ }
+ m.signatureAlgorithms = sigAlgs
+ case extensionCertificateAuthorities:
+ cas, rest, ok := parseCAs(contents)
+ if !ok || len(rest) != 0 {
+ return false
+ }
+ m.hasCAExtension = true
+ m.certificateAuthorities = cas
+ }
+ }
+ } else {
+ if m.hasSignatureAlgorithm {
+ sigAlgs, rest, ok := parseSignatureAlgorithms(data)
+ if !ok {
+ return false
+ }
+ m.signatureAlgorithms = sigAlgs
+ data = rest
+ }
+
+ cas, rest, ok := parseCAs(data)
+ if !ok {
+ return false
+ }
+ m.certificateAuthorities = cas
+ data = rest
+
+ // Ignore certificate extensions.
+ if len(data) < 2 {
+ return false
+ }
+ extsLength := int(data[0])<<8 | int(data[1])
+ if len(data) < 2+extsLength {
+ return false
+ }
+ data = data[2+extsLength:]
+ }
} else {
numCertTypes := int(data[0])
if len(data) < 1+numCertTypes {
@@ -1950,66 +2112,22 @@
m.certificateTypes = make([]byte, numCertTypes)
copy(m.certificateTypes, data[1:])
data = data[1+numCertTypes:]
- }
- if m.hasSignatureAlgorithm {
- if len(data) < 2 {
- return false
- }
- sigAlgsLen := uint16(data[0])<<8 | uint16(data[1])
- data = data[2:]
- if sigAlgsLen&1 != 0 {
- return false
- }
- if len(data) < int(sigAlgsLen) {
- return false
- }
- numSigAlgs := sigAlgsLen / 2
- m.signatureAlgorithms = make([]signatureAlgorithm, numSigAlgs)
- for i := range m.signatureAlgorithms {
- m.signatureAlgorithms[i] = signatureAlgorithm(data[0])<<8 | signatureAlgorithm(data[1])
- data = data[2:]
- }
- }
-
- if len(data) < 2 {
- return false
- }
- casLength := uint16(data[0])<<8 | uint16(data[1])
- data = data[2:]
- if len(data) < int(casLength) {
- return false
- }
- cas := make([]byte, casLength)
- copy(cas, data)
- data = data[casLength:]
-
- m.certificateAuthorities = nil
- for len(cas) > 0 {
- if len(cas) < 2 {
- return false
- }
- caLen := uint16(cas[0])<<8 | uint16(cas[1])
- cas = cas[2:]
-
- if len(cas) < int(caLen) {
- return false
+ if m.hasSignatureAlgorithm {
+ sigAlgs, rest, ok := parseSignatureAlgorithms(data)
+ if !ok {
+ return false
+ }
+ m.signatureAlgorithms = sigAlgs
+ data = rest
}
- m.certificateAuthorities = append(m.certificateAuthorities, cas[:caLen])
- cas = cas[caLen:]
- }
-
- if m.hasRequestContext {
- // Ignore certificate extensions.
- if len(data) < 2 {
+ cas, rest, ok := parseCAs(data)
+ if !ok {
return false
}
- extsLength := int(data[0])<<8 | int(data[1])
- if len(data) < 2+extsLength {
- return false
- }
- data = data[2+extsLength:]
+ m.certificateAuthorities = cas
+ data = rest
}
if len(data) > 0 {
@@ -2090,15 +2208,17 @@
}
type newSessionTicketMsg struct {
- raw []byte
- version uint16
- ticketLifetime uint32
- ticketAgeAdd uint32
- ticket []byte
- maxEarlyDataSize uint32
- customExtension string
- duplicateEarlyDataInfo bool
- hasGREASEExtension bool
+ raw []byte
+ vers uint16
+ isDTLS bool
+ ticketLifetime uint32
+ ticketAgeAdd uint32
+ ticketNonce []byte
+ ticket []byte
+ maxEarlyDataSize uint32
+ customExtension string
+ duplicateEarlyDataExtension bool
+ hasGREASEExtension bool
}
func (m *newSessionTicketMsg) marshal() []byte {
@@ -2106,25 +2226,37 @@
return m.raw
}
+ version, ok := wireToVersion(m.vers, m.isDTLS)
+ if !ok {
+ panic("unknown version")
+ }
+
// See http://tools.ietf.org/html/rfc5077#section-3.3
ticketMsg := newByteBuilder()
ticketMsg.addU8(typeNewSessionTicket)
body := ticketMsg.addU24LengthPrefixed()
body.addU32(m.ticketLifetime)
- if m.version >= VersionTLS13 {
+ if version >= VersionTLS13 {
body.addU32(m.ticketAgeAdd)
+ if isDraft21(m.vers) {
+ body.addU8LengthPrefixed().addBytes(m.ticketNonce)
+ }
}
ticket := body.addU16LengthPrefixed()
ticket.addBytes(m.ticket)
- if m.version >= VersionTLS13 {
+ if version >= VersionTLS13 {
extensions := body.addU16LengthPrefixed()
if m.maxEarlyDataSize > 0 {
- extensions.addU16(extensionTicketEarlyDataInfo)
+ extID := extensionTicketEarlyDataInfo
+ if isDraft21(m.vers) {
+ extID = extensionEarlyData
+ }
+ extensions.addU16(extID)
extensions.addU16LengthPrefixed().addU32(m.maxEarlyDataSize)
- if m.duplicateEarlyDataInfo {
- extensions.addU16(extensionTicketEarlyDataInfo)
+ if m.duplicateEarlyDataExtension {
+ extensions.addU16(extID)
extensions.addU16LengthPrefixed().addU32(m.maxEarlyDataSize)
}
}
@@ -2141,18 +2273,32 @@
func (m *newSessionTicketMsg) unmarshal(data []byte) bool {
m.raw = data
+ version, ok := wireToVersion(m.vers, m.isDTLS)
+ if !ok {
+ panic("unknown version")
+ }
+
if len(data) < 8 {
return false
}
m.ticketLifetime = uint32(data[4])<<24 | uint32(data[5])<<16 | uint32(data[6])<<8 | uint32(data[7])
data = data[8:]
- if m.version >= VersionTLS13 {
+ if version >= VersionTLS13 {
if len(data) < 4 {
return false
}
m.ticketAgeAdd = uint32(data[0])<<24 | uint32(data[1])<<16 | uint32(data[2])<<8 | uint32(data[3])
data = data[4:]
+ if isDraft21(m.vers) {
+ nonceLen := int(data[0])
+ data = data[1:]
+ if len(data) < nonceLen {
+ return false
+ }
+ m.ticketNonce = data[:nonceLen]
+ data = data[nonceLen:]
+ }
}
if len(data) < 2 {
@@ -2164,14 +2310,14 @@
return false
}
- if m.version >= VersionTLS13 && ticketLen == 0 {
+ if version >= VersionTLS13 && ticketLen == 0 {
return false
}
m.ticket = data[:ticketLen]
data = data[ticketLen:]
- if m.version >= VersionTLS13 {
+ if version >= VersionTLS13 {
if len(data) < 2 {
return false
}
@@ -2182,6 +2328,11 @@
return false
}
+ extID := extensionTicketEarlyDataInfo
+ if isDraft21(m.vers) {
+ extID = extensionEarlyData
+ }
+
for len(data) != 0 {
if len(data) < 4 {
return false
@@ -2194,7 +2345,7 @@
}
switch extension {
- case extensionTicketEarlyDataInfo:
+ case extID:
if length != 4 {
return false
}
@@ -2381,6 +2532,21 @@
return m.keyUpdateRequest == keyUpdateNotRequested || m.keyUpdateRequest == keyUpdateRequested
}
+type endOfEarlyDataMsg struct {
+ nonEmpty bool
+}
+
+func (m *endOfEarlyDataMsg) marshal() []byte {
+ if m.nonEmpty {
+ return []byte{typeEndOfEarlyData, 0, 0, 1, 42}
+ }
+ return []byte{typeEndOfEarlyData, 0, 0, 0}
+}
+
+func (*endOfEarlyDataMsg) unmarshal(data []byte) bool {
+ return len(data) == 4
+}
+
// ssl3NoCertificateMsg is a dummy message to handle SSL 3.0 using a warning
// alert in the handshake.
type ssl3NoCertificateMsg struct{}
diff --git a/src/ssl/test/runner/handshake_server.go b/src/ssl/test/runner/handshake_server.go
index f50772e..dd6f48f 100644
--- a/src/ssl/test/runner/handshake_server.go
+++ b/src/ssl/test/runner/handshake_server.go
@@ -412,7 +412,7 @@
hs.hello.cipherSuite = c.config.Bugs.SendCipherSuite
}
- hs.finishedHash = newFinishedHash(c.vers, hs.suite)
+ hs.finishedHash = newFinishedHash(c.wireVersion, c.isDTLS, hs.suite)
hs.finishedHash.discardHandshakeBuffer()
hs.writeClientHash(hs.clientHello.marshal())
@@ -496,7 +496,7 @@
// AcceptAnyBinder is set. See https://crbug.com/boringssl/115.
if hs.sessionState != nil && !config.Bugs.AcceptAnySession {
binderToVerify := hs.clientHello.pskBinders[pskIndex]
- if err := verifyPSKBinder(hs.clientHello, hs.sessionState, binderToVerify, []byte{}); err != nil {
+ if err := verifyPSKBinder(c.wireVersion, hs.clientHello, hs.sessionState, binderToVerify, []byte{}, []byte{}); err != nil {
return err
}
}
@@ -520,8 +520,13 @@
ResendHelloRetryRequest:
var sendHelloRetryRequest bool
+ cipherSuite := hs.suite.id
+ if config.Bugs.SendHelloRetryRequestCipherSuite != 0 {
+ cipherSuite = config.Bugs.SendHelloRetryRequestCipherSuite
+ }
helloRetryRequest := &helloRetryRequestMsg{
vers: c.wireVersion,
+ cipherSuite: cipherSuite,
duplicateExtensions: config.Bugs.DuplicateHelloRetryRequestExtensions,
}
@@ -571,6 +576,12 @@
}
if sendHelloRetryRequest {
+ if isDraft21(c.wireVersion) {
+ if err := hs.finishedHash.UpdateForHelloRetryRequest(); err != nil {
+ return err
+ }
+ }
+
oldClientHelloBytes := hs.clientHello.marshal()
hs.writeServerHash(helloRetryRequest.marshal())
c.writeRecord(recordTypeHandshake, helloRetryRequest.marshal())
@@ -592,6 +603,10 @@
}
hs.writeClientHash(newClientHello.marshal())
+ if config.Bugs.ExpectNoTLS13PSKAfterHRR && len(newClientHello.pskIdentities) > 0 {
+ return fmt.Errorf("tls: client offered unexpected PSK identities after HelloRetryRequest")
+ }
+
if newClientHello.hasEarlyData {
return errors.New("tls: EarlyData sent in new ClientHello")
}
@@ -626,11 +641,15 @@
// PSK binders and obfuscated ticket age are both updated in the
// second ClientHello.
- if len(oldClientHelloCopy.pskIdentities) != len(newClientHelloCopy.pskIdentities) {
- return errors.New("tls: PSK identity count from old and new ClientHello do not match")
- }
- for i, identity := range oldClientHelloCopy.pskIdentities {
- newClientHelloCopy.pskIdentities[i].obfuscatedTicketAge = identity.obfuscatedTicketAge
+ if isDraft21(c.wireVersion) && len(oldClientHelloCopy.pskIdentities) != len(newClientHelloCopy.pskIdentities) {
+ newClientHelloCopy.pskIdentities = oldClientHelloCopy.pskIdentities
+ } else {
+ if len(oldClientHelloCopy.pskIdentities) != len(newClientHelloCopy.pskIdentities) {
+ return errors.New("tls: PSK identity count from old and new ClientHello do not match")
+ }
+ for i, identity := range oldClientHelloCopy.pskIdentities {
+ newClientHelloCopy.pskIdentities[i].obfuscatedTicketAge = identity.obfuscatedTicketAge
+ }
}
newClientHelloCopy.pskBinders = oldClientHelloCopy.pskBinders
newClientHelloCopy.hasEarlyData = oldClientHelloCopy.hasEarlyData
@@ -648,7 +667,7 @@
// AcceptAnyBinder is set. See https://crbug.com/115.
if hs.sessionState != nil && !config.Bugs.AcceptAnySession {
binderToVerify := newClientHello.pskBinders[pskIndex]
- if err := verifyPSKBinder(newClientHello, hs.sessionState, binderToVerify, append(oldClientHelloBytes, helloRetryRequest.marshal()...)); err != nil {
+ if err := verifyPSKBinder(c.wireVersion, newClientHello, hs.sessionState, binderToVerify, oldClientHelloBytes, helloRetryRequest.marshal()); err != nil {
return err
}
}
@@ -662,7 +681,12 @@
}
}
if encryptedExtensions.extensions.hasEarlyData {
- earlyTrafficSecret := hs.finishedHash.deriveSecret(earlyTrafficLabel)
+ earlyLabel := earlyTrafficLabel
+ if isDraft21(c.wireVersion) {
+ earlyLabel = earlyTrafficLabelDraft21
+ }
+
+ earlyTrafficSecret := hs.finishedHash.deriveSecret(earlyLabel)
if err := c.useInTrafficSecret(c.wireVersion, hs.suite, earlyTrafficSecret); err != nil {
return err
}
@@ -716,6 +740,7 @@
c.sendAlert(alertHandshakeFailure)
return err
}
+ hs.finishedHash.nextSecret()
hs.finishedHash.addEntropy(ecdheSecret)
hs.hello.hasKeyShare = true
@@ -740,6 +765,7 @@
}
}
} else {
+ hs.finishedHash.nextSecret()
hs.finishedHash.addEntropy(hs.finishedHash.zeroSecret())
}
@@ -760,11 +786,18 @@
c.writeRecord(recordTypeChangeCipherSpec, []byte{1})
}
+ clientLabel := clientHandshakeTrafficLabel
+ serverLabel := serverHandshakeTrafficLabel
+ if isDraft21(c.wireVersion) {
+ clientLabel = clientHandshakeTrafficLabelDraft21
+ serverLabel = serverHandshakeTrafficLabelDraft21
+ }
+
// Switch to handshake traffic keys.
- serverHandshakeTrafficSecret := hs.finishedHash.deriveSecret(serverHandshakeTrafficLabel)
+ serverHandshakeTrafficSecret := hs.finishedHash.deriveSecret(serverLabel)
c.useOutTrafficSecret(c.wireVersion, hs.suite, serverHandshakeTrafficSecret)
// Derive handshake traffic read key, but don't switch yet.
- clientHandshakeTrafficSecret := hs.finishedHash.deriveSecret(clientHandshakeTrafficLabel)
+ clientHandshakeTrafficSecret := hs.finishedHash.deriveSecret(clientLabel)
// Send EncryptedExtensions.
hs.writeServerHash(encryptedExtensions.marshal())
@@ -779,9 +812,11 @@
if config.ClientAuth >= RequestClientCert {
// Request a client certificate
certReq := &certificateRequestMsg{
- hasSignatureAlgorithm: true,
+ vers: c.wireVersion,
+ hasSignatureAlgorithm: !config.Bugs.OmitCertificateRequestAlgorithms,
hasRequestContext: true,
requestContext: config.Bugs.SendRequestContext,
+ customExtension: config.Bugs.SendCustomCertificateRequest,
}
if !config.Bugs.NoSignatureAlgorithms {
certReq.signatureAlgorithms = config.verifySignatureAlgorithms()
@@ -896,10 +931,21 @@
// The various secrets do not incorporate the client's final leg, so
// derive them now before updating the handshake context.
+ hs.finishedHash.nextSecret()
hs.finishedHash.addEntropy(hs.finishedHash.zeroSecret())
- clientTrafficSecret := hs.finishedHash.deriveSecret(clientApplicationTrafficLabel)
- serverTrafficSecret := hs.finishedHash.deriveSecret(serverApplicationTrafficLabel)
- c.exporterSecret = hs.finishedHash.deriveSecret(exporterLabel)
+
+ clientLabel = clientApplicationTrafficLabel
+ serverLabel = serverApplicationTrafficLabel
+ exportLabel := exporterLabel
+ if isDraft21(c.wireVersion) {
+ clientLabel = clientApplicationTrafficLabelDraft21
+ serverLabel = serverApplicationTrafficLabelDraft21
+ exportLabel = exporterLabelDraft21
+ }
+
+ clientTrafficSecret := hs.finishedHash.deriveSecret(clientLabel)
+ serverTrafficSecret := hs.finishedHash.deriveSecret(serverLabel)
+ c.exporterSecret = hs.finishedHash.deriveSecret(exportLabel)
// Switch to application data keys on write. In particular, any alerts
// from the client certificate are sent over these keys.
@@ -912,13 +958,27 @@
}
}
- // Read end_of_early_data alert.
+ // Read end_of_early_data.
if encryptedExtensions.extensions.hasEarlyData {
- if err := c.readRecord(recordTypeAlert); err != errEndOfEarlyDataAlert {
- if err == nil {
- panic("readRecord(recordTypeAlert) returned nil")
+ if isDraft21(c.wireVersion) {
+ msg, err := c.readHandshake()
+ if err != nil {
+ return err
}
- return err
+
+ endOfEarlyData, ok := msg.(*endOfEarlyDataMsg)
+ if !ok {
+ c.sendAlert(alertUnexpectedMessage)
+ return unexpectedMessageError(endOfEarlyData, msg)
+ }
+ hs.writeClientHash(endOfEarlyData.marshal())
+ } else {
+ if err := c.readRecord(recordTypeAlert); err != errEndOfEarlyDataAlert {
+ if err == nil {
+ panic("readRecord(recordTypeAlert) returned nil")
+ }
+ return err
+ }
}
}
@@ -1040,14 +1100,20 @@
}
c.cipherSuite = hs.suite
- c.resumptionSecret = hs.finishedHash.deriveSecret(resumptionLabel)
+
+ resumeLabel := resumptionLabel
+ if isDraft21(c.wireVersion) {
+ resumeLabel = resumptionLabelDraft21
+ }
+
+ c.resumptionSecret = hs.finishedHash.deriveSecret(resumeLabel)
// TODO(davidben): Allow configuring the number of tickets sent for
// testing.
if !c.config.SessionTicketsDisabled && foundKEMode {
ticketCount := 2
for i := 0; i < ticketCount; i++ {
- c.SendNewSessionTicket()
+ c.SendNewSessionTicket([]byte{byte(i)})
}
}
return nil
@@ -1408,7 +1474,7 @@
hs.hello.extensions.ocspStapling = true
}
- hs.finishedHash = newFinishedHash(c.vers, hs.suite)
+ hs.finishedHash = newFinishedHash(c.wireVersion, c.isDTLS, hs.suite)
hs.finishedHash.discardHandshakeBuffer()
hs.writeClientHash(hs.clientHello.marshal())
hs.writeServerHash(hs.hello.marshal())
@@ -1460,7 +1526,7 @@
}
}
- hs.finishedHash = newFinishedHash(c.vers, hs.suite)
+ hs.finishedHash = newFinishedHash(c.wireVersion, c.isDTLS, hs.suite)
hs.writeClientHash(hs.clientHello.marshal())
hs.writeServerHash(hs.hello.marshal())
@@ -1514,6 +1580,7 @@
if config.ClientAuth >= RequestClientCert {
// Request a client certificate
certReq := &certificateRequestMsg{
+ vers: c.wireVersion,
certificateTypes: config.ClientCertificateTypes,
}
if certReq.certificateTypes == nil {
@@ -1787,6 +1854,8 @@
}
m := new(newSessionTicketMsg)
+ m.vers = c.wireVersion
+ m.isDTLS = c.isDTLS
if c.config.Bugs.SendTicketLifetime != 0 {
m.ticketLifetime = uint32(c.config.Bugs.SendTicketLifetime / time.Second)
}
@@ -2000,9 +2069,6 @@
if version < VersionTLS12 && candidate.flags&suiteTLS12 != 0 {
continue
}
- if c.isDTLS && candidate.flags&suiteNoDTLS != 0 {
- continue
- }
return candidate
}
}
@@ -2025,7 +2091,7 @@
return val&0x0f0f == 0x0a0a && val&0xff == val>>8
}
-func verifyPSKBinder(clientHello *clientHelloMsg, sessionState *sessionState, binderToVerify, transcript []byte) error {
+func verifyPSKBinder(version uint16, clientHello *clientHelloMsg, sessionState *sessionState, binderToVerify, firstClientHello, helloRetryRequest []byte) error {
binderLen := 2
for _, binder := range clientHello.pskBinders {
binderLen += 1 + len(binder)
@@ -2038,7 +2104,11 @@
return errors.New("tls: Unknown cipher suite for PSK in session")
}
- binder := computePSKBinder(sessionState.masterSecret, resumptionPSKBinderLabel, pskCipherSuite, transcript, truncatedHello)
+ binderLabel := resumptionPSKBinderLabel
+ if isDraft21(version) {
+ binderLabel = resumptionPSKBinderLabelDraft21
+ }
+ binder := computePSKBinder(sessionState.masterSecret, version, binderLabel, pskCipherSuite, firstClientHello, helloRetryRequest, truncatedHello)
if !bytes.Equal(binder, binderToVerify) {
return errors.New("tls: PSK binder does not verify")
}
diff --git a/src/ssl/test/runner/prf.go b/src/ssl/test/runner/prf.go
index cfc383d..6fa3c4c 100644
--- a/src/ssl/test/runner/prf.go
+++ b/src/ssl/test/runner/prf.go
@@ -180,9 +180,14 @@
return
}
-func newFinishedHash(version uint16, cipherSuite *cipherSuite) finishedHash {
+func newFinishedHash(wireVersion uint16, isDTLS bool, cipherSuite *cipherSuite) finishedHash {
var ret finishedHash
+ version, ok := wireToVersion(wireVersion, isDTLS)
+ if !ok {
+ panic("unknown version")
+ }
+
if version >= VersionTLS12 {
ret.hash = cipherSuite.hash()
@@ -207,6 +212,7 @@
ret.buffer = []byte{}
ret.version = version
+ ret.wireVersion = wireVersion
return ret
}
@@ -226,13 +232,28 @@
// full buffer is required.
buffer []byte
- version uint16
- prf func(result, secret, label, seed []byte)
+ version uint16
+ wireVersion uint16
+ prf func(result, secret, label, seed []byte)
// secret, in TLS 1.3, is the running input secret.
secret []byte
}
+func (h *finishedHash) UpdateForHelloRetryRequest() (err error) {
+ data := newByteBuilder()
+ data.addU8(typeMessageHash)
+ data.addU24(h.hash.Size())
+ data.addBytes(h.Sum())
+ h.client = h.hash.New()
+ h.server = h.hash.New()
+ if h.buffer != nil {
+ h.buffer = []byte{}
+ }
+ h.Write(data.finish())
+ return nil
+}
+
func (h *finishedHash) Write(msg []byte) (n int, err error) {
h.client.Write(msg)
h.server.Write(msg)
@@ -307,7 +328,7 @@
return out
}
- clientFinishedKey := hkdfExpandLabel(h.hash, baseKey, finishedLabel, nil, h.hash.Size())
+ clientFinishedKey := hkdfExpandLabel(h.hash, h.wireVersion, baseKey, finishedLabel, nil, h.hash.Size())
finishedHMAC := hmac.New(h.hash.New, clientFinishedKey)
finishedHMAC.Write(h.appendContextHashes(nil))
return finishedHMAC.Sum(nil)
@@ -326,7 +347,7 @@
return out
}
- serverFinishedKey := hkdfExpandLabel(h.hash, baseKey, finishedLabel, nil, h.hash.Size())
+ serverFinishedKey := hkdfExpandLabel(h.hash, h.wireVersion, baseKey, finishedLabel, nil, h.hash.Size())
finishedHMAC := hmac.New(h.hash.New, serverFinishedKey)
finishedHMAC.Write(h.appendContextHashes(nil))
return finishedHMAC.Sum(nil)
@@ -374,20 +395,33 @@
h.secret = hkdfExtract(h.hash.New, h.secret, ikm)
}
+func (h *finishedHash) nextSecret() {
+ if isDraft21(h.wireVersion) {
+ derivedLabel := []byte("derived")
+ h.secret = hkdfExpandLabel(h.hash, h.wireVersion, h.secret, derivedLabel, h.hash.New().Sum(nil), h.hash.Size())
+ }
+}
+
// hkdfExpandLabel implements TLS 1.3's HKDF-Expand-Label function, as defined
// in section 7.1 of draft-ietf-tls-tls13-16.
-func hkdfExpandLabel(hash crypto.Hash, secret, label, hashValue []byte, length int) []byte {
+func hkdfExpandLabel(hash crypto.Hash, version uint16, secret, label, hashValue []byte, length int) []byte {
if len(label) > 255 || len(hashValue) > 255 {
panic("hkdfExpandLabel: label or hashValue too long")
}
- hkdfLabel := make([]byte, 3+9+len(label)+1+len(hashValue))
+
+ versionLabel := []byte("TLS 1.3, ")
+ if isDraft21(version) {
+ versionLabel = []byte("tls13 ")
+ }
+
+ hkdfLabel := make([]byte, 3+len(versionLabel)+len(label)+1+len(hashValue))
x := hkdfLabel
x[0] = byte(length >> 8)
x[1] = byte(length)
- x[2] = byte(9 + len(label))
+ x[2] = byte(len(versionLabel) + len(label))
x = x[3:]
- copy(x, []byte("TLS 1.3, "))
- x = x[9:]
+ copy(x, versionLabel)
+ x = x[len(versionLabel):]
copy(x, label)
x = x[len(label):]
x[0] = byte(len(hashValue))
@@ -414,12 +448,25 @@
applicationTrafficLabel = []byte("application traffic secret")
exporterLabel = []byte("exporter master secret")
resumptionLabel = []byte("resumption master secret")
+
+ externalPSKBinderLabelDraft21 = []byte("ext binder")
+ resumptionPSKBinderLabelDraft21 = []byte("res binder")
+ earlyTrafficLabelDraft21 = []byte("c e traffic")
+ clientHandshakeTrafficLabelDraft21 = []byte("c hs traffic")
+ serverHandshakeTrafficLabelDraft21 = []byte("s hs traffic")
+ clientApplicationTrafficLabelDraft21 = []byte("c ap traffic")
+ serverApplicationTrafficLabelDraft21 = []byte("s ap traffic")
+ applicationTrafficLabelDraft21 = []byte("traffic upd")
+ exporterLabelDraft21 = []byte("exp master")
+ resumptionLabelDraft21 = []byte("res master")
+
+ resumptionPSKLabel = []byte("resumption")
)
// deriveSecret implements TLS 1.3's Derive-Secret function, as defined in
// section 7.1 of draft ietf-tls-tls13-16.
func (h *finishedHash) deriveSecret(label []byte) []byte {
- return hkdfExpandLabel(h.hash, h.secret, label, h.appendContextHashes(nil), h.hash.Size())
+ return hkdfExpandLabel(h.hash, h.wireVersion, h.secret, label, h.appendContextHashes(nil), h.hash.Size())
}
// The following are context strings for CertificateVerify in TLS 1.3.
@@ -458,21 +505,34 @@
// deriveTrafficAEAD derives traffic keys and constructs an AEAD given a traffic
// secret.
func deriveTrafficAEAD(version uint16, suite *cipherSuite, secret []byte, side trafficDirection) interface{} {
- key := hkdfExpandLabel(suite.hash(), secret, keyTLS13, nil, suite.keyLen)
- iv := hkdfExpandLabel(suite.hash(), secret, ivTLS13, nil, suite.ivLen(version))
+ key := hkdfExpandLabel(suite.hash(), version, secret, keyTLS13, nil, suite.keyLen)
+ iv := hkdfExpandLabel(suite.hash(), version, secret, ivTLS13, nil, suite.ivLen(version))
return suite.aead(version, key, iv)
}
-func updateTrafficSecret(hash crypto.Hash, secret []byte) []byte {
- return hkdfExpandLabel(hash, secret, applicationTrafficLabel, nil, hash.Size())
+func updateTrafficSecret(hash crypto.Hash, version uint16, secret []byte) []byte {
+ trafficLabel := applicationTrafficLabel
+ if isDraft21(version) {
+ trafficLabel = applicationTrafficLabelDraft21
+ }
+ return hkdfExpandLabel(hash, version, secret, trafficLabel, nil, hash.Size())
}
-func computePSKBinder(psk, label []byte, cipherSuite *cipherSuite, transcript, truncatedHello []byte) []byte {
- finishedHash := newFinishedHash(VersionTLS13, cipherSuite)
+func computePSKBinder(psk []byte, version uint16, label []byte, cipherSuite *cipherSuite, clientHello, helloRetryRequest, truncatedHello []byte) []byte {
+ finishedHash := newFinishedHash(version, false, cipherSuite)
finishedHash.addEntropy(psk)
binderKey := finishedHash.deriveSecret(label)
- finishedHash.Write(transcript)
+ finishedHash.Write(clientHello)
+ if isDraft21(version) && len(helloRetryRequest) != 0 {
+ finishedHash.UpdateForHelloRetryRequest()
+ }
+ finishedHash.Write(helloRetryRequest)
finishedHash.Write(truncatedHello)
return finishedHash.clientSum(binderKey)
}
+
+func deriveSessionPSK(suite *cipherSuite, version uint16, masterSecret []byte, nonce []byte) []byte {
+ hash := suite.hash()
+ return hkdfExpandLabel(hash, version, masterSecret, resumptionPSKLabel, nonce, hash.Size())
+}
diff --git a/src/ssl/test/runner/runner.go b/src/ssl/test/runner/runner.go
index d34eaa6..ce50fa8 100644
--- a/src/ssl/test/runner/runner.go
+++ b/src/ssl/test/runner/runner.go
@@ -1305,6 +1305,13 @@
tls13Variant: TLS13Default,
},
{
+ name: "TLS13Draft21",
+ version: VersionTLS13,
+ excludeFlag: "-no-tls13",
+ versionWire: tls13Draft21Version,
+ tls13Variant: TLS13Draft21,
+ },
+ {
name: "TLS13Experiment",
version: VersionTLS13,
excludeFlag: "-no-tls13",
@@ -1394,10 +1401,6 @@
return strings.HasPrefix(suiteName, "AEAD-")
}
-func isDTLSCipher(suiteName string) bool {
- return !hasComponent(suiteName, "RC4") && !hasComponent(suiteName, "NULL")
-}
-
func bigFromHex(hex string) *big.Int {
ret, ok := new(big.Int).SetString(hex, 16)
if !ok {
@@ -2948,10 +2951,6 @@
shouldClientFail = true
shouldServerFail = true
}
- if !isDTLSCipher(suite.name) && protocol == dtls {
- shouldClientFail = true
- shouldServerFail = true
- }
var sendCipherSuite uint16
var expectedServerError, expectedClientError string
@@ -3138,7 +3137,7 @@
},
},
shouldFail: true,
- expectedError: ":UNKNOWN_CIPHER_RETURNED:",
+ expectedError: ":WRONG_CIPHER_RETURNED:",
})
// The server must be tolerant to bogus ciphers.
@@ -3791,6 +3790,25 @@
"-use-client-ca-list", "<NULL>",
},
})
+
+ // Test that an empty client CA list doesn't send a CA extension.
+ testCases = append(testCases, testCase{
+ testType: serverTest,
+ name: "TLS13Draft21-Empty-Client-CA-List",
+ config: Config{
+ MaxVersion: VersionTLS13,
+ Certificates: []Certificate{rsaCertificate},
+ Bugs: ProtocolBugs{
+ ExpectNoCertificateAuthoritiesExtension: true,
+ },
+ },
+ tls13Variant: TLS13Draft21,
+ flags: []string{
+ "-require-any-client-certificate",
+ "-use-client-ca-list", "<EMPTY>",
+ },
+ })
+
}
func addExtendedMasterSecretTests() {
@@ -4161,7 +4179,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-accept-early-data",
"-on-resume-shim-writes-first",
},
@@ -4190,7 +4208,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-accept-early-data",
"-on-resume-read-with-unfinished-write",
"-on-resume-shim-writes-first",
@@ -4219,7 +4237,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
"-on-resume-read-with-unfinished-write",
"-on-resume-shim-writes-first",
@@ -5153,14 +5171,13 @@
}
// When running and shim have different TLS 1.3 variants enabled,
// shim clients are expected to fall back to TLS 1.2, while shim
- // servers support both variants when enabled when the experiment is
- // enabled.
+ // servers support multiple variants.
expectedServerVersion := expectedVersion
expectedClientVersion := expectedVersion
if expectedVersion == VersionTLS13 && runnerVers.tls13Variant != shimVers.tls13Variant {
expectedClientVersion = VersionTLS12
expectedServerVersion = VersionTLS12
- if shimVers.tls13Variant != TLS13Default {
+ if shimVers.tls13Variant != TLS13Default && runnerVers.tls13Variant != TLS13Draft21 {
expectedServerVersion = VersionTLS13
}
}
@@ -9189,7 +9206,7 @@
flags: []string{
"-enable-client-custom-extension",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
},
})
@@ -9208,7 +9225,7 @@
flags: []string{
"-enable-client-custom-extension",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-accept-early-data",
},
})
@@ -9229,7 +9246,7 @@
flags: []string{
"-enable-client-custom-extension",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
},
})
@@ -9260,7 +9277,7 @@
flags: []string{
"-enable-client-custom-extension",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
},
})
@@ -9282,7 +9299,7 @@
flags: []string{
"-enable-server-custom-extension",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
},
})
@@ -10044,7 +10061,7 @@
},
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
},
})
@@ -10065,7 +10082,7 @@
MaxVersion: VersionTLS13,
MaxEarlyDataSize: 16384,
Bugs: ProtocolBugs{
- DuplicateTicketEarlyDataInfo: true,
+ DuplicateTicketEarlyData: true,
},
},
shouldFail: true,
@@ -10079,7 +10096,7 @@
config: Config{
MaxVersion: VersionTLS13,
Bugs: ProtocolBugs{
- ExpectTicketEarlyDataInfo: true,
+ ExpectTicketEarlyData: true,
},
},
flags: []string{
@@ -10964,7 +10981,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-accept-early-data",
"-on-resume-shim-writes-first",
},
@@ -10988,7 +11005,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
"-on-resume-shim-writes-first",
},
@@ -11229,6 +11246,49 @@
})
testCases = append(testCases, testCase{
+ name: "TLS13Draft21-HelloRetryRequest-CipherChange",
+ config: Config{
+ MaxVersion: VersionTLS13,
+ // P-384 requires HelloRetryRequest in BoringSSL.
+ CurvePreferences: []CurveID{CurveP384},
+ Bugs: ProtocolBugs{
+ SendCipherSuite: TLS_AES_128_GCM_SHA256,
+ SendHelloRetryRequestCipherSuite: TLS_CHACHA20_POLY1305_SHA256,
+ },
+ },
+ tls13Variant: TLS13Draft21,
+ shouldFail: true,
+ expectedError: ":WRONG_CIPHER_RETURNED:",
+ })
+
+ // Test that the client does not offer a PSK in the second ClientHello if the
+ // HelloRetryRequest is incompatible with it.
+ testCases = append(testCases, testCase{
+ testType: clientTest,
+ name: "TLS13Draft21-HelloRetryRequest-NonResumableCipher",
+ config: Config{
+ MaxVersion: VersionTLS13,
+ CipherSuites: []uint16{
+ TLS_AES_128_GCM_SHA256,
+ },
+ },
+ resumeConfig: &Config{
+ MaxVersion: VersionTLS13,
+ // P-384 requires HelloRetryRequest in BoringSSL.
+ CurvePreferences: []CurveID{CurveP384},
+ Bugs: ProtocolBugs{
+ ExpectNoTLS13PSKAfterHRR: true,
+ },
+ CipherSuites: []uint16{
+ TLS_AES_256_GCM_SHA384,
+ },
+ },
+ tls13Variant: TLS13Draft21,
+ resumeSession: true,
+ expectResumeRejected: true,
+ })
+
+ testCases = append(testCases, testCase{
name: "DisabledCurve-HelloRetryRequest",
config: Config{
MaxVersion: VersionTLS13,
@@ -11454,6 +11514,42 @@
})
testCases = append(testCases, testCase{
+ name: "TLS13-UnknownInCertificateRequest",
+ config: Config{
+ MaxVersion: VersionTLS13,
+ MinVersion: VersionTLS13,
+ ClientAuth: RequireAnyClientCert,
+ Bugs: ProtocolBugs{
+ SendCustomCertificateRequest: 0x1212,
+ },
+ },
+ tls13Variant: TLS13Draft21,
+ flags: []string{
+ "-cert-file", path.Join(*resourceDir, rsaCertificateFile),
+ "-key-file", path.Join(*resourceDir, rsaKeyFile),
+ },
+ })
+
+ testCases = append(testCases, testCase{
+ name: "TLS13-MissingSignatureAlgorithmsInCertificateRequest",
+ config: Config{
+ MaxVersion: VersionTLS13,
+ MinVersion: VersionTLS13,
+ ClientAuth: RequireAnyClientCert,
+ Bugs: ProtocolBugs{
+ OmitCertificateRequestAlgorithms: true,
+ },
+ },
+ tls13Variant: TLS13Draft21,
+ flags: []string{
+ "-cert-file", path.Join(*resourceDir, rsaCertificateFile),
+ "-key-file", path.Join(*resourceDir, rsaKeyFile),
+ },
+ shouldFail: true,
+ expectedError: ":DECODE_ERROR:",
+ })
+
+ testCases = append(testCases, testCase{
testType: serverTest,
name: "TLS13-TrailingKeyShareData",
config: Config{
@@ -11532,7 +11628,7 @@
expectResumeRejected: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
"-on-resume-shim-writes-first",
"-on-initial-expect-peer-cert-file", path.Join(*resourceDir, rsaCertificateFile),
@@ -11560,7 +11656,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
},
})
@@ -11584,7 +11680,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
},
shouldFail: true,
expectedError: ":UNEXPECTED_EXTENSION:",
@@ -11605,7 +11701,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
},
shouldFail: true,
expectedError: ":WRONG_VERSION_ON_EARLY_DATA:",
@@ -11631,7 +11727,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
},
shouldFail: true,
@@ -11664,7 +11760,7 @@
flags: []string{
"-advertise-alpn", "\x03foo\x03bar",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
"-on-initial-expect-alpn", "foo",
"-on-resume-expect-alpn", "foo",
@@ -11690,7 +11786,7 @@
flags: []string{
"-advertise-alpn", "\x03foo\x03bar",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
"-on-initial-expect-alpn", "",
"-on-resume-expect-alpn", "",
@@ -11717,7 +11813,7 @@
flags: []string{
"-advertise-alpn", "\x03foo\x03bar",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-reject-early-data",
"-on-initial-expect-alpn", "foo",
"-on-resume-expect-alpn", "foo",
@@ -11749,7 +11845,7 @@
flags: []string{
"-advertise-alpn", "\x03foo\x03bar",
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-on-initial-expect-alpn", "foo",
"-on-resume-expect-alpn", "foo",
"-on-retry-expect-alpn", "bar",
@@ -11771,7 +11867,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-no-offer-early-data",
"-on-initial-advertise-alpn", "\x03foo",
"-on-resume-advertise-alpn", "\x03bar",
@@ -11892,7 +11988,7 @@
expectedError: ":UNEXPECTED_EXTENSION_ON_EARLY_DATA:",
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-send-channel-id", path.Join(*resourceDir, channelIDKeyFile),
},
})
@@ -11914,7 +12010,7 @@
expectChannelID: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-send-channel-id", path.Join(*resourceDir, channelIDKeyFile),
"-expect-reject-early-data",
},
@@ -11932,7 +12028,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-send-channel-id", path.Join(*resourceDir, channelIDKeyFile),
"-expect-accept-early-data",
},
@@ -12038,7 +12134,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-accept-early-data",
"-expect-version", strconv.Itoa(VersionTLS13),
},
@@ -12063,7 +12159,7 @@
resumeSession: true,
flags: []string{
"-enable-early-data",
- "-expect-early-data-info",
+ "-expect-ticket-supports-early-data",
"-expect-accept-early-data",
},
shouldFail: true,
@@ -12096,6 +12192,34 @@
expectedError: ":DIGEST_CHECK_FAILED:",
expectedLocalError: "remote error: error decrypting message",
})
+
+ testCases = append(testCases, testCase{
+ testType: serverTest,
+ name: "TLS13Draft21-Server-NonEmptyEndOfEarlyData",
+ config: Config{
+ MaxVersion: VersionTLS13,
+ MaxEarlyDataSize: 16384,
+ },
+ resumeConfig: &Config{
+ MaxVersion: VersionTLS13,
+ MaxEarlyDataSize: 16384,
+ Bugs: ProtocolBugs{
+ SendEarlyData: [][]byte{{1, 2, 3, 4}},
+ ExpectEarlyDataAccepted: true,
+ NonEmptyEndOfEarlyData: true,
+ },
+ },
+ resumeSession: true,
+ flags: []string{
+ "-enable-early-data",
+ "-expect-ticket-supports-early-data",
+ "-expect-accept-early-data",
+ },
+ tls13Variant: TLS13Draft21,
+ shouldFail: true,
+ expectedError: ":DECODE_ERROR:",
+ })
+
testCases = append(testCases, testCase{
testType: serverTest,
name: "TLS13-ServerSkipCertificateVerify",
diff --git a/src/ssl/test/test_config.cc b/src/ssl/test/test_config.cc
index 3354851..2d9f725 100644
--- a/src/ssl/test/test_config.cc
+++ b/src/ssl/test/test_config.cc
@@ -81,7 +81,8 @@
{ "-tls-unique", &TestConfig::tls_unique },
{ "-expect-ticket-renewal", &TestConfig::expect_ticket_renewal },
{ "-expect-no-session", &TestConfig::expect_no_session },
- { "-expect-early-data-info", &TestConfig::expect_early_data_info },
+ { "-expect-ticket-supports-early-data",
+ &TestConfig::expect_ticket_supports_early_data },
{ "-use-ticket-callback", &TestConfig::use_ticket_callback },
{ "-renew-ticket", &TestConfig::renew_ticket },
{ "-enable-early-data", &TestConfig::enable_early_data },
diff --git a/src/ssl/test/test_config.h b/src/ssl/test/test_config.h
index b96d9e5..b742f94 100644
--- a/src/ssl/test/test_config.h
+++ b/src/ssl/test/test_config.h
@@ -87,7 +87,7 @@
bool tls_unique = false;
bool expect_ticket_renewal = false;
bool expect_no_session = false;
- bool expect_early_data_info = false;
+ bool expect_ticket_supports_early_data = false;
bool expect_accept_early_data = false;
bool expect_reject_early_data = false;
bool expect_no_offer_early_data = false;
diff --git a/src/ssl/tls13_client.cc b/src/ssl/tls13_client.cc
index b6307ee..9c09309 100644
--- a/src/ssl/tls13_client.cc
+++ b/src/ssl/tls13_client.cc
@@ -63,8 +63,10 @@
}
CBS body = msg.body, extensions;
- uint16_t server_version;
+ uint16_t server_version, cipher_suite = 0;
if (!CBS_get_u16(&body, &server_version) ||
+ (ssl_is_draft21(ssl->version) &&
+ !CBS_get_u16(&body, &cipher_suite)) ||
!CBS_get_u16_length_prefixed(&body, &extensions) ||
// HelloRetryRequest may not be empty.
CBS_len(&extensions) == 0 ||
@@ -74,6 +76,26 @@
return ssl_hs_error;
}
+ if (ssl_is_draft21(ssl->version)) {
+ const SSL_CIPHER *cipher = SSL_get_cipher_by_value(cipher_suite);
+ // Check if the cipher is a TLS 1.3 cipher.
+ if (cipher == NULL ||
+ SSL_CIPHER_get_min_version(cipher) > ssl_protocol_version(ssl) ||
+ SSL_CIPHER_get_max_version(cipher) < ssl_protocol_version(ssl)) {
+ OPENSSL_PUT_ERROR(SSL, SSL_R_WRONG_CIPHER_RETURNED);
+ ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_ILLEGAL_PARAMETER);
+ return ssl_hs_error;
+ }
+
+ hs->new_cipher = cipher;
+
+ if (!hs->transcript.InitHash(ssl_protocol_version(ssl), hs->new_cipher) ||
+ !hs->transcript.UpdateForHelloRetryRequest()) {
+ return ssl_hs_error;
+ }
+ }
+
+
bool have_cookie, have_key_share;
CBS cookie, key_share;
const SSL_EXTENSION_TYPE ext_types[] = {
@@ -206,16 +228,20 @@
OPENSSL_memcpy(ssl->s3->server_random, CBS_data(&server_random),
SSL3_RANDOM_SIZE);
+ // Check if the cipher is a TLS 1.3 cipher.
const SSL_CIPHER *cipher = SSL_get_cipher_by_value(cipher_suite);
- if (cipher == NULL) {
- OPENSSL_PUT_ERROR(SSL, SSL_R_UNKNOWN_CIPHER_RETURNED);
+ if (cipher == nullptr ||
+ SSL_CIPHER_get_min_version(cipher) > ssl_protocol_version(ssl) ||
+ SSL_CIPHER_get_max_version(cipher) < ssl_protocol_version(ssl)) {
+ OPENSSL_PUT_ERROR(SSL, SSL_R_WRONG_CIPHER_RETURNED);
ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_ILLEGAL_PARAMETER);
return ssl_hs_error;
}
- // Check if the cipher is a TLS 1.3 cipher.
- if (SSL_CIPHER_get_min_version(cipher) > ssl_protocol_version(ssl) ||
- SSL_CIPHER_get_max_version(cipher) < ssl_protocol_version(ssl)) {
+ // Check that the cipher matches the one in the HelloRetryRequest.
+ if (ssl_is_draft21(ssl->version) &&
+ hs->received_hello_retry_request &&
+ hs->new_cipher != cipher) {
OPENSSL_PUT_ERROR(SSL, SSL_R_WRONG_CIPHER_RETURNED);
ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_ILLEGAL_PARAMETER);
return ssl_hs_error;
@@ -302,18 +328,16 @@
hs->new_session->cipher = cipher;
hs->new_cipher = cipher;
- // The PRF hash is now known. Set up the key schedule.
- if (!tls13_init_key_schedule(hs)) {
- return ssl_hs_error;
- }
+ size_t hash_len =
+ EVP_MD_size(ssl_get_handshake_digest(ssl_protocol_version(ssl), cipher));
- // Incorporate the PSK into the running secret.
+ // Set up the key schedule and incorporate the PSK into the running secret.
if (ssl->s3->session_reused) {
- if (!tls13_advance_key_schedule(hs, hs->new_session->master_key,
- hs->new_session->master_key_length)) {
+ if (!tls13_init_key_schedule(hs, hs->new_session->master_key,
+ hs->new_session->master_key_length)) {
return ssl_hs_error;
}
- } else if (!tls13_advance_key_schedule(hs, kZeroes, hs->hash_len)) {
+ } else if (!tls13_init_key_schedule(hs, kZeroes, hash_len)) {
return ssl_hs_error;
}
@@ -445,37 +469,81 @@
return ssl_hs_ok;
}
- CBS body = msg.body, context, supported_signature_algorithms;
- if (!CBS_get_u8_length_prefixed(&body, &context) ||
- // The request context is always empty during the handshake.
- CBS_len(&context) != 0 ||
- !CBS_get_u16_length_prefixed(&body, &supported_signature_algorithms) ||
- CBS_len(&supported_signature_algorithms) == 0 ||
- !tls1_parse_peer_sigalgs(hs, &supported_signature_algorithms)) {
- ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_DECODE_ERROR);
- OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
- return ssl_hs_error;
- }
- uint8_t alert = SSL_AD_DECODE_ERROR;
- UniquePtr<STACK_OF(CRYPTO_BUFFER)> ca_names =
- ssl_parse_client_CA_list(ssl, &alert, &body);
- if (!ca_names) {
- ssl_send_alert(ssl, SSL3_AL_FATAL, alert);
- return ssl_hs_error;
- }
+ if (ssl_is_draft21(ssl->version)) {
+ bool have_sigalgs = false, have_ca = false;
+ CBS sigalgs, ca;
+ const SSL_EXTENSION_TYPE ext_types[] = {
+ {TLSEXT_TYPE_signature_algorithms, &have_sigalgs, &sigalgs},
+ {TLSEXT_TYPE_certificate_authorities, &have_ca, &ca},
+ };
- // Ignore extensions.
- CBS extensions;
- if (!CBS_get_u16_length_prefixed(&body, &extensions) ||
- CBS_len(&body) != 0) {
- ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_DECODE_ERROR);
- OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
- return ssl_hs_error;
+ CBS body = msg.body, context, extensions, supported_signature_algorithms;
+ uint8_t alert = SSL_AD_DECODE_ERROR;
+ if (!CBS_get_u8_length_prefixed(&body, &context) ||
+ // The request context is always empty during the handshake.
+ CBS_len(&context) != 0 ||
+ !CBS_get_u16_length_prefixed(&body, &extensions) ||
+ CBS_len(&body) != 0 ||
+ !ssl_parse_extensions(&extensions, &alert, ext_types,
+ OPENSSL_ARRAY_SIZE(ext_types),
+ 1 /* accept unknown */) ||
+ (have_ca && CBS_len(&ca) == 0) ||
+ !have_sigalgs ||
+ !CBS_get_u16_length_prefixed(&sigalgs,
+ &supported_signature_algorithms) ||
+ CBS_len(&supported_signature_algorithms) == 0 ||
+ !tls1_parse_peer_sigalgs(hs, &supported_signature_algorithms)) {
+ ssl_send_alert(ssl, SSL3_AL_FATAL, alert);
+ OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
+ return ssl_hs_error;
+ }
+
+ if (have_ca) {
+ hs->ca_names = ssl_parse_client_CA_list(ssl, &alert, &ca);
+ if (!hs->ca_names) {
+ ssl_send_alert(ssl, SSL3_AL_FATAL, alert);
+ return ssl_hs_error;
+ }
+ } else {
+ hs->ca_names.reset(sk_CRYPTO_BUFFER_new_null());
+ if (!hs->ca_names) {
+ OPENSSL_PUT_ERROR(SSL, ERR_R_MALLOC_FAILURE);
+ ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_INTERNAL_ERROR);
+ return ssl_hs_error;
+ }
+ }
+ } else {
+ CBS body = msg.body, context, supported_signature_algorithms;
+ if (!CBS_get_u8_length_prefixed(&body, &context) ||
+ // The request context is always empty during the handshake.
+ CBS_len(&context) != 0 ||
+ !CBS_get_u16_length_prefixed(&body, &supported_signature_algorithms) ||
+ CBS_len(&supported_signature_algorithms) == 0 ||
+ !tls1_parse_peer_sigalgs(hs, &supported_signature_algorithms)) {
+ ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_DECODE_ERROR);
+ OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
+ return ssl_hs_error;
+ }
+
+ uint8_t alert = SSL_AD_DECODE_ERROR;
+ hs->ca_names = ssl_parse_client_CA_list(ssl, &alert, &body);
+ if (!hs->ca_names) {
+ ssl_send_alert(ssl, SSL3_AL_FATAL, alert);
+ return ssl_hs_error;
+ }
+
+ // Ignore extensions.
+ CBS extensions;
+ if (!CBS_get_u16_length_prefixed(&body, &extensions) ||
+ CBS_len(&body) != 0) {
+ ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_DECODE_ERROR);
+ OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
+ return ssl_hs_error;
+ }
}
hs->cert_request = true;
- hs->ca_names = std::move(ca_names);
ssl->ctx->x509_method->hs_flush_cached_ca_names(hs);
if (!ssl_hash_message(hs, msg)) {
@@ -557,9 +625,19 @@
if (ssl->early_data_accepted) {
hs->can_early_write = false;
- if (!ssl->method->add_alert(ssl, SSL3_AL_WARNING,
- TLS1_AD_END_OF_EARLY_DATA)) {
- return ssl_hs_error;
+ if (ssl_is_draft21(ssl->version)) {
+ ScopedCBB cbb;
+ CBB body;
+ if (!ssl->method->init_message(ssl, cbb.get(), &body,
+ SSL3_MT_END_OF_EARLY_DATA) ||
+ !ssl_add_message_cbb(ssl, cbb.get())) {
+ return ssl_hs_error;
+ }
+ } else {
+ if (!ssl->method->add_alert(ssl, SSL3_AL_WARNING,
+ TLS1_AD_END_OF_EARLY_DATA)) {
+ return ssl_hs_error;
+ }
}
}
@@ -790,9 +868,11 @@
ssl_session_rebase_time(ssl, session.get());
uint32_t server_timeout;
- CBS body = msg.body, ticket, extensions;
+ CBS body = msg.body, ticket_nonce, ticket, extensions;
if (!CBS_get_u32(&body, &server_timeout) ||
!CBS_get_u32(&body, &session->ticket_age_add) ||
+ (ssl_is_draft21(ssl->version) &&
+ !CBS_get_u8_length_prefixed(&body, &ticket_nonce)) ||
!CBS_get_u16_length_prefixed(&body, &ticket) ||
!CBS_stow(&ticket, &session->tlsext_tick, &session->tlsext_ticklen) ||
!CBS_get_u16_length_prefixed(&body, &extensions) ||
@@ -808,12 +888,18 @@
session->timeout = server_timeout;
}
+ if (!tls13_derive_session_psk(session.get(), ticket_nonce)) {
+ return 0;
+ }
+
// Parse out the extensions.
bool have_early_data_info = false;
CBS early_data_info;
+ uint16_t ext_id = ssl_is_draft21(ssl->version)
+ ? TLSEXT_TYPE_early_data
+ : TLSEXT_TYPE_ticket_early_data_info;
const SSL_EXTENSION_TYPE ext_types[] = {
- {TLSEXT_TYPE_ticket_early_data_info, &have_early_data_info,
- &early_data_info},
+ {ext_id, &have_early_data_info, &early_data_info},
};
uint8_t alert = SSL_AD_DECODE_ERROR;
diff --git a/src/ssl/tls13_enc.cc b/src/ssl/tls13_enc.cc
index 6c7e1da..14f4a78 100644
--- a/src/ssl/tls13_enc.cc
+++ b/src/ssl/tls13_enc.cc
@@ -46,32 +46,33 @@
return 1;
}
-int tls13_init_key_schedule(SSL_HANDSHAKE *hs) {
+int tls13_init_key_schedule(SSL_HANDSHAKE *hs, const uint8_t *psk,
+ size_t psk_len) {
if (!init_key_schedule(hs, ssl_protocol_version(hs->ssl), hs->new_cipher)) {
return 0;
}
hs->transcript.FreeBuffer();
- return 1;
+ return HKDF_extract(hs->secret, &hs->hash_len, hs->transcript.Digest(), psk,
+ psk_len, hs->secret, hs->hash_len);
}
-int tls13_init_early_key_schedule(SSL_HANDSHAKE *hs) {
+int tls13_init_early_key_schedule(SSL_HANDSHAKE *hs, const uint8_t *psk,
+ size_t psk_len) {
SSL *const ssl = hs->ssl;
return init_key_schedule(hs, ssl_session_protocol_version(ssl->session),
- ssl->session->cipher);
+ ssl->session->cipher) &&
+ HKDF_extract(hs->secret, &hs->hash_len, hs->transcript.Digest(), psk,
+ psk_len, hs->secret, hs->hash_len);
}
-int tls13_advance_key_schedule(SSL_HANDSHAKE *hs, const uint8_t *in,
- size_t len) {
- return HKDF_extract(hs->secret, &hs->hash_len, hs->transcript.Digest(), in,
- len, hs->secret, hs->hash_len);
-}
-
-static int hkdf_expand_label(uint8_t *out, const EVP_MD *digest,
- const uint8_t *secret, size_t secret_len,
- const uint8_t *label, size_t label_len,
- const uint8_t *hash, size_t hash_len, size_t len) {
- static const char kTLS13LabelVersion[] = "TLS 1.3, ";
+static int hkdf_expand_label(uint8_t *out, uint16_t version,
+ const EVP_MD *digest, const uint8_t *secret,
+ size_t secret_len, const uint8_t *label,
+ size_t label_len, const uint8_t *hash,
+ size_t hash_len, size_t len) {
+ const char *kTLS13LabelVersion =
+ ssl_is_draft21(version) ? "tls13 " : "TLS 1.3, ";
ScopedCBB cbb;
CBB child;
@@ -96,6 +97,34 @@
return ret;
}
+static const char kTLS13LabelDerived[] = "derived";
+
+int tls13_advance_key_schedule(SSL_HANDSHAKE *hs, const uint8_t *in,
+ size_t len) {
+ SSL *const ssl = hs->ssl;
+
+ // Draft 18 does not include the extra Derive-Secret step.
+ if (ssl_is_draft21(ssl->version)) {
+ uint8_t derive_context[EVP_MAX_MD_SIZE];
+ unsigned derive_context_len;
+ if (!EVP_Digest(nullptr, 0, derive_context, &derive_context_len,
+ hs->transcript.Digest(), nullptr)) {
+ return 0;
+ }
+
+ if (!hkdf_expand_label(hs->secret, ssl->version, hs->transcript.Digest(),
+ hs->secret, hs->hash_len,
+ (const uint8_t *)kTLS13LabelDerived,
+ strlen(kTLS13LabelDerived), derive_context,
+ derive_context_len, hs->hash_len)) {
+ return 0;
+ }
+ }
+
+ return HKDF_extract(hs->secret, &hs->hash_len, hs->transcript.Digest(), in,
+ len, hs->secret, hs->hash_len);
+}
+
// derive_secret derives a secret of length |len| and writes the result in |out|
// with the given label and the current base secret and most recently-saved
// handshake context. It returns one on success and zero on error.
@@ -107,9 +136,10 @@
return 0;
}
- return hkdf_expand_label(out, hs->transcript.Digest(), hs->secret,
- hs->hash_len, label, label_len, context_hash,
- context_hash_len, len);
+ return hkdf_expand_label(out, SSL_get_session(hs->ssl)->ssl_version,
+ hs->transcript.Digest(), hs->secret, hs->hash_len,
+ label, label_len, context_hash, context_hash_len,
+ len);
}
int tls13_set_traffic_key(SSL *ssl, enum evp_aead_direction_t direction,
@@ -136,16 +166,18 @@
// Derive the key.
size_t key_len = EVP_AEAD_key_length(aead);
uint8_t key[EVP_AEAD_MAX_KEY_LENGTH];
- if (!hkdf_expand_label(key, digest, traffic_secret, traffic_secret_len,
- (const uint8_t *)"key", 3, NULL, 0, key_len)) {
+ if (!hkdf_expand_label(key, session->ssl_version, digest, traffic_secret,
+ traffic_secret_len, (const uint8_t *)"key", 3, NULL, 0,
+ key_len)) {
return 0;
}
// Derive the IV.
size_t iv_len = EVP_AEAD_nonce_length(aead);
uint8_t iv[EVP_AEAD_MAX_NONCE_LENGTH];
- if (!hkdf_expand_label(iv, digest, traffic_secret, traffic_secret_len,
- (const uint8_t *)"iv", 2, NULL, 0, iv_len)) {
+ if (!hkdf_expand_label(iv, session->ssl_version, digest, traffic_secret,
+ traffic_secret_len, (const uint8_t *)"iv", 2, NULL, 0,
+ iv_len)) {
return 0;
}
@@ -195,28 +227,49 @@
static const char kTLS13LabelServerApplicationTraffic[] =
"server application traffic secret";
+static const char kTLS13Draft21LabelExporter[] = "exp master";
+static const char kTLS13Draft21LabelEarlyExporter[] = "e exp master";
+
+static const char kTLS13Draft21LabelClientEarlyTraffic[] = "c e traffic";
+static const char kTLS13Draft21LabelClientHandshakeTraffic[] = "c hs traffic";
+static const char kTLS13Draft21LabelServerHandshakeTraffic[] = "s hs traffic";
+static const char kTLS13Draft21LabelClientApplicationTraffic[] = "c ap traffic";
+static const char kTLS13Draft21LabelServerApplicationTraffic[] = "s ap traffic";
+
int tls13_derive_early_secrets(SSL_HANDSHAKE *hs) {
SSL *const ssl = hs->ssl;
+ uint16_t version = SSL_get_session(ssl)->ssl_version;
+
+ const char *early_traffic_label = ssl_is_draft21(version)
+ ? kTLS13Draft21LabelClientEarlyTraffic
+ : kTLS13LabelClientEarlyTraffic;
+ const char *early_exporter_label = ssl_is_draft21(version)
+ ? kTLS13Draft21LabelEarlyExporter
+ : kTLS13LabelEarlyExporter;
return derive_secret(hs, hs->early_traffic_secret, hs->hash_len,
- (const uint8_t *)kTLS13LabelClientEarlyTraffic,
- strlen(kTLS13LabelClientEarlyTraffic)) &&
+ (const uint8_t *)early_traffic_label,
+ strlen(early_traffic_label)) &&
ssl_log_secret(ssl, "CLIENT_EARLY_TRAFFIC_SECRET",
hs->early_traffic_secret, hs->hash_len) &&
derive_secret(hs, ssl->s3->early_exporter_secret, hs->hash_len,
- (const uint8_t *)kTLS13LabelEarlyExporter,
- strlen(kTLS13LabelEarlyExporter));
+ (const uint8_t *)early_exporter_label,
+ strlen(early_exporter_label));
}
int tls13_derive_handshake_secrets(SSL_HANDSHAKE *hs) {
SSL *const ssl = hs->ssl;
+ const char *client_label = ssl_is_draft21(ssl->version)
+ ? kTLS13Draft21LabelClientHandshakeTraffic
+ : kTLS13LabelClientHandshakeTraffic;
+ const char *server_label = ssl_is_draft21(ssl->version)
+ ? kTLS13Draft21LabelServerHandshakeTraffic
+ : kTLS13LabelServerHandshakeTraffic;
return derive_secret(hs, hs->client_handshake_secret, hs->hash_len,
- (const uint8_t *)kTLS13LabelClientHandshakeTraffic,
- strlen(kTLS13LabelClientHandshakeTraffic)) &&
+ (const uint8_t *)client_label, strlen(client_label)) &&
ssl_log_secret(ssl, "CLIENT_HANDSHAKE_TRAFFIC_SECRET",
hs->client_handshake_secret, hs->hash_len) &&
derive_secret(hs, hs->server_handshake_secret, hs->hash_len,
- (const uint8_t *)kTLS13LabelServerHandshakeTraffic,
- strlen(kTLS13LabelServerHandshakeTraffic)) &&
+ (const uint8_t *)server_label, strlen(server_label)) &&
ssl_log_secret(ssl, "SERVER_HANDSHAKE_TRAFFIC_SECRET",
hs->server_handshake_secret, hs->hash_len);
}
@@ -224,25 +277,33 @@
int tls13_derive_application_secrets(SSL_HANDSHAKE *hs) {
SSL *const ssl = hs->ssl;
ssl->s3->exporter_secret_len = hs->hash_len;
+ const char *client_label = ssl_is_draft21(ssl->version)
+ ? kTLS13Draft21LabelClientApplicationTraffic
+ : kTLS13LabelClientApplicationTraffic;
+ const char *server_label = ssl_is_draft21(ssl->version)
+ ? kTLS13Draft21LabelServerApplicationTraffic
+ : kTLS13LabelServerApplicationTraffic;
+ const char *exporter_label = ssl_is_draft21(ssl->version)
+ ? kTLS13Draft21LabelExporter
+ : kTLS13LabelExporter;
return derive_secret(hs, hs->client_traffic_secret_0, hs->hash_len,
- (const uint8_t *)kTLS13LabelClientApplicationTraffic,
- strlen(kTLS13LabelClientApplicationTraffic)) &&
+ (const uint8_t *)client_label, strlen(client_label)) &&
ssl_log_secret(ssl, "CLIENT_TRAFFIC_SECRET_0",
hs->client_traffic_secret_0, hs->hash_len) &&
derive_secret(hs, hs->server_traffic_secret_0, hs->hash_len,
- (const uint8_t *)kTLS13LabelServerApplicationTraffic,
- strlen(kTLS13LabelServerApplicationTraffic)) &&
+ (const uint8_t *)server_label, strlen(server_label)) &&
ssl_log_secret(ssl, "SERVER_TRAFFIC_SECRET_0",
hs->server_traffic_secret_0, hs->hash_len) &&
derive_secret(hs, ssl->s3->exporter_secret, hs->hash_len,
- (const uint8_t *)kTLS13LabelExporter,
- strlen(kTLS13LabelExporter)) &&
+ (const uint8_t *)exporter_label,
+ strlen(exporter_label)) &&
ssl_log_secret(ssl, "EXPORTER_SECRET", ssl->s3->exporter_secret,
hs->hash_len);
}
static const char kTLS13LabelApplicationTraffic[] =
"application traffic secret";
+static const char kTLS13Draft21LabelApplicationTraffic[] = "traffic upd";
int tls13_rotate_traffic_key(SSL *ssl, enum evp_aead_direction_t direction) {
uint8_t *secret;
@@ -255,11 +316,14 @@
secret_len = ssl->s3->write_traffic_secret_len;
}
+ const char *traffic_label = ssl_is_draft21(ssl->version)
+ ? kTLS13Draft21LabelApplicationTraffic
+ : kTLS13LabelApplicationTraffic;
+
const EVP_MD *digest = ssl_session_get_digest(SSL_get_session(ssl));
- if (!hkdf_expand_label(secret, digest, secret, secret_len,
- (const uint8_t *)kTLS13LabelApplicationTraffic,
- strlen(kTLS13LabelApplicationTraffic), NULL, 0,
- secret_len)) {
+ if (!hkdf_expand_label(secret, ssl->version, digest, secret, secret_len,
+ (const uint8_t *)traffic_label, strlen(traffic_label),
+ NULL, 0, secret_len)) {
return 0;
}
@@ -267,30 +331,33 @@
}
static const char kTLS13LabelResumption[] = "resumption master secret";
+static const char kTLS13Draft21LabelResumption[] = "res master";
int tls13_derive_resumption_secret(SSL_HANDSHAKE *hs) {
if (hs->hash_len > SSL_MAX_MASTER_KEY_LENGTH) {
OPENSSL_PUT_ERROR(SSL, ERR_R_INTERNAL_ERROR);
return 0;
}
-
+ const char *resumption_label = ssl_is_draft21(hs->ssl->version)
+ ? kTLS13Draft21LabelResumption
+ : kTLS13LabelResumption;
hs->new_session->master_key_length = hs->hash_len;
return derive_secret(
hs, hs->new_session->master_key, hs->new_session->master_key_length,
- (const uint8_t *)kTLS13LabelResumption, strlen(kTLS13LabelResumption));
+ (const uint8_t *)resumption_label, strlen(resumption_label));
}
static const char kTLS13LabelFinished[] = "finished";
// tls13_verify_data sets |out| to be the HMAC of |context| using a derived
// Finished key for both Finished messages and the PSK binder.
-static int tls13_verify_data(const EVP_MD *digest, uint8_t *out,
- size_t *out_len, const uint8_t *secret,
- size_t hash_len, uint8_t *context,
- size_t context_len) {
+static int tls13_verify_data(const EVP_MD *digest, uint16_t version,
+ uint8_t *out, size_t *out_len,
+ const uint8_t *secret, size_t hash_len,
+ uint8_t *context, size_t context_len) {
uint8_t key[EVP_MAX_MD_SIZE];
unsigned len;
- if (!hkdf_expand_label(key, digest, secret, hash_len,
+ if (!hkdf_expand_label(key, version, digest, secret, hash_len,
(const uint8_t *)kTLS13LabelFinished,
strlen(kTLS13LabelFinished), NULL, 0, hash_len) ||
HMAC(digest, key, hash_len, context, context_len, out, &len) == NULL) {
@@ -312,35 +379,79 @@
uint8_t context_hash[EVP_MAX_MD_SIZE];
size_t context_hash_len;
if (!hs->transcript.GetHash(context_hash, &context_hash_len) ||
- !tls13_verify_data(hs->transcript.Digest(), out, out_len, traffic_secret,
- hs->hash_len, context_hash, context_hash_len)) {
+ !tls13_verify_data(hs->transcript.Digest(), hs->ssl->version, out,
+ out_len, traffic_secret, hs->hash_len, context_hash,
+ context_hash_len)) {
return 0;
}
return 1;
}
+static const char kTLS13LabelResumptionPSK[] = "resumption";
+
+bool tls13_derive_session_psk(SSL_SESSION *session, Span<const uint8_t> nonce) {
+ if (!ssl_is_draft21(session->ssl_version)) {
+ return true;
+ }
+
+ const EVP_MD *digest = ssl_session_get_digest(session);
+ return hkdf_expand_label(session->master_key, session->ssl_version, digest,
+ session->master_key, session->master_key_length,
+ (const uint8_t *)kTLS13LabelResumptionPSK,
+ strlen(kTLS13LabelResumptionPSK), nonce.data(),
+ nonce.size(), session->master_key_length);
+}
+
+static const char kTLS13LabelExportKeying[] = "exporter";
+
int tls13_export_keying_material(SSL *ssl, uint8_t *out, size_t out_len,
const char *label, size_t label_len,
- const uint8_t *context, size_t context_len,
- int use_context) {
- const uint8_t *hash = NULL;
- size_t hash_len = 0;
+ const uint8_t *context_in,
+ size_t context_in_len, int use_context) {
+ const uint8_t *context = NULL;
+ size_t context_len = 0;
if (use_context) {
- hash = context;
- hash_len = context_len;
+ context = context_in;
+ context_len = context_in_len;
+ }
+
+ if (!ssl_is_draft21(ssl->version)) {
+ const EVP_MD *digest = ssl_session_get_digest(SSL_get_session(ssl));
+ return hkdf_expand_label(
+ out, ssl->version, digest, ssl->s3->exporter_secret,
+ ssl->s3->exporter_secret_len, (const uint8_t *)label, label_len,
+ context, context_len, out_len);
}
const EVP_MD *digest = ssl_session_get_digest(SSL_get_session(ssl));
- return hkdf_expand_label(out, digest, ssl->s3->exporter_secret,
- ssl->s3->exporter_secret_len, (const uint8_t *)label,
- label_len, hash, hash_len, out_len);
+
+ uint8_t hash[EVP_MAX_MD_SIZE];
+ uint8_t export_context[EVP_MAX_MD_SIZE];
+ uint8_t derived_secret[EVP_MAX_MD_SIZE];
+ unsigned hash_len;
+ unsigned export_context_len;
+ unsigned derived_secret_len = EVP_MD_size(digest);
+ if (!EVP_Digest(context, context_len, hash, &hash_len, digest, NULL) ||
+ !EVP_Digest(NULL, 0, export_context, &export_context_len, digest, NULL)) {
+ return 0;
+ }
+ return hkdf_expand_label(
+ derived_secret, ssl->version, digest, ssl->s3->exporter_secret,
+ ssl->s3->exporter_secret_len, (const uint8_t *)label, label_len,
+ export_context, export_context_len, derived_secret_len) &&
+ hkdf_expand_label(
+ out, ssl->version, digest, derived_secret, derived_secret_len,
+ (const uint8_t *)kTLS13LabelExportKeying,
+ strlen(kTLS13LabelExportKeying), hash, hash_len, out_len);
}
static const char kTLS13LabelPSKBinder[] = "resumption psk binder key";
+static const char kTLS13Draft21LabelPSKBinder[] = "res binder";
-static int tls13_psk_binder(uint8_t *out, const EVP_MD *digest, uint8_t *psk,
- size_t psk_len, uint8_t *context,
- size_t context_len, size_t hash_len) {
+static int tls13_psk_binder(uint8_t *out, uint16_t version,
+ const EVP_MD *digest, uint8_t *psk, size_t psk_len,
+ uint8_t *context, size_t context_len,
+ size_t hash_len) {
uint8_t binder_context[EVP_MAX_MD_SIZE];
unsigned binder_context_len;
if (!EVP_Digest(NULL, 0, binder_context, &binder_context_len, digest, NULL)) {
@@ -353,15 +464,17 @@
NULL, 0)) {
return 0;
}
+ const char *binder_label = ssl_is_draft21(version)
+ ? kTLS13Draft21LabelPSKBinder
+ : kTLS13LabelPSKBinder;
uint8_t binder_key[EVP_MAX_MD_SIZE] = {0};
size_t len;
- if (!hkdf_expand_label(binder_key, digest, early_secret, hash_len,
- (const uint8_t *)kTLS13LabelPSKBinder,
- strlen(kTLS13LabelPSKBinder), binder_context,
- binder_context_len, hash_len) ||
- !tls13_verify_data(digest, out, &len, binder_key, hash_len, context,
- context_len)) {
+ if (!hkdf_expand_label(binder_key, version, digest, early_secret, hash_len,
+ (const uint8_t *)binder_label, strlen(binder_label),
+ binder_context, binder_context_len, hash_len) ||
+ !tls13_verify_data(digest, version, out, &len, binder_key, hash_len,
+ context, context_len)) {
return 0;
}
@@ -381,6 +494,7 @@
ScopedEVP_MD_CTX ctx;
uint8_t context[EVP_MAX_MD_SIZE];
unsigned context_len;
+
if (!EVP_DigestInit_ex(ctx.get(), digest, NULL) ||
!EVP_DigestUpdate(ctx.get(), hs->transcript.buffer().data(),
hs->transcript.buffer().size()) ||
@@ -390,7 +504,8 @@
}
uint8_t verify_data[EVP_MAX_MD_SIZE] = {0};
- if (!tls13_psk_binder(verify_data, digest, ssl->session->master_key,
+ if (!tls13_psk_binder(verify_data, ssl->session->ssl_version, digest,
+ ssl->session->master_key,
ssl->session->master_key_length, context, context_len,
hash_len)) {
return 0;
@@ -422,7 +537,7 @@
uint8_t verify_data[EVP_MAX_MD_SIZE] = {0};
CBS binder;
- if (!tls13_psk_binder(verify_data, hs->transcript.Digest(),
+ if (!tls13_psk_binder(verify_data, hs->ssl->version, hs->transcript.Digest(),
session->master_key, session->master_key_length,
context, context_len, hash_len) ||
// We only consider the first PSK, so compare against the first binder.
diff --git a/src/ssl/tls13_server.cc b/src/ssl/tls13_server.cc
index 89c9d46..9afd0d4 100644
--- a/src/ssl/tls13_server.cc
+++ b/src/ssl/tls13_server.cc
@@ -160,33 +160,46 @@
ssl_session_rebase_time(ssl, hs->new_session.get());
for (int i = 0; i < kNumTickets; i++) {
- if (!RAND_bytes((uint8_t *)&hs->new_session->ticket_age_add, 4)) {
+ UniquePtr<SSL_SESSION> session(
+ SSL_SESSION_dup(hs->new_session.get(), SSL_SESSION_INCLUDE_NONAUTH));
+ if (!session) {
return 0;
}
- hs->new_session->ticket_age_add_valid = 1;
+ if (!RAND_bytes((uint8_t *)&session->ticket_age_add, 4)) {
+ return 0;
+ }
+ session->ticket_age_add_valid = 1;
if (ssl->cert->enable_early_data) {
- hs->new_session->ticket_max_early_data = kMaxEarlyDataAccepted;
+ session->ticket_max_early_data = kMaxEarlyDataAccepted;
}
+ static_assert(kNumTickets < 256, "Too many tickets");
+ uint8_t nonce[] = {static_cast<uint8_t>(i)};
+
ScopedCBB cbb;
- CBB body, ticket, extensions;
+ CBB body, nonce_cbb, ticket, extensions;
if (!ssl->method->init_message(ssl, cbb.get(), &body,
SSL3_MT_NEW_SESSION_TICKET) ||
- !CBB_add_u32(&body, hs->new_session->timeout) ||
- !CBB_add_u32(&body, hs->new_session->ticket_age_add) ||
+ !CBB_add_u32(&body, session->timeout) ||
+ !CBB_add_u32(&body, session->ticket_age_add) ||
+ (ssl_is_draft21(ssl->version) &&
+ (!CBB_add_u8_length_prefixed(&body, &nonce_cbb) ||
+ !CBB_add_bytes(&nonce_cbb, nonce, sizeof(nonce)))) ||
!CBB_add_u16_length_prefixed(&body, &ticket) ||
- !ssl_encrypt_ticket(ssl, &ticket, hs->new_session.get()) ||
+ !tls13_derive_session_psk(session.get(), nonce) ||
+ !ssl_encrypt_ticket(ssl, &ticket, session.get()) ||
!CBB_add_u16_length_prefixed(&body, &extensions)) {
return 0;
}
if (ssl->cert->enable_early_data) {
CBB early_data_info;
- if (!CBB_add_u16(&extensions, TLSEXT_TYPE_ticket_early_data_info) ||
+ if (!CBB_add_u16(&extensions, ssl_is_draft21(ssl->version)
+ ? TLSEXT_TYPE_early_data
+ : TLSEXT_TYPE_ticket_early_data_info) ||
!CBB_add_u16_length_prefixed(&extensions, &early_data_info) ||
- !CBB_add_u32(&early_data_info,
- hs->new_session->ticket_max_early_data) ||
+ !CBB_add_u32(&early_data_info, session->ticket_max_early_data) ||
!CBB_flush(&extensions)) {
return 0;
}
@@ -244,8 +257,11 @@
// The PRF hash is now known. Set up the key schedule and hash the
// ClientHello.
- if (!tls13_init_key_schedule(hs) ||
- !ssl_hash_message(hs, msg)) {
+ if (!hs->transcript.InitHash(ssl_protocol_version(ssl), hs->new_cipher)) {
+ return ssl_hs_error;
+ }
+
+ if (!ssl_hash_message(hs, msg)) {
return ssl_hs_error;
}
@@ -429,13 +445,16 @@
return ssl_hs_error;
}
- // Incorporate the PSK into the running secret.
+ size_t hash_len = EVP_MD_size(
+ ssl_get_handshake_digest(ssl_protocol_version(ssl), hs->new_cipher));
+
+ // Set up the key schedule and incorporate the PSK into the running secret.
if (ssl->s3->session_reused) {
- if (!tls13_advance_key_schedule(hs, hs->new_session->master_key,
+ if (!tls13_init_key_schedule(hs, hs->new_session->master_key,
hs->new_session->master_key_length)) {
return ssl_hs_error;
}
- } else if (!tls13_advance_key_schedule(hs, kZeroes, hs->hash_len)) {
+ } else if (!tls13_init_key_schedule(hs, kZeroes, hash_len)) {
return ssl_hs_error;
}
@@ -454,6 +473,10 @@
ssl->early_data_accepted = false;
ssl->s3->skip_early_data = true;
ssl->method->next_message(ssl);
+ if (ssl_is_draft21(ssl->version) &&
+ !hs->transcript.UpdateForHelloRetryRequest()) {
+ return ssl_hs_error;
+ }
hs->tls13_state = state_send_hello_retry_request;
return ssl_hs_ok;
}
@@ -473,6 +496,8 @@
if (!ssl->method->init_message(ssl, cbb.get(), &body,
SSL3_MT_HELLO_RETRY_REQUEST) ||
!CBB_add_u16(&body, ssl->version) ||
+ (ssl_is_draft21(ssl->version) &&
+ !CBB_add_u16(&body, ssl_cipher_get_value(hs->new_cipher))) ||
!tls1_get_shared_group(hs, &group_id) ||
!CBB_add_u16_length_prefixed(&body, &extensions) ||
!CBB_add_u16(&extensions, TLSEXT_TYPE_key_share) ||
@@ -582,16 +607,48 @@
// Send a CertificateRequest, if necessary.
if (hs->cert_request) {
- CBB sigalgs_cbb;
- if (!ssl->method->init_message(ssl, cbb.get(), &body,
- SSL3_MT_CERTIFICATE_REQUEST) ||
- !CBB_add_u8(&body, 0 /* no certificate_request_context. */) ||
- !CBB_add_u16_length_prefixed(&body, &sigalgs_cbb) ||
- !tls12_add_verify_sigalgs(ssl, &sigalgs_cbb) ||
- !ssl_add_client_CA_list(ssl, &body) ||
- !CBB_add_u16(&body, 0 /* empty certificate_extensions. */) ||
- !ssl_add_message_cbb(ssl, cbb.get())) {
- return ssl_hs_error;
+ if (ssl_is_draft21(ssl->version)) {
+ CBB cert_request_extensions, sigalg_contents, sigalgs_cbb;
+ if (!ssl->method->init_message(ssl, cbb.get(), &body,
+ SSL3_MT_CERTIFICATE_REQUEST) ||
+ !CBB_add_u8(&body, 0 /* no certificate_request_context. */) ||
+ !CBB_add_u16_length_prefixed(&body, &cert_request_extensions) ||
+ !CBB_add_u16(&cert_request_extensions,
+ TLSEXT_TYPE_signature_algorithms) ||
+ !CBB_add_u16_length_prefixed(&cert_request_extensions,
+ &sigalg_contents) ||
+ !CBB_add_u16_length_prefixed(&sigalg_contents, &sigalgs_cbb) ||
+ !tls12_add_verify_sigalgs(ssl, &sigalgs_cbb)) {
+ return ssl_hs_error;
+ }
+
+ if (ssl_has_client_CAs(ssl)) {
+ CBB ca_contents;
+ if (!CBB_add_u16(&cert_request_extensions,
+ TLSEXT_TYPE_certificate_authorities) ||
+ !CBB_add_u16_length_prefixed(&cert_request_extensions,
+ &ca_contents) ||
+ !ssl_add_client_CA_list(ssl, &ca_contents) ||
+ !CBB_flush(&cert_request_extensions)) {
+ return ssl_hs_error;
+ }
+ }
+
+ if (!ssl_add_message_cbb(ssl, cbb.get())) {
+ return ssl_hs_error;
+ }
+ } else {
+ CBB sigalgs_cbb;
+ if (!ssl->method->init_message(ssl, cbb.get(), &body,
+ SSL3_MT_CERTIFICATE_REQUEST) ||
+ !CBB_add_u8(&body, 0 /* no certificate_request_context. */) ||
+ !CBB_add_u16_length_prefixed(&body, &sigalgs_cbb) ||
+ !tls12_add_verify_sigalgs(ssl, &sigalgs_cbb) ||
+ !ssl_add_client_CA_list(ssl, &body) ||
+ !CBB_add_u16(&body, 0 /* empty certificate_extensions. */) ||
+ !ssl_add_message_cbb(ssl, cbb.get())) {
+ return ssl_hs_error;
+ }
}
}
@@ -648,6 +705,15 @@
// the wire sooner and also avoids triggering a write on |SSL_read| when
// processing the client Finished. This requires computing the client
// Finished early. See draft-ietf-tls-tls13-18, section 4.5.1.
+ if (ssl_is_draft21(ssl->version)) {
+ static const uint8_t kEndOfEarlyData[4] = {SSL3_MT_END_OF_EARLY_DATA, 0,
+ 0, 0};
+ if (!hs->transcript.Update(kEndOfEarlyData)) {
+ OPENSSL_PUT_ERROR(SSL, ERR_R_INTERNAL_ERROR);
+ return ssl_hs_error;
+ }
+ }
+
size_t finished_len;
if (!tls13_finished_mac(hs, hs->expected_client_finished, &finished_len,
0 /* client */)) {
@@ -698,11 +764,30 @@
}
static enum ssl_hs_wait_t do_process_end_of_early_data(SSL_HANDSHAKE *hs) {
+ SSL *const ssl = hs->ssl;
hs->tls13_state = state_process_change_cipher_spec;
- // If early data was accepted, the ChangeCipherSpec message will be in the
- // discarded early data.
- if (hs->early_data_offered && !hs->ssl->early_data_accepted) {
- return ssl_hs_ok;
+ if (hs->early_data_offered) {
+ // If early data was not accepted, the EndOfEarlyData and ChangeCipherSpec
+ // message will be in the discarded early data.
+ if (!hs->ssl->early_data_accepted) {
+ return ssl_hs_ok;
+ }
+ if (ssl_is_draft21(ssl->version)) {
+ SSLMessage msg;
+ if (!ssl->method->get_message(ssl, &msg)) {
+ return ssl_hs_read_message;
+ }
+
+ if (!ssl_check_message_type(ssl, msg, SSL3_MT_END_OF_EARLY_DATA)) {
+ return ssl_hs_error;
+ }
+ if (CBS_len(&msg.body) != 0) {
+ ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_DECODE_ERROR);
+ OPENSSL_PUT_ERROR(SSL, SSL_R_DECODE_ERROR);
+ return ssl_hs_error;
+ }
+ ssl->method->next_message(ssl);
+ }
}
return ssl_is_resumption_client_ccs_experiment(hs->ssl->version)
? ssl_hs_read_change_cipher_spec
diff --git a/src/ssl/tls_method.cc b/src/ssl/tls_method.cc
index c5b0178..4eacf64 100644
--- a/src/ssl/tls_method.cc
+++ b/src/ssl/tls_method.cc
@@ -67,8 +67,6 @@
namespace bssl {
-static bool ssl3_supports_cipher(const SSL_CIPHER *cipher) { return true; }
-
static void ssl3_on_handshake_complete(SSL *ssl) {
// The handshake should have released its final message.
assert(!ssl->s3->has_message);
@@ -113,7 +111,6 @@
ssl3_open_app_data,
ssl3_write_app_data,
ssl3_dispatch_alert,
- ssl3_supports_cipher,
ssl3_init_message,
ssl3_finish_message,
ssl3_add_message,
diff --git a/src/ssl/tls_record.cc b/src/ssl/tls_record.cc
index bc641fa..a062012 100644
--- a/src/ssl/tls_record.cc
+++ b/src/ssl/tls_record.cc
@@ -320,7 +320,8 @@
if (type == SSL3_RT_ALERT) {
// Return end_of_early_data alerts as-is for the caller to process.
- if (out->size() == 2 &&
+ if (!ssl_is_draft21(ssl->version) &&
+ out->size() == 2 &&
(*out)[0] == SSL3_AL_WARNING &&
(*out)[1] == TLS1_AD_END_OF_EARLY_DATA) {
*out_type = type;
diff --git a/src/third_party/fiat/CMakeLists.txt b/src/third_party/fiat/CMakeLists.txt
new file mode 100644
index 0000000..fcc77d5
--- /dev/null
+++ b/src/third_party/fiat/CMakeLists.txt
@@ -0,0 +1,9 @@
+include_directories(../../include)
+
+add_library(
+ fiat
+
+ OBJECT
+
+ curve25519.c
+)
diff --git a/src/third_party/fiat/LICENSE b/src/third_party/fiat/LICENSE
new file mode 100644
index 0000000..bd46c61
--- /dev/null
+++ b/src/third_party/fiat/LICENSE
@@ -0,0 +1,22 @@
+The MIT License (MIT)
+
+Copyright (c) 2015-2016 the fiat-crypto authors (see
+https://github.com/mit-plv/fiat-crypto/blob/master/AUTHORS).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/src/third_party/fiat/METADATA b/src/third_party/fiat/METADATA
new file mode 100644
index 0000000..bae0285
--- /dev/null
+++ b/src/third_party/fiat/METADATA
@@ -0,0 +1,14 @@
+name: "fiat"
+description:
+ "Fiat-Crypto: Synthesizing Correct-by-Construction Code for Cryptographic Primitives".
+
+third_party {
+ url {
+ type: HOMEPAGE
+ value: "https://github.com/mit-plv/fiat-crypto"
+ }
+ version: "6c4d4afb26de639718fcac39094353ca7feec365"
+ last_upgrade_date { year: 2017 month: 11 day: 3 }
+
+ local_modifications: "Fiat-generated code has been integrated into existing BoringSSL code"
+}
diff --git a/src/third_party/fiat/README.md b/src/third_party/fiat/README.md
new file mode 100644
index 0000000..5512715
--- /dev/null
+++ b/src/third_party/fiat/README.md
@@ -0,0 +1,5 @@
+# Fiat
+
+Some of the code in this directory is generated by
+[Fiat](https://github.com/mit-plv/fiat-crypto) and thus these files are
+licensed under the MIT license. (See LICENSE file.)
diff --git a/src/third_party/fiat/curve25519.c b/src/third_party/fiat/curve25519.c
new file mode 100644
index 0000000..d54aa83
--- /dev/null
+++ b/src/third_party/fiat/curve25519.c
@@ -0,0 +1,5062 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+// Some of this code is taken from the ref10 version of Ed25519 in SUPERCOP
+// 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
+// public domain but parts have been replaced with code generated by Fiat
+// (https://github.com/mit-plv/fiat-crypto), which is MIT licensed.
+//
+// The field functions are shared by Ed25519 and X25519 where possible.
+
+#include <openssl/curve25519.h>
+
+#include <assert.h>
+#include <string.h>
+
+#include <openssl/cpu.h>
+#include <openssl/mem.h>
+#include <openssl/rand.h>
+#include <openssl/sha.h>
+
+#include "internal.h"
+#include "../../crypto/internal.h"
+
+
+static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
+static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
+
+static uint64_t load_3(const uint8_t *in) {
+ uint64_t result;
+ result = (uint64_t)in[0];
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ return result;
+}
+
+static uint64_t load_4(const uint8_t *in) {
+ uint64_t result;
+ result = (uint64_t)in[0];
+ result |= ((uint64_t)in[1]) << 8;
+ result |= ((uint64_t)in[2]) << 16;
+ result |= ((uint64_t)in[3]) << 24;
+ return result;
+}
+
+#define assert_fe(f) do { \
+ for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
+ assert(f[_assert_fe_i] < 1.125*(1<<(26-(_assert_fe_i&1)))); \
+ } \
+} while (0)
+
+#define assert_fe_loose(f) do { \
+ for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
+ assert(f[_assert_fe_i] < 3.375*(1<<(26-(_assert_fe_i&1)))); \
+ } \
+} while (0)
+
+static void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) {
+ // Ignores top bit of s.
+ uint32_t a0 = load_4(s);
+ uint32_t a1 = load_4(s+4);
+ uint32_t a2 = load_4(s+8);
+ uint32_t a3 = load_4(s+12);
+ uint32_t a4 = load_4(s+16);
+ uint32_t a5 = load_4(s+20);
+ uint32_t a6 = load_4(s+24);
+ uint32_t a7 = load_4(s+28);
+ h[0] = a0&((1<<26)-1); // 26 used, 32-26 left. 26
+ h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); // (32-26) + 19 = 6+19 = 25
+ h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); // (32-19) + 13 = 13+13 = 26
+ h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); // (32-13) + 6 = 19+ 6 = 25
+ h[4] = (a3>> 6); // (32- 6) = 26
+ h[5] = a4&((1<<25)-1); // 25
+ h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); // (32-25) + 19 = 7+19 = 26
+ h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); // (32-19) + 12 = 13+12 = 25
+ h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); // (32-12) + 6 = 20+ 6 = 26
+ h[9] = (a7>> 6)&((1<<25)-1); // 25
+ assert_fe(h);
+}
+
+static void fe_frombytes(fe *h, const uint8_t *s) {
+ fe_frombytes_impl(h->v, s);
+}
+
+// Preconditions:
+// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//
+// Write p=2^255-19; q=floor(h/p).
+// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+//
+// Proof:
+// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+// Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+//
+// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+// Then 0<y<1.
+//
+// Write r=h-pq.
+// Have 0<=r<=p-1=2^255-20.
+// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+//
+// Write x=r+19(2^-255)r+y.
+// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+//
+// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+static void fe_tobytes_impl(uint8_t *s, const uint32_t h[10]) {
+ assert_fe_loose(h);
+ int32_t h0 = h[0];
+ int32_t h1 = h[1];
+ int32_t h2 = h[2];
+ int32_t h3 = h[3];
+ int32_t h4 = h[4];
+ int32_t h5 = h[5];
+ int32_t h6 = h[6];
+ int32_t h7 = h[7];
+ int32_t h8 = h[8];
+ int32_t h9 = h[9];
+ int32_t q;
+
+ q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+ q = (h0 + q) >> 26;
+ q = (h1 + q) >> 25;
+ q = (h2 + q) >> 26;
+ q = (h3 + q) >> 25;
+ q = (h4 + q) >> 26;
+ q = (h5 + q) >> 25;
+ q = (h6 + q) >> 26;
+ q = (h7 + q) >> 25;
+ q = (h8 + q) >> 26;
+ q = (h9 + q) >> 25;
+
+ // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
+ h0 += 19 * q;
+ // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
+
+ h1 += h0 >> 26; h0 &= kBottom26Bits;
+ h2 += h1 >> 25; h1 &= kBottom25Bits;
+ h3 += h2 >> 26; h2 &= kBottom26Bits;
+ h4 += h3 >> 25; h3 &= kBottom25Bits;
+ h5 += h4 >> 26; h4 &= kBottom26Bits;
+ h6 += h5 >> 25; h5 &= kBottom25Bits;
+ h7 += h6 >> 26; h6 &= kBottom26Bits;
+ h8 += h7 >> 25; h7 &= kBottom25Bits;
+ h9 += h8 >> 26; h8 &= kBottom26Bits;
+ h9 &= kBottom25Bits;
+ // h10 = carry9
+
+ // Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+ // Have h0+...+2^230 h9 between 0 and 2^255-1;
+ // evidently 2^255 h10-2^255 q = 0.
+ // Goal: Output h0+...+2^230 h9.
+
+ s[0] = h0 >> 0;
+ s[1] = h0 >> 8;
+ s[2] = h0 >> 16;
+ s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
+ s[4] = h1 >> 6;
+ s[5] = h1 >> 14;
+ s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
+ s[7] = h2 >> 5;
+ s[8] = h2 >> 13;
+ s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
+ s[10] = h3 >> 3;
+ s[11] = h3 >> 11;
+ s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
+ s[13] = h4 >> 2;
+ s[14] = h4 >> 10;
+ s[15] = h4 >> 18;
+ s[16] = h5 >> 0;
+ s[17] = h5 >> 8;
+ s[18] = h5 >> 16;
+ s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
+ s[20] = h6 >> 7;
+ s[21] = h6 >> 15;
+ s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
+ s[23] = h7 >> 5;
+ s[24] = h7 >> 13;
+ s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
+ s[26] = h8 >> 4;
+ s[27] = h8 >> 12;
+ s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
+ s[29] = h9 >> 2;
+ s[30] = h9 >> 10;
+ s[31] = h9 >> 18;
+}
+
+static void fe_tobytes(uint8_t *s, const fe *h) {
+ fe_tobytes_impl(s, h->v);
+}
+
+static void fe_loose_tobytes(uint8_t *s, const fe_loose *h) {
+ fe_tobytes_impl(s, h->v);
+}
+
+// h = f
+static void fe_copy(fe *h, const fe *f) {
+ OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
+}
+
+static void fe_copy_lt(fe_loose *h, const fe *f) {
+ OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
+}
+#if !defined(OPENSSL_SMALL)
+static void fe_copy_ll(fe_loose *h, const fe_loose *f) {
+ OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
+}
+#endif // !defined(OPENSSL_SMALL)
+
+// h = 0
+static void fe_0(fe *h) {
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
+}
+
+static void fe_loose_0(fe_loose *h) {
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
+}
+
+// h = 1
+static void fe_1(fe *h) {
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
+ h->v[0] = 1;
+}
+
+static void fe_loose_1(fe_loose *h) {
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
+ h->v[0] = 1;
+}
+
+static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = (x5 + x23);
+ out[1] = (x7 + x25);
+ out[2] = (x9 + x27);
+ out[3] = (x11 + x29);
+ out[4] = (x13 + x31);
+ out[5] = (x15 + x33);
+ out[6] = (x17 + x35);
+ out[7] = (x19 + x37);
+ out[8] = (x21 + x39);
+ out[9] = (x20 + x38);
+ }}}}}}}}}}}}}}}}}}}}
+}
+
+// h = f + g
+// Can overlap h with f or g.
+//
+// Preconditions:
+// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+// |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Postconditions:
+// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+static void fe_add(fe_loose *h, const fe *f, const fe *g) {
+ assert_fe(f->v);
+ assert_fe(g->v);
+ fe_add_impl(h->v, f->v, g->v);
+ assert_fe_loose(h->v);
+}
+
+static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = ((0x7ffffda + x5) - x23);
+ out[1] = ((0x3fffffe + x7) - x25);
+ out[2] = ((0x7fffffe + x9) - x27);
+ out[3] = ((0x3fffffe + x11) - x29);
+ out[4] = ((0x7fffffe + x13) - x31);
+ out[5] = ((0x3fffffe + x15) - x33);
+ out[6] = ((0x7fffffe + x17) - x35);
+ out[7] = ((0x3fffffe + x19) - x37);
+ out[8] = ((0x7fffffe + x21) - x39);
+ out[9] = ((0x3fffffe + x20) - x38);
+ }}}}}}}}}}}}}}}}}}}}
+}
+
+// h = f - g
+// Can overlap h with f or g.
+//
+// Preconditions:
+// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+// |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Postconditions:
+// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+static void fe_sub(fe_loose *h, const fe *f, const fe *g) {
+ assert_fe(f->v);
+ assert_fe(g->v);
+ fe_sub_impl(h->v, f->v, g->v);
+ assert_fe_loose(h->v);
+}
+
+static void fe_carry_impl(uint32_t out[10], const uint32_t in1[10]) {
+ { const uint32_t x17 = in1[9];
+ { const uint32_t x18 = in1[8];
+ { const uint32_t x16 = in1[7];
+ { const uint32_t x14 = in1[6];
+ { const uint32_t x12 = in1[5];
+ { const uint32_t x10 = in1[4];
+ { const uint32_t x8 = in1[3];
+ { const uint32_t x6 = in1[2];
+ { const uint32_t x4 = in1[1];
+ { const uint32_t x2 = in1[0];
+ { uint32_t x19 = (x2 >> 0x1a);
+ { uint32_t x20 = (x2 & 0x3ffffff);
+ { uint32_t x21 = (x19 + x4);
+ { uint32_t x22 = (x21 >> 0x19);
+ { uint32_t x23 = (x21 & 0x1ffffff);
+ { uint32_t x24 = (x22 + x6);
+ { uint32_t x25 = (x24 >> 0x1a);
+ { uint32_t x26 = (x24 & 0x3ffffff);
+ { uint32_t x27 = (x25 + x8);
+ { uint32_t x28 = (x27 >> 0x19);
+ { uint32_t x29 = (x27 & 0x1ffffff);
+ { uint32_t x30 = (x28 + x10);
+ { uint32_t x31 = (x30 >> 0x1a);
+ { uint32_t x32 = (x30 & 0x3ffffff);
+ { uint32_t x33 = (x31 + x12);
+ { uint32_t x34 = (x33 >> 0x19);
+ { uint32_t x35 = (x33 & 0x1ffffff);
+ { uint32_t x36 = (x34 + x14);
+ { uint32_t x37 = (x36 >> 0x1a);
+ { uint32_t x38 = (x36 & 0x3ffffff);
+ { uint32_t x39 = (x37 + x16);
+ { uint32_t x40 = (x39 >> 0x19);
+ { uint32_t x41 = (x39 & 0x1ffffff);
+ { uint32_t x42 = (x40 + x18);
+ { uint32_t x43 = (x42 >> 0x1a);
+ { uint32_t x44 = (x42 & 0x3ffffff);
+ { uint32_t x45 = (x43 + x17);
+ { uint32_t x46 = (x45 >> 0x19);
+ { uint32_t x47 = (x45 & 0x1ffffff);
+ { uint32_t x48 = (x20 + (0x13 * x46));
+ { uint32_t x49 = (x48 >> 0x1a);
+ { uint32_t x50 = (x48 & 0x3ffffff);
+ { uint32_t x51 = (x49 + x23);
+ { uint32_t x52 = (x51 >> 0x19);
+ { uint32_t x53 = (x51 & 0x1ffffff);
+ out[0] = x50;
+ out[1] = x53;
+ out[2] = (x52 + x26);
+ out[3] = x29;
+ out[4] = x32;
+ out[5] = x35;
+ out[6] = x38;
+ out[7] = x41;
+ out[8] = x44;
+ out[9] = x47;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
+
+static void fe_carry(fe *h, const fe_loose* f) {
+ assert_fe_loose(f->v);
+ fe_carry_impl(h->v, f->v);
+ assert_fe(h->v);
+}
+
+static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
+ assert_fe_loose(in1);
+ assert_fe_loose(in2);
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
+}
+
+static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_ttt(fe *h, const fe *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) {
+ assert_fe_loose(in1);
+ { const uint32_t x17 = in1[9];
+ { const uint32_t x18 = in1[8];
+ { const uint32_t x16 = in1[7];
+ { const uint32_t x14 = in1[6];
+ { const uint32_t x12 = in1[5];
+ { const uint32_t x10 = in1[4];
+ { const uint32_t x8 = in1[3];
+ { const uint32_t x6 = in1[2];
+ { const uint32_t x4 = in1[1];
+ { const uint32_t x2 = in1[0];
+ { uint64_t x19 = ((uint64_t)x2 * x2);
+ { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
+ { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
+ { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
+ { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
+ { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
+ { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
+ { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
+ { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
+ { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
+ { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
+ { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
+ { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
+ { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
+ { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
+ { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
+ { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
+ { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
+ { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
+ { uint64_t x38 = (x27 + (x37 << 0x4));
+ { uint64_t x39 = (x38 + (x37 << 0x1));
+ { uint64_t x40 = (x39 + x37);
+ { uint64_t x41 = (x26 + (x36 << 0x4));
+ { uint64_t x42 = (x41 + (x36 << 0x1));
+ { uint64_t x43 = (x42 + x36);
+ { uint64_t x44 = (x25 + (x35 << 0x4));
+ { uint64_t x45 = (x44 + (x35 << 0x1));
+ { uint64_t x46 = (x45 + x35);
+ { uint64_t x47 = (x24 + (x34 << 0x4));
+ { uint64_t x48 = (x47 + (x34 << 0x1));
+ { uint64_t x49 = (x48 + x34);
+ { uint64_t x50 = (x23 + (x33 << 0x4));
+ { uint64_t x51 = (x50 + (x33 << 0x1));
+ { uint64_t x52 = (x51 + x33);
+ { uint64_t x53 = (x22 + (x32 << 0x4));
+ { uint64_t x54 = (x53 + (x32 << 0x1));
+ { uint64_t x55 = (x54 + x32);
+ { uint64_t x56 = (x21 + (x31 << 0x4));
+ { uint64_t x57 = (x56 + (x31 << 0x1));
+ { uint64_t x58 = (x57 + x31);
+ { uint64_t x59 = (x20 + (x30 << 0x4));
+ { uint64_t x60 = (x59 + (x30 << 0x1));
+ { uint64_t x61 = (x60 + x30);
+ { uint64_t x62 = (x19 + (x29 << 0x4));
+ { uint64_t x63 = (x62 + (x29 << 0x1));
+ { uint64_t x64 = (x63 + x29);
+ { uint64_t x65 = (x64 >> 0x1a);
+ { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
+ { uint64_t x67 = (x65 + x61);
+ { uint64_t x68 = (x67 >> 0x19);
+ { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
+ { uint64_t x70 = (x68 + x58);
+ { uint64_t x71 = (x70 >> 0x1a);
+ { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
+ { uint64_t x73 = (x71 + x55);
+ { uint64_t x74 = (x73 >> 0x19);
+ { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
+ { uint64_t x76 = (x74 + x52);
+ { uint64_t x77 = (x76 >> 0x1a);
+ { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
+ { uint64_t x79 = (x77 + x49);
+ { uint64_t x80 = (x79 >> 0x19);
+ { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
+ { uint64_t x82 = (x80 + x46);
+ { uint64_t x83 = (x82 >> 0x1a);
+ { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
+ { uint64_t x85 = (x83 + x43);
+ { uint64_t x86 = (x85 >> 0x19);
+ { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
+ { uint64_t x88 = (x86 + x40);
+ { uint64_t x89 = (x88 >> 0x1a);
+ { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
+ { uint64_t x91 = (x89 + x28);
+ { uint64_t x92 = (x91 >> 0x19);
+ { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
+ { uint64_t x94 = (x66 + (0x13 * x92));
+ { uint32_t x95 = (uint32_t) (x94 >> 0x1a);
+ { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
+ { uint32_t x97 = (x95 + x69);
+ { uint32_t x98 = (x97 >> 0x19);
+ { uint32_t x99 = (x97 & 0x1ffffff);
+ out[0] = x96;
+ out[1] = x99;
+ out[2] = (x98 + x72);
+ out[3] = x75;
+ out[4] = x78;
+ out[5] = x81;
+ out[6] = x84;
+ out[7] = x87;
+ out[8] = x90;
+ out[9] = x93;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
+}
+
+static void fe_sq_tl(fe *h, const fe_loose *f) {
+ fe_sqr_impl(h->v, f->v);
+}
+
+static void fe_sq_tt(fe *h, const fe *f) {
+ fe_sqr_impl(h->v, f->v);
+}
+
+static void fe_loose_invert(fe *out, const fe_loose *z) {
+ fe t0;
+ fe t1;
+ fe t2;
+ fe t3;
+ int i;
+
+ fe_sq_tl(&t0, z);
+ fe_sq_tt(&t1, &t0);
+ for (i = 1; i < 2; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_tlt(&t1, z, &t1);
+ fe_mul_ttt(&t0, &t0, &t1);
+ fe_sq_tt(&t2, &t0);
+ fe_mul_ttt(&t1, &t1, &t2);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 5; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 10; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t2, &t2, &t1);
+ fe_sq_tt(&t3, &t2);
+ for (i = 1; i < 20; ++i) {
+ fe_sq_tt(&t3, &t3);
+ }
+ fe_mul_ttt(&t2, &t3, &t2);
+ fe_sq_tt(&t2, &t2);
+ for (i = 1; i < 10; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 50; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t2, &t2, &t1);
+ fe_sq_tt(&t3, &t2);
+ for (i = 1; i < 100; ++i) {
+ fe_sq_tt(&t3, &t3);
+ }
+ fe_mul_ttt(&t2, &t3, &t2);
+ fe_sq_tt(&t2, &t2);
+ for (i = 1; i < 50; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
+ for (i = 1; i < 5; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(out, &t1, &t0);
+}
+
+static void fe_invert(fe *out, const fe *z) {
+ fe_loose l;
+ fe_copy_lt(&l, z);
+ fe_loose_invert(out, &l);
+}
+
+static void fe_neg_impl(uint32_t out[10], const uint32_t in2[10]) {
+ { const uint32_t x20 = 0;
+ { const uint32_t x21 = 0;
+ { const uint32_t x19 = 0;
+ { const uint32_t x17 = 0;
+ { const uint32_t x15 = 0;
+ { const uint32_t x13 = 0;
+ { const uint32_t x11 = 0;
+ { const uint32_t x9 = 0;
+ { const uint32_t x7 = 0;
+ { const uint32_t x5 = 0;
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = ((0x7ffffda + x5) - x23);
+ out[1] = ((0x3fffffe + x7) - x25);
+ out[2] = ((0x7fffffe + x9) - x27);
+ out[3] = ((0x3fffffe + x11) - x29);
+ out[4] = ((0x7fffffe + x13) - x31);
+ out[5] = ((0x3fffffe + x15) - x33);
+ out[6] = ((0x7fffffe + x17) - x35);
+ out[7] = ((0x3fffffe + x19) - x37);
+ out[8] = ((0x7fffffe + x21) - x39);
+ out[9] = ((0x3fffffe + x20) - x38);
+ }}}}}}}}}}}}}}}}}}}}
+}
+
+// h = -f
+//
+// Preconditions:
+// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Postconditions:
+// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+static void fe_neg(fe_loose *h, const fe *f) {
+ assert_fe(f->v);
+ fe_neg_impl(h->v, f->v);
+ assert_fe_loose(h->v);
+}
+
+// Replace (f,g) with (g,g) if b == 1;
+// replace (f,g) with (f,g) if b == 0.
+//
+// Preconditions: b in {0,1}.
+static void fe_cmov(fe_loose *f, const fe_loose *g, unsigned b) {
+ b = 0-b;
+ unsigned i;
+ for (i = 0; i < 10; i++) {
+ uint32_t x = f->v[i] ^ g->v[i];
+ x &= b;
+ f->v[i] ^= x;
+ }
+}
+
+// return 0 if f == 0
+// return 1 if f != 0
+//
+// Preconditions:
+// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+static int fe_isnonzero(const fe_loose *f) {
+ uint8_t s[32];
+ fe_loose_tobytes(s, f);
+
+ static const uint8_t zero[32] = {0};
+ return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
+}
+
+// return 1 if f is in {1,3,5,...,q-2}
+// return 0 if f is in {0,2,4,...,q-1}
+//
+// Preconditions:
+// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+static int fe_isnegative(const fe *f) {
+ uint8_t s[32];
+ fe_tobytes(s, f);
+ return s[0] & 1;
+}
+
+// NOTE: based on fiat-crypto fe_mul, edited for in2=2*in1
+static void fe_sq2_impl(uint32_t out[10], const uint32_t in1[10]) {
+ assert_fe_loose(in1);
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = 2*in1[9];
+ { const uint32_t x39 = 2*in1[8];
+ { const uint32_t x37 = 2*in1[7];
+ { const uint32_t x35 = 2*in1[6];
+ { const uint32_t x33 = 2*in1[5];
+ { const uint32_t x31 = 2*in1[4];
+ { const uint32_t x29 = 2*in1[3];
+ { const uint32_t x27 = 2*in1[2];
+ { const uint32_t x25 = 2*in1[1];
+ { const uint32_t x23 = 2*in1[0];
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
+}
+
+static void fe_sq2_tt(fe *h, const fe *f) {
+ fe_sq2_impl(h->v, f->v);
+}
+
+static void fe_pow22523(fe *out, const fe *z) {
+ fe t0;
+ fe t1;
+ fe t2;
+ int i;
+
+ fe_sq_tt(&t0, z);
+ fe_sq_tt(&t1, &t0);
+ for (i = 1; i < 2; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(&t1, z, &t1);
+ fe_mul_ttt(&t0, &t0, &t1);
+ fe_sq_tt(&t0, &t0);
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t1, &t0);
+ for (i = 1; i < 5; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t1, &t0);
+ for (i = 1; i < 10; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(&t1, &t1, &t0);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 20; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
+ for (i = 1; i < 10; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t1, &t0);
+ for (i = 1; i < 50; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(&t1, &t1, &t0);
+ fe_sq_tt(&t2, &t1);
+ for (i = 1; i < 100; ++i) {
+ fe_sq_tt(&t2, &t2);
+ }
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
+ for (i = 1; i < 50; ++i) {
+ fe_sq_tt(&t1, &t1);
+ }
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t0, &t0);
+ for (i = 1; i < 2; ++i) {
+ fe_sq_tt(&t0, &t0);
+ }
+ fe_mul_ttt(out, &t0, z);
+}
+
+void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) {
+ fe recip;
+ fe x;
+ fe y;
+
+ fe_invert(&recip, &h->Z);
+ fe_mul_ttt(&x, &h->X, &recip);
+ fe_mul_ttt(&y, &h->Y, &recip);
+ fe_tobytes(s, &y);
+ s[31] ^= fe_isnegative(&x) << 7;
+}
+
+static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
+ fe recip;
+ fe x;
+ fe y;
+
+ fe_invert(&recip, &h->Z);
+ fe_mul_ttt(&x, &h->X, &recip);
+ fe_mul_ttt(&y, &h->Y, &recip);
+ fe_tobytes(s, &y);
+ s[31] ^= fe_isnegative(&x) << 7;
+}
+
+static const fe d = {{56195235, 13857412, 51736253, 6949390, 114729,
+ 24766616, 60832955, 30306712, 48412415, 21499315}};
+
+static const fe sqrtm1 = {{34513072, 25610706, 9377949, 3500415, 12389472,
+ 33281959, 41962654, 31548777, 326685, 11406482}};
+
+int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
+ fe u;
+ fe_loose v;
+ fe v3;
+ fe vxx;
+ fe_loose check;
+
+ fe_frombytes(&h->Y, s);
+ fe_1(&h->Z);
+ fe_sq_tt(&v3, &h->Y);
+ fe_mul_ttt(&vxx, &v3, &d);
+ fe_sub(&v, &v3, &h->Z); // u = y^2-1
+ fe_carry(&u, &v);
+ fe_add(&v, &vxx, &h->Z); // v = dy^2+1
+
+ fe_sq_tl(&v3, &v);
+ fe_mul_ttl(&v3, &v3, &v); // v3 = v^3
+ fe_sq_tt(&h->X, &v3);
+ fe_mul_ttl(&h->X, &h->X, &v);
+ fe_mul_ttt(&h->X, &h->X, &u); // x = uv^7
+
+ fe_pow22523(&h->X, &h->X); // x = (uv^7)^((q-5)/8)
+ fe_mul_ttt(&h->X, &h->X, &v3);
+ fe_mul_ttt(&h->X, &h->X, &u); // x = uv^3(uv^7)^((q-5)/8)
+
+ fe_sq_tt(&vxx, &h->X);
+ fe_mul_ttl(&vxx, &vxx, &v);
+ fe_sub(&check, &vxx, &u);
+ if (fe_isnonzero(&check)) {
+ fe_add(&check, &vxx, &u);
+ if (fe_isnonzero(&check)) {
+ return -1;
+ }
+ fe_mul_ttt(&h->X, &h->X, &sqrtm1);
+ }
+
+ if (fe_isnegative(&h->X) != (s[31] >> 7)) {
+ fe_loose t;
+ fe_neg(&t, &h->X);
+ fe_carry(&h->X, &t);
+ }
+
+ fe_mul_ttt(&h->T, &h->X, &h->Y);
+ return 0;
+}
+
+static void ge_p2_0(ge_p2 *h) {
+ fe_0(&h->X);
+ fe_1(&h->Y);
+ fe_1(&h->Z);
+}
+
+static void ge_p3_0(ge_p3 *h) {
+ fe_0(&h->X);
+ fe_1(&h->Y);
+ fe_1(&h->Z);
+ fe_0(&h->T);
+}
+
+static void ge_cached_0(ge_cached *h) {
+ fe_loose_1(&h->YplusX);
+ fe_loose_1(&h->YminusX);
+ fe_loose_1(&h->Z);
+ fe_loose_0(&h->T2d);
+}
+
+static void ge_precomp_0(ge_precomp *h) {
+ fe_loose_1(&h->yplusx);
+ fe_loose_1(&h->yminusx);
+ fe_loose_0(&h->xy2d);
+}
+
+// r = p
+static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+ fe_copy(&r->X, &p->X);
+ fe_copy(&r->Y, &p->Y);
+ fe_copy(&r->Z, &p->Z);
+}
+
+static const fe d2 = {{45281625, 27714825, 36363642, 13898781, 229458,
+ 15978800, 54557047, 27058993, 29715967, 9444199}};
+
+// r = p
+void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+ fe_add(&r->YplusX, &p->Y, &p->X);
+ fe_sub(&r->YminusX, &p->Y, &p->X);
+ fe_copy_lt(&r->Z, &p->Z);
+ fe_mul_ltt(&r->T2d, &p->T, &d2);
+}
+
+// r = p
+void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+ fe_mul_tll(&r->X, &p->X, &p->T);
+ fe_mul_tll(&r->Y, &p->Y, &p->Z);
+ fe_mul_tll(&r->Z, &p->Z, &p->T);
+}
+
+// r = p
+void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+ fe_mul_tll(&r->X, &p->X, &p->T);
+ fe_mul_tll(&r->Y, &p->Y, &p->Z);
+ fe_mul_tll(&r->Z, &p->Z, &p->T);
+ fe_mul_tll(&r->T, &p->X, &p->Y);
+}
+
+// r = p
+static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) {
+ ge_p3 t;
+ x25519_ge_p1p1_to_p3(&t, p);
+ x25519_ge_p3_to_cached(r, &t);
+}
+
+// r = 2 * p
+static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+ fe trX, trZ, trT;
+ fe t0;
+
+ fe_sq_tt(&trX, &p->X);
+ fe_sq_tt(&trZ, &p->Y);
+ fe_sq2_tt(&trT, &p->Z);
+ fe_add(&r->Y, &p->X, &p->Y);
+ fe_sq_tl(&t0, &r->Y);
+
+ fe_add(&r->Y, &trZ, &trX);
+ fe_sub(&r->Z, &trZ, &trX);
+ fe_carry(&trZ, &r->Y);
+ fe_sub(&r->X, &t0, &trZ);
+ fe_carry(&trZ, &r->Z);
+ fe_sub(&r->T, &trT, &trZ);
+}
+
+// r = 2 * p
+static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+ ge_p2 q;
+ ge_p3_to_p2(&q, p);
+ ge_p2_dbl(r, &q);
+}
+
+// r = p + q
+static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+ fe trY, trZ, trT;
+
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->yplusx);
+ fe_mul_tll(&trY, &r->Y, &q->yminusx);
+ fe_mul_tlt(&trT, &q->xy2d, &p->T);
+ fe_add(&r->T, &p->Z, &p->Z);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_add(&r->Z, &trZ, &trT);
+ fe_sub(&r->T, &trZ, &trT);
+}
+
+// r = p - q
+static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+ fe trY, trZ, trT;
+
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->yminusx);
+ fe_mul_tll(&trY, &r->Y, &q->yplusx);
+ fe_mul_tlt(&trT, &q->xy2d, &p->T);
+ fe_add(&r->T, &p->Z, &p->Z);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_sub(&r->Z, &trZ, &trT);
+ fe_add(&r->T, &trZ, &trT);
+}
+
+// r = p + q
+void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+ fe trX, trY, trZ, trT;
+
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->YplusX);
+ fe_mul_tll(&trY, &r->Y, &q->YminusX);
+ fe_mul_tlt(&trT, &q->T2d, &p->T);
+ fe_mul_ttl(&trX, &p->Z, &q->Z);
+ fe_add(&r->T, &trX, &trX);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_add(&r->Z, &trZ, &trT);
+ fe_sub(&r->T, &trZ, &trT);
+}
+
+// r = p - q
+void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+ fe trX, trY, trZ, trT;
+
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->YminusX);
+ fe_mul_tll(&trY, &r->Y, &q->YplusX);
+ fe_mul_tlt(&trT, &q->T2d, &p->T);
+ fe_mul_ttl(&trX, &p->Z, &q->Z);
+ fe_add(&r->T, &trX, &trX);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_sub(&r->Z, &trZ, &trT);
+ fe_add(&r->T, &trZ, &trT);
+}
+
+static uint8_t equal(signed char b, signed char c) {
+ uint8_t ub = b;
+ uint8_t uc = c;
+ uint8_t x = ub ^ uc; // 0: yes; 1..255: no
+ uint32_t y = x; // 0: yes; 1..255: no
+ y -= 1; // 4294967295: yes; 0..254: no
+ y >>= 31; // 1: yes; 0: no
+ return y;
+}
+
+static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
+ fe_cmov(&t->yplusx, &u->yplusx, b);
+ fe_cmov(&t->yminusx, &u->yminusx, b);
+ fe_cmov(&t->xy2d, &u->xy2d, b);
+}
+
+void x25519_ge_scalarmult_small_precomp(
+ ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) {
+ // precomp_table is first expanded into matching |ge_precomp|
+ // elements.
+ ge_precomp multiples[15];
+
+ unsigned i;
+ for (i = 0; i < 15; i++) {
+ const uint8_t *bytes = &precomp_table[i*(2 * 32)];
+ fe x, y;
+ fe_frombytes(&x, bytes);
+ fe_frombytes(&y, bytes + 32);
+
+ ge_precomp *out = &multiples[i];
+ fe_add(&out->yplusx, &y, &x);
+ fe_sub(&out->yminusx, &y, &x);
+ fe_mul_ltt(&out->xy2d, &x, &y);
+ fe_mul_llt(&out->xy2d, &out->xy2d, &d2);
+ }
+
+ // See the comment above |k25519SmallPrecomp| about the structure of the
+ // precomputed elements. This loop does 64 additions and 64 doublings to
+ // calculate the result.
+ ge_p3_0(h);
+
+ for (i = 63; i < 64; i--) {
+ unsigned j;
+ signed char index = 0;
+
+ for (j = 0; j < 4; j++) {
+ const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7));
+ index |= (bit << j);
+ }
+
+ ge_precomp e;
+ ge_precomp_0(&e);
+
+ for (j = 1; j < 16; j++) {
+ cmov(&e, &multiples[j-1], equal(index, j));
+ }
+
+ ge_cached cached;
+ ge_p1p1 r;
+ x25519_ge_p3_to_cached(&cached, h);
+ x25519_ge_add(&r, h, &cached);
+ x25519_ge_p1p1_to_p3(h, &r);
+
+ ge_madd(&r, h, &e);
+ x25519_ge_p1p1_to_p3(h, &r);
+ }
+}
+
+#if defined(OPENSSL_SMALL)
+
+// This block of code replaces the standard base-point table with a much smaller
+// one. The standard table is 30,720 bytes while this one is just 960.
+//
+// This table contains 15 pairs of group elements, (x, y), where each field
+// element is serialised with |fe_tobytes|. If |i| is the index of the group
+// element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
+// is the most significant bit). The value of the group element is then:
+// (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator.
+static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
+ 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
+ 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
+ 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
+ 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
+ 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
+ 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
+ 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
+ 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
+ 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
+ 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
+ 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
+ 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
+ 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
+ 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
+ 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
+ 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
+ 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
+ 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
+ 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
+ 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
+ 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
+ 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
+ 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
+ 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
+ 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
+ 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
+ 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
+ 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
+ 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
+ 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
+ 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
+ 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
+ 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
+ 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
+ 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
+ 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
+ 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
+ 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
+ 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
+ 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
+ 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
+ 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
+ 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
+ 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
+ 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
+ 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
+ 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
+ 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
+ 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
+ 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
+ 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
+ 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
+ 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
+ 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
+ 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
+ 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
+ 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
+ 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
+ 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
+ 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
+ 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
+ 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
+ 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
+ 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
+ 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
+ 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
+ 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
+ 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
+ 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
+ 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
+ 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
+ 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
+ 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
+ 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
+ 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
+ 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
+ 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
+ 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
+ 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
+ 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
+};
+
+void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) {
+ x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp);
+}
+
+#else
+
+// k25519Precomp[i][j] = (j+1)*256^i*B
+static const ge_precomp k25519Precomp[32][8] = {
+ {
+ {
+ {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786,
+ 27544626, 21800161, 61029707, 2047604}},
+ {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
+ 5043384, 19500929, 18085054}},
+ {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052,
+ 29287918, 11864899, 42594502, 29115885}},
+ },
+ {
+ {{54292951, 20578084, 45527620, 11784319, 41753206, 30803714,
+ 55390960, 29739860, 66750418, 23343128}},
+ {{45405608, 6903824, 27185491, 6451973, 37531140, 24000426,
+ 51492312, 11189267, 40279186, 28235350}},
+ {{26966623, 11152617, 32442495, 15396054, 14353839, 20802097,
+ 63980037, 24013313, 51636816, 29387734}},
+ },
+ {
+ {{15636272, 23865875, 24204772, 25642034, 616976, 16869170,
+ 27787599, 18782243, 28944399, 32004408}},
+ {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389,
+ 16354576, 21778470, 7689661, 11199574}},
+ {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852,
+ 7512774, 10017326, 49359771, 23634074}},
+ },
+ {
+ {{50071967, 13921891, 10945806, 27521001, 27105051, 17470053,
+ 38182653, 15006022, 3284568, 27277892}},
+ {{23599295, 25248385, 55915199, 25867015, 13236773, 10506355,
+ 7464579, 9656445, 13059162, 10374397}},
+ {{7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
+ 29715387, 66467155, 33453106}},
+ },
+ {
+ {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860,
+ 32867885, 14515107, 51670560, 10819379}},
+ {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
+ 12483687, 54440373, 5581305}},
+ {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317,
+ 28542349, 13850243, 43430843, 17738489}},
+ },
+ {
+ {{51736881, 20691677, 32573249, 4720197, 40672342, 5875510,
+ 47920237, 18329612, 57289923, 21468654}},
+ {{58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240,
+ 17864545, 1762327, 14866737}},
+ {{48909169, 17603008, 56635573, 1707277, 49922944, 3916100,
+ 38872452, 3959420, 27914454, 4383652}},
+ },
+ {
+ {{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
+ 5230134, 43156425, 18378665}},
+ {{36839857, 30090922, 7665485, 10083793, 28475525, 1649722,
+ 20654025, 16520125, 30598449, 7715701}},
+ {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315,
+ 35708204, 1370707, 29794553, 32145132}},
+ },
+ {
+ {{14499471, 30824833, 33917750, 29299779, 28494861, 14271267,
+ 30290735, 10876454, 33954766, 2381725}},
+ {{59913433, 30899068, 52378708, 462250, 39384538, 3941371,
+ 60872247, 3696004, 34808032, 15351954}},
+ {{27431194, 8222322, 16448760, 29646437, 48401861, 11938354,
+ 34147463, 30583916, 29551812, 10109425}},
+ },
+ },
+ {
+ {
+ {{53451805, 20399000, 35825113, 11777097, 21447386, 6519384,
+ 64730580, 31926875, 10092782, 28790261}},
+ {{27939166, 14210322, 4677035, 16277044, 44144402, 21156292,
+ 34600109, 12005537, 49298737, 12803509}},
+ {{17228999, 17892808, 65875336, 300139, 65883994, 21839654,
+ 30364212, 24516238, 18016356, 4397660}},
+ },
+ {
+ {{56150021, 25864224, 4776340, 18600194, 27850027, 17952220,
+ 40489757, 14544524, 49631360, 982638}},
+ {{29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899,
+ 29434304, 46061167, 9934962}},
+ {{5793284, 16271923, 42977250, 23438027, 29188559, 1206517,
+ 52360934, 4559894, 36984942, 22656481}},
+ },
+ {
+ {{39464912, 22061425, 16282656, 22517939, 28414020, 18542168,
+ 24191033, 4541697, 53770555, 5500567}},
+ {{12650548, 32057319, 9052870, 11355358, 49428827, 25154267,
+ 49678271, 12264342, 10874051, 13524335}},
+ {{25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037,
+ 5080568, 44580805, 5376627}},
+ },
+ {
+ {{41020600, 29543379, 50095164, 30016803, 60382070, 1920896,
+ 44787559, 24106988, 4535767, 1569007}},
+ {{64853442, 14606629, 45416424, 25514613, 28430648, 8775819,
+ 36614302, 3044289, 31848280, 12543772}},
+ {{45080285, 2943892, 35251351, 6777305, 13784462, 29262229,
+ 39731668, 31491700, 7718481, 14474653}},
+ },
+ {
+ {{2385296, 2454213, 44477544, 46602, 62670929, 17874016, 656964,
+ 26317767, 24316167, 28300865}},
+ {{13741529, 10911568, 33875447, 24950694, 46931033, 32521134,
+ 33040650, 20129900, 46379407, 8321685}},
+ {{21060490, 31341688, 15712756, 29218333, 1639039, 10656336,
+ 23845965, 21679594, 57124405, 608371}},
+ },
+ {
+ {{53436132, 18466845, 56219170, 25997372, 61071954, 11305546,
+ 1123968, 26773855, 27229398, 23887}},
+ {{43864724, 33260226, 55364135, 14712570, 37643165, 31524814,
+ 12797023, 27114124, 65475458, 16678953}},
+ {{37608244, 4770661, 51054477, 14001337, 7830047, 9564805,
+ 65600720, 28759386, 49939598, 4904952}},
+ },
+ {
+ {{24059538, 14617003, 19037157, 18514524, 19766092, 18648003,
+ 5169210, 16191880, 2128236, 29227599}},
+ {{50127693, 4124965, 58568254, 22900634, 30336521, 19449185,
+ 37302527, 916032, 60226322, 30567899}},
+ {{44477957, 12419371, 59974635, 26081060, 50629959, 16739174,
+ 285431, 2763829, 15736322, 4143876}},
+ },
+ {
+ {{2379333, 11839345, 62998462, 27565766, 11274297, 794957, 212801,
+ 18959769, 23527083, 17096164}},
+ {{33431108, 22423954, 49269897, 17927531, 8909498, 8376530,
+ 34483524, 4087880, 51919953, 19138217}},
+ {{1767664, 7197987, 53903638, 31531796, 54017513, 448825, 5799055,
+ 4357868, 62334673, 17231393}},
+ },
+ },
+ {
+ {
+ {{6721966, 13833823, 43585476, 32003117, 26354292, 21691111,
+ 23365146, 29604700, 7390889, 2759800}},
+ {{4409022, 2052381, 23373853, 10530217, 7676779, 20668478, 21302352,
+ 29290375, 1244379, 20634787}},
+ {{62687625, 7169618, 4982368, 30596842, 30256824, 30776892, 14086412,
+ 9208236, 15886429, 16489664}},
+ },
+ {
+ {{1996056, 10375649, 14346367, 13311202, 60234729, 17116020,
+ 53415665, 398368, 36502409, 32841498}},
+ {{41801399, 9795879, 64331450, 14878808, 33577029, 14780362,
+ 13348553, 12076947, 36272402, 5113181}},
+ {{49338080, 11797795, 31950843, 13929123, 41220562, 12288343,
+ 36767763, 26218045, 13847710, 5387222}},
+ },
+ {
+ {{48526701, 30138214, 17824842, 31213466, 22744342, 23111821,
+ 8763060, 3617786, 47508202, 10370990}},
+ {{20246567, 19185054, 22358228, 33010720, 18507282, 23140436,
+ 14554436, 24808340, 32232923, 16763880}},
+ {{9648486, 10094563, 26416693, 14745928, 36734546, 27081810,
+ 11094160, 15689506, 3140038, 17044340}},
+ },
+ {
+ {{50948792, 5472694, 31895588, 4744994, 8823515, 10365685,
+ 39884064, 9448612, 38334410, 366294}},
+ {{19153450, 11523972, 56012374, 27051289, 42461232, 5420646,
+ 28344573, 8041113, 719605, 11671788}},
+ {{8678006, 2694440, 60300850, 2517371, 4964326, 11152271, 51675948,
+ 18287915, 27000812, 23358879}},
+ },
+ {
+ {{51950941, 7134311, 8639287, 30739555, 59873175, 10421741, 564065,
+ 5336097, 6750977, 19033406}},
+ {{11836410, 29574944, 26297893, 16080799, 23455045, 15735944,
+ 1695823, 24735310, 8169719, 16220347}},
+ {{48993007, 8653646, 17578566, 27461813, 59083086, 17541668,
+ 55964556, 30926767, 61118155, 19388398}},
+ },
+ {
+ {{43800366, 22586119, 15213227, 23473218, 36255258, 22504427,
+ 27884328, 2847284, 2655861, 1738395}},
+ {{39571412, 19301410, 41772562, 25551651, 57738101, 8129820,
+ 21651608, 30315096, 48021414, 22549153}},
+ {{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
+ 5821408, 10478196, 8544890}},
+ },
+ {
+ {{32173102, 17425121, 24896206, 3921497, 22579056, 30143578,
+ 19270448, 12217473, 17789017, 30158437}},
+ {{36555903, 31326030, 51530034, 23407230, 13243888, 517024,
+ 15479401, 29701199, 30460519, 1052596}},
+ {{55493970, 13323617, 32618793, 8175907, 51878691, 12596686,
+ 27491595, 28942073, 3179267, 24075541}},
+ },
+ {
+ {{31947050, 19187781, 62468280, 18214510, 51982886, 27514722,
+ 52352086, 17142691, 19072639, 24043372}},
+ {{11685058, 11822410, 3158003, 19601838, 33402193, 29389366,
+ 5977895, 28339415, 473098, 5040608}},
+ {{46817982, 8198641, 39698732, 11602122, 1290375, 30754672,
+ 28326861, 1721092, 47550222, 30422825}},
+ },
+ },
+ {
+ {
+ {{7881532, 10687937, 7578723, 7738378, 48157852, 31000479, 21820785,
+ 8076149, 39240368, 11538388}},
+ {{47173198, 3899860, 18283497, 26752864, 51380203, 22305220,
+ 8754524, 7446702, 61432810, 5797015}},
+ {{55813245, 29760862, 51326753, 25589858, 12708868, 25098233,
+ 2014098, 24503858, 64739691, 27677090}},
+ },
+ {
+ {{44636488, 21985690, 39426843, 1146374, 18956691, 16640559,
+ 1192730, 29840233, 15123618, 10811505}},
+ {{14352079, 30134717, 48166819, 10822654, 32750596, 4699007, 67038501,
+ 15776355, 38222085, 21579878}},
+ {{38867681, 25481956, 62129901, 28239114, 29416930, 1847569,
+ 46454691, 17069576, 4714546, 23953777}},
+ },
+ {
+ {{15200332, 8368572, 19679101, 15970074, 35236190, 1959450,
+ 24611599, 29010600, 55362987, 12340219}},
+ {{12876937, 23074376, 33134380, 6590940, 60801088, 14872439,
+ 9613953, 8241152, 15370987, 9608631}},
+ {{62965568, 21540023, 8446280, 33162829, 4407737, 13629032, 59383996,
+ 15866073, 38898243, 24740332}},
+ },
+ {
+ {{26660628, 17876777, 8393733, 358047, 59707573, 992987, 43204631,
+ 858696, 20571223, 8420556}},
+ {{14620696, 13067227, 51661590, 8264466, 14106269, 15080814,
+ 33531827, 12516406, 45534429, 21077682}},
+ {{236881, 10476226, 57258, 18877408, 6472997, 2466984, 17258519,
+ 7256740, 8791136, 15069930}},
+ },
+ {
+ {{1276391, 24182514, 22949634, 17231625, 43615824, 27852245,
+ 14711874, 4874229, 36445724, 31223040}},
+ {{5855666, 4990204, 53397016, 7294283, 59304582, 1924646, 65685689,
+ 25642053, 34039526, 9234252}},
+ {{20590503, 24535444, 31529743, 26201766, 64402029, 10650547,
+ 31559055, 21944845, 18979185, 13396066}},
+ },
+ {
+ {{24474287, 4968103, 22267082, 4407354, 24063882, 25229252,
+ 48291976, 13594781, 33514650, 7021958}},
+ {{55541958, 26988926, 45743778, 15928891, 40950559, 4315420,
+ 41160136, 29637754, 45628383, 12868081}},
+ {{38473832, 13504660, 19988037, 31421671, 21078224, 6443208,
+ 45662757, 2244499, 54653067, 25465048}},
+ },
+ {
+ {{36513336, 13793478, 61256044, 319135, 41385692, 27290532,
+ 33086545, 8957937, 51875216, 5540520}},
+ {{55478669, 22050529, 58989363, 25911358, 2620055, 1022908,
+ 43398120, 31985447, 50980335, 18591624}},
+ {{23152952, 775386, 27395463, 14006635, 57407746, 4649511, 1689819,
+ 892185, 55595587, 18348483}},
+ },
+ {
+ {{9770129, 9586738, 26496094, 4324120, 1556511, 30004408, 27453818,
+ 4763127, 47929250, 5867133}},
+ {{34343820, 1927589, 31726409, 28801137, 23962433, 17534932,
+ 27846558, 5931263, 37359161, 17445976}},
+ {{27461885, 30576896, 22380809, 1815854, 44075111, 30522493,
+ 7283489, 18406359, 47582163, 7734628}},
+ },
+ },
+ {
+ {
+ {{59098600, 23963614, 55988460, 6196037, 29344158, 20123547,
+ 7585294, 30377806, 18549496, 15302069}},
+ {{34450527, 27383209, 59436070, 22502750, 6258877, 13504381,
+ 10458790, 27135971, 58236621, 8424745}},
+ {{24687186, 8613276, 36441818, 30320886, 1863891, 31723888,
+ 19206233, 7134917, 55824382, 32725512}},
+ },
+ {
+ {{11334899, 24336410, 8025292, 12707519, 17523892, 23078361,
+ 10243737, 18868971, 62042829, 16498836}},
+ {{8911542, 6887158, 57524604, 26595841, 11145640, 24010752, 17303924,
+ 19430194, 6536640, 10543906}},
+ {{38162480, 15479762, 49642029, 568875, 65611181, 11223453,
+ 64439674, 16928857, 39873154, 8876770}},
+ },
+ {
+ {{41365946, 20987567, 51458897, 32707824, 34082177, 32758143,
+ 33627041, 15824473, 66504438, 24514614}},
+ {{10330056, 70051, 7957388, 24551765, 9764901, 15609756, 27698697,
+ 28664395, 1657393, 3084098}},
+ {{10477963, 26084172, 12119565, 20303627, 29016246, 28188843,
+ 31280318, 14396151, 36875289, 15272408}},
+ },
+ {
+ {{54820555, 3169462, 28813183, 16658753, 25116432, 27923966,
+ 41934906, 20918293, 42094106, 1950503}},
+ {{40928506, 9489186, 11053416, 18808271, 36055143, 5825629,
+ 58724558, 24786899, 15341278, 8373727}},
+ {{28685821, 7759505, 52730348, 21551571, 35137043, 4079241,
+ 298136, 23321830, 64230656, 15190419}},
+ },
+ {
+ {{34175969, 13806335, 52771379, 17760000, 43104243, 10940927,
+ 8669718, 2742393, 41075551, 26679428}},
+ {{65528476, 21825014, 41129205, 22109408, 49696989, 22641577,
+ 9291593, 17306653, 54954121, 6048604}},
+ {{36803549, 14843443, 1539301, 11864366, 20201677, 1900163,
+ 13934231, 5128323, 11213262, 9168384}},
+ },
+ {
+ {{40828332, 11007846, 19408960, 32613674, 48515898, 29225851,
+ 62020803, 22449281, 20470156, 17155731}},
+ {{43972811, 9282191, 14855179, 18164354, 59746048, 19145871,
+ 44324911, 14461607, 14042978, 5230683}},
+ {{29969548, 30812838, 50396996, 25001989, 9175485, 31085458,
+ 21556950, 3506042, 61174973, 21104723}},
+ },
+ {
+ {{63964118, 8744660, 19704003, 4581278, 46678178, 6830682,
+ 45824694, 8971512, 38569675, 15326562}},
+ {{47644235, 10110287, 49846336, 30050539, 43608476, 1355668,
+ 51585814, 15300987, 46594746, 9168259}},
+ {{61755510, 4488612, 43305616, 16314346, 7780487, 17915493,
+ 38160505, 9601604, 33087103, 24543045}},
+ },
+ {
+ {{47665694, 18041531, 46311396, 21109108, 37284416, 10229460,
+ 39664535, 18553900, 61111993, 15664671}},
+ {{23294591, 16921819, 44458082, 25083453, 27844203, 11461195,
+ 13099750, 31094076, 18151675, 13417686}},
+ {{42385932, 29377914, 35958184, 5988918, 40250079, 6685064,
+ 1661597, 21002991, 15271675, 18101767}},
+ },
+ },
+ {
+ {
+ {{11433023, 20325767, 8239630, 28274915, 65123427, 32828713,
+ 48410099, 2167543, 60187563, 20114249}},
+ {{35672693, 15575145, 30436815, 12192228, 44645511, 9395378,
+ 57191156, 24915434, 12215109, 12028277}},
+ {{14098381, 6555944, 23007258, 5757252, 51681032, 20603929,
+ 30123439, 4617780, 50208775, 32898803}},
+ },
+ {
+ {{63082644, 18313596, 11893167, 13718664, 52299402, 1847384,
+ 51288865, 10154008, 23973261, 20869958}},
+ {{40577025, 29858441, 65199965, 2534300, 35238307, 17004076,
+ 18341389, 22134481, 32013173, 23450893}},
+ {{41629544, 10876442, 55337778, 18929291, 54739296, 1838103,
+ 21911214, 6354752, 4425632, 32716610}},
+ },
+ {
+ {{56675475, 18941465, 22229857, 30463385, 53917697, 776728,
+ 49693489, 21533969, 4725004, 14044970}},
+ {{19268631, 26250011, 1555348, 8692754, 45634805, 23643767, 6347389,
+ 32142648, 47586572, 17444675}},
+ {{42244775, 12986007, 56209986, 27995847, 55796492, 33405905,
+ 19541417, 8180106, 9282262, 10282508}},
+ },
+ {
+ {{40903763, 4428546, 58447668, 20360168, 4098401, 19389175,
+ 15522534, 8372215, 5542595, 22851749}},
+ {{56546323, 14895632, 26814552, 16880582, 49628109, 31065071,
+ 64326972, 6993760, 49014979, 10114654}},
+ {{47001790, 32625013, 31422703, 10427861, 59998115, 6150668,
+ 38017109, 22025285, 25953724, 33448274}},
+ },
+ {
+ {{62874467, 25515139, 57989738, 3045999, 2101609, 20947138,
+ 19390019, 6094296, 63793585, 12831124}},
+ {{51110167, 7578151, 5310217, 14408357, 33560244, 33329692,
+ 31575953, 6326196, 7381791, 31132593}},
+ {{46206085, 3296810, 24736065, 17226043, 18374253, 7318640,
+ 6295303, 8082724, 51746375, 12339663}},
+ },
+ {
+ {{27724736, 2291157, 6088201, 19369634, 1792726, 5857634, 13848414,
+ 15768922, 25091167, 14856294}},
+ {{48242193, 8331042, 24373479, 8541013, 66406866, 24284974, 12927299,
+ 20858939, 44926390, 24541532}},
+ {{55685435, 28132841, 11632844, 3405020, 30536730, 21880393,
+ 39848098, 13866389, 30146206, 9142070}},
+ },
+ {
+ {{3924129, 18246916, 53291741, 23499471, 12291819, 32886066,
+ 39406089, 9326383, 58871006, 4171293}},
+ {{51186905, 16037936, 6713787, 16606682, 45496729, 2790943,
+ 26396185, 3731949, 345228, 28091483}},
+ {{45781307, 13448258, 25284571, 1143661, 20614966, 24705045,
+ 2031538, 21163201, 50855680, 19972348}},
+ },
+ {
+ {{31016192, 16832003, 26371391, 19103199, 62081514, 14854136,
+ 17477601, 3842657, 28012650, 17149012}},
+ {{62033029, 9368965, 58546785, 28953529, 51858910, 6970559,
+ 57918991, 16292056, 58241707, 3507939}},
+ {{29439664, 3537914, 23333589, 6997794, 49553303, 22536363,
+ 51899661, 18503164, 57943934, 6580395}},
+ },
+ },
+ {
+ {
+ {{54923003, 25874643, 16438268, 10826160, 58412047, 27318820,
+ 17860443, 24280586, 65013061, 9304566}},
+ {{20714545, 29217521, 29088194, 7406487, 11426967, 28458727,
+ 14792666, 18945815, 5289420, 33077305}},
+ {{50443312, 22903641, 60948518, 20248671, 9192019, 31751970,
+ 17271489, 12349094, 26939669, 29802138}},
+ },
+ {
+ {{54218966, 9373457, 31595848, 16374215, 21471720, 13221525,
+ 39825369, 21205872, 63410057, 117886}},
+ {{22263325, 26994382, 3984569, 22379786, 51994855, 32987646,
+ 28311252, 5358056, 43789084, 541963}},
+ {{16259200, 3261970, 2309254, 18019958, 50223152, 28972515,
+ 24134069, 16848603, 53771797, 20002236}},
+ },
+ {
+ {{9378160, 20414246, 44262881, 20809167, 28198280, 26310334,
+ 64709179, 32837080, 690425, 14876244}},
+ {{24977353, 33240048, 58884894, 20089345, 28432342, 32378079,
+ 54040059, 21257083, 44727879, 6618998}},
+ {{65570671, 11685645, 12944378, 13682314, 42719353, 19141238,
+ 8044828, 19737104, 32239828, 27901670}},
+ },
+ {
+ {{48505798, 4762989, 66182614, 8885303, 38696384, 30367116, 9781646,
+ 23204373, 32779358, 5095274}},
+ {{34100715, 28339925, 34843976, 29869215, 9460460, 24227009,
+ 42507207, 14506723, 21639561, 30924196}},
+ {{50707921, 20442216, 25239337, 15531969, 3987758, 29055114,
+ 65819361, 26690896, 17874573, 558605}},
+ },
+ {
+ {{53508735, 10240080, 9171883, 16131053, 46239610, 9599699,
+ 33499487, 5080151, 2085892, 5119761}},
+ {{44903700, 31034903, 50727262, 414690, 42089314, 2170429,
+ 30634760, 25190818, 35108870, 27794547}},
+ {{60263160, 15791201, 8550074, 32241778, 29928808, 21462176,
+ 27534429, 26362287, 44757485, 12961481}},
+ },
+ {
+ {{42616785, 23983660, 10368193, 11582341, 43711571, 31309144,
+ 16533929, 8206996, 36914212, 28394793}},
+ {{55987368, 30172197, 2307365, 6362031, 66973409, 8868176, 50273234,
+ 7031274, 7589640, 8945490}},
+ {{34956097, 8917966, 6661220, 21876816, 65916803, 17761038,
+ 7251488, 22372252, 24099108, 19098262}},
+ },
+ {
+ {{5019539, 25646962, 4244126, 18840076, 40175591, 6453164,
+ 47990682, 20265406, 60876967, 23273695}},
+ {{10853575, 10721687, 26480089, 5861829, 44113045, 1972174,
+ 65242217, 22996533, 63745412, 27113307}},
+ {{50106456, 5906789, 221599, 26991285, 7828207, 20305514, 24362660,
+ 31546264, 53242455, 7421391}},
+ },
+ {
+ {{8139908, 27007935, 32257645, 27663886, 30375718, 1886181,
+ 45933756, 15441251, 28826358, 29431403}},
+ {{6267067, 9695052, 7709135, 16950835, 34239795, 31668296,
+ 14795159, 25714308, 13746020, 31812384}},
+ {{28584883, 7787108, 60375922, 18503702, 22846040, 25983196,
+ 63926927, 33190907, 4771361, 25134474}},
+ },
+ },
+ {
+ {
+ {{24949256, 6376279, 39642383, 25379823, 48462709, 23623825,
+ 33543568, 21412737, 3569626, 11342593}},
+ {{26514970, 4740088, 27912651, 3697550, 19331575, 22082093, 6809885,
+ 4608608, 7325975, 18753361}},
+ {{55490446, 19000001, 42787651, 7655127, 65739590, 5214311,
+ 39708324, 10258389, 49462170, 25367739}},
+ },
+ {
+ {{11431185, 15823007, 26570245, 14329124, 18029990, 4796082,
+ 35662685, 15580663, 9280358, 29580745}},
+ {{66948081, 23228174, 44253547, 29249434, 46247496, 19933429,
+ 34297962, 22372809, 51563772, 4387440}},
+ {{46309467, 12194511, 3937617, 27748540, 39954043, 9340369,
+ 42594872, 8548136, 20617071, 26072431}},
+ },
+ {
+ {{66170039, 29623845, 58394552, 16124717, 24603125, 27329039,
+ 53333511, 21678609, 24345682, 10325460}},
+ {{47253587, 31985546, 44906155, 8714033, 14007766, 6928528,
+ 16318175, 32543743, 4766742, 3552007}},
+ {{45357481, 16823515, 1351762, 32751011, 63099193, 3950934, 3217514,
+ 14481909, 10988822, 29559670}},
+ },
+ {
+ {{15564307, 19242862, 3101242, 5684148, 30446780, 25503076,
+ 12677126, 27049089, 58813011, 13296004}},
+ {{57666574, 6624295, 36809900, 21640754, 62437882, 31497052,
+ 31521203, 9614054, 37108040, 12074673}},
+ {{4771172, 33419193, 14290748, 20464580, 27992297, 14998318,
+ 65694928, 31997715, 29832612, 17163397}},
+ },
+ {
+ {{7064884, 26013258, 47946901, 28486894, 48217594, 30641695,
+ 25825241, 5293297, 39986204, 13101589}},
+ {{64810282, 2439669, 59642254, 1719964, 39841323, 17225986,
+ 32512468, 28236839, 36752793, 29363474}},
+ {{37102324, 10162315, 33928688, 3981722, 50626726, 20484387,
+ 14413973, 9515896, 19568978, 9628812}},
+ },
+ {
+ {{33053803, 199357, 15894591, 1583059, 27380243, 28973997, 49269969,
+ 27447592, 60817077, 3437739}},
+ {{48129987, 3884492, 19469877, 12726490, 15913552, 13614290,
+ 44147131, 70103, 7463304, 4176122}},
+ {{39984863, 10659916, 11482427, 17484051, 12771466, 26919315,
+ 34389459, 28231680, 24216881, 5944158}},
+ },
+ {
+ {{8894125, 7450974, 64444715, 23788679, 39028346, 21165316,
+ 19345745, 14680796, 11632993, 5847885}},
+ {{26942781, 31239115, 9129563, 28647825, 26024104, 11769399,
+ 55590027, 6367193, 57381634, 4782139}},
+ {{19916442, 28726022, 44198159, 22140040, 25606323, 27581991,
+ 33253852, 8220911, 6358847, 31680575}},
+ },
+ {
+ {{801428, 31472730, 16569427, 11065167, 29875704, 96627, 7908388,
+ 29073952, 53570360, 1387154}},
+ {{19646058, 5720633, 55692158, 12814208, 11607948, 12749789,
+ 14147075, 15156355, 45242033, 11835259}},
+ {{19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523,
+ 15467869, 40548314, 5052482}},
+ },
+ },
+ {
+ {
+ {{64091413, 10058205, 1980837, 3964243, 22160966, 12322533, 60677741,
+ 20936246, 12228556, 26550755}},
+ {{32944382, 14922211, 44263970, 5188527, 21913450, 24834489,
+ 4001464, 13238564, 60994061, 8653814}},
+ {{22865569, 28901697, 27603667, 21009037, 14348957, 8234005,
+ 24808405, 5719875, 28483275, 2841751}},
+ },
+ {
+ {{50687877, 32441126, 66781144, 21446575, 21886281, 18001658,
+ 65220897, 33238773, 19932057, 20815229}},
+ {{55452759, 10087520, 58243976, 28018288, 47830290, 30498519,
+ 3999227, 13239134, 62331395, 19644223}},
+ {{1382174, 21859713, 17266789, 9194690, 53784508, 9720080,
+ 20403944, 11284705, 53095046, 3093229}},
+ },
+ {
+ {{16650902, 22516500, 66044685, 1570628, 58779118, 7352752, 66806440,
+ 16271224, 43059443, 26862581}},
+ {{45197768, 27626490, 62497547, 27994275, 35364760, 22769138,
+ 24123613, 15193618, 45456747, 16815042}},
+ {{57172930, 29264984, 41829040, 4372841, 2087473, 10399484,
+ 31870908, 14690798, 17361620, 11864968}},
+ },
+ {
+ {{55801235, 6210371, 13206574, 5806320, 38091172, 19587231,
+ 54777658, 26067830, 41530403, 17313742}},
+ {{14668443, 21284197, 26039038, 15305210, 25515617, 4542480,
+ 10453892, 6577524, 9145645, 27110552}},
+ {{5974855, 3053895, 57675815, 23169240, 35243739, 3225008,
+ 59136222, 3936127, 61456591, 30504127}},
+ },
+ {
+ {{30625386, 28825032, 41552902, 20761565, 46624288, 7695098,
+ 17097188, 17250936, 39109084, 1803631}},
+ {{63555773, 9865098, 61880298, 4272700, 61435032, 16864731,
+ 14911343, 12196514, 45703375, 7047411}},
+ {{20093258, 9920966, 55970670, 28210574, 13161586, 12044805,
+ 34252013, 4124600, 34765036, 23296865}},
+ },
+ {
+ {{46320040, 14084653, 53577151, 7842146, 19119038, 19731827,
+ 4752376, 24839792, 45429205, 2288037}},
+ {{40289628, 30270716, 29965058, 3039786, 52635099, 2540456,
+ 29457502, 14625692, 42289247, 12570231}},
+ {{66045306, 22002608, 16920317, 12494842, 1278292, 27685323,
+ 45948920, 30055751, 55134159, 4724942}},
+ },
+ {
+ {{17960970, 21778898, 62967895, 23851901, 58232301, 32143814,
+ 54201480, 24894499, 37532563, 1903855}},
+ {{23134274, 19275300, 56426866, 31942495, 20684484, 15770816,
+ 54119114, 3190295, 26955097, 14109738}},
+ {{15308788, 5320727, 36995055, 19235554, 22902007, 7767164,
+ 29425325, 22276870, 31960941, 11934971}},
+ },
+ {
+ {{39713153, 8435795, 4109644, 12222639, 42480996, 14818668,
+ 20638173, 4875028, 10491392, 1379718}},
+ {{53949449, 9197840, 3875503, 24618324, 65725151, 27674630,
+ 33518458, 16176658, 21432314, 12180697}},
+ {{55321537, 11500837, 13787581, 19721842, 44678184, 10140204,
+ 1465425, 12689540, 56807545, 19681548}},
+ },
+ },
+ {
+ {
+ {{5414091, 18168391, 46101199, 9643569, 12834970, 1186149,
+ 64485948, 32212200, 26128230, 6032912}},
+ {{40771450, 19788269, 32496024, 19900513, 17847800, 20885276,
+ 3604024, 8316894, 41233830, 23117073}},
+ {{3296484, 6223048, 24680646, 21307972, 44056843, 5903204,
+ 58246567, 28915267, 12376616, 3188849}},
+ },
+ {
+ {{29190469, 18895386, 27549112, 32370916, 3520065, 22857131,
+ 32049514, 26245319, 50999629, 23702124}},
+ {{52364359, 24245275, 735817, 32955454, 46701176, 28496527,
+ 25246077, 17758763, 18640740, 32593455}},
+ {{60180029, 17123636, 10361373, 5642961, 4910474, 12345252,
+ 35470478, 33060001, 10530746, 1053335}},
+ },
+ {
+ {{37842897, 19367626, 53570647, 21437058, 47651804, 22899047,
+ 35646494, 30605446, 24018830, 15026644}},
+ {{44516310, 30409154, 64819587, 5953842, 53668675, 9425630,
+ 25310643, 13003497, 64794073, 18408815}},
+ {{39688860, 32951110, 59064879, 31885314, 41016598, 13987818,
+ 39811242, 187898, 43942445, 31022696}},
+ },
+ {
+ {{45364466, 19743956, 1844839, 5021428, 56674465, 17642958,
+ 9716666, 16266922, 62038647, 726098}},
+ {{29370903, 27500434, 7334070, 18212173, 9385286, 2247707,
+ 53446902, 28714970, 30007387, 17731091}},
+ {{66172485, 16086690, 23751945, 33011114, 65941325, 28365395, 9137108,
+ 730663, 9835848, 4555336}},
+ },
+ {
+ {{43732429, 1410445, 44855111, 20654817, 30867634, 15826977,
+ 17693930, 544696, 55123566, 12422645}},
+ {{31117226, 21338698, 53606025, 6561946, 57231997, 20796761,
+ 61990178, 29457725, 29120152, 13924425}},
+ {{49707966, 19321222, 19675798, 30819676, 56101901, 27695611,
+ 57724924, 22236731, 7240930, 33317044}},
+ },
+ {
+ {{35747106, 22207651, 52101416, 27698213, 44655523, 21401660,
+ 1222335, 4389483, 3293637, 18002689}},
+ {{50424044, 19110186, 11038543, 11054958, 53307689, 30215898,
+ 42789283, 7733546, 12796905, 27218610}},
+ {{58349431, 22736595, 41689999, 10783768, 36493307, 23807620,
+ 38855524, 3647835, 3222231, 22393970}},
+ },
+ {
+ {{18606113, 1693100, 41660478, 18384159, 4112352, 10045021,
+ 23603893, 31506198, 59558087, 2484984}},
+ {{9255298, 30423235, 54952701, 32550175, 13098012, 24339566,
+ 16377219, 31451620, 47306788, 30519729}},
+ {{44379556, 7496159, 61366665, 11329248, 19991973, 30206930,
+ 35390715, 9936965, 37011176, 22935634}},
+ },
+ {
+ {{21878571, 28553135, 4338335, 13643897, 64071999, 13160959,
+ 19708896, 5415497, 59748361, 29445138}},
+ {{27736842, 10103576, 12500508, 8502413, 63695848, 23920873,
+ 10436917, 32004156, 43449720, 25422331}},
+ {{19492550, 21450067, 37426887, 32701801, 63900692, 12403436,
+ 30066266, 8367329, 13243957, 8709688}},
+ },
+ },
+ {
+ {
+ {{12015105, 2801261, 28198131, 10151021, 24818120, 28811299,
+ 55914672, 27908697, 5150967, 7274186}},
+ {{2831347, 21062286, 1478974, 6122054, 23825128, 20820846,
+ 31097298, 6083058, 31021603, 23760822}},
+ {{64578913, 31324785, 445612, 10720828, 53259337, 22048494,
+ 43601132, 16354464, 15067285, 19406725}},
+ },
+ {
+ {{7840923, 14037873, 33744001, 15934015, 66380651, 29911725,
+ 21403987, 1057586, 47729402, 21151211}},
+ {{915865, 17085158, 15608284, 24765302, 42751837, 6060029,
+ 49737545, 8410996, 59888403, 16527024}},
+ {{32922597, 32997445, 20336073, 17369864, 10903704, 28169945,
+ 16957573, 52992, 23834301, 6588044}},
+ },
+ {
+ {{32752011, 11232950, 3381995, 24839566, 22652987, 22810329,
+ 17159698, 16689107, 46794284, 32248439}},
+ {{62419196, 9166775, 41398568, 22707125, 11576751, 12733943,
+ 7924251, 30802151, 1976122, 26305405}},
+ {{21251203, 16309901, 64125849, 26771309, 30810596, 12967303, 156041,
+ 30183180, 12331344, 25317235}},
+ },
+ {
+ {{8651595, 29077400, 51023227, 28557437, 13002506, 2950805,
+ 29054427, 28447462, 10008135, 28886531}},
+ {{31486061, 15114593, 52847614, 12951353, 14369431, 26166587,
+ 16347320, 19892343, 8684154, 23021480}},
+ {{19443825, 11385320, 24468943, 23895364, 43189605, 2187568,
+ 40845657, 27467510, 31316347, 14219878}},
+ },
+ {
+ {{38514374, 1193784, 32245219, 11392485, 31092169, 15722801,
+ 27146014, 6992409, 29126555, 9207390}},
+ {{32382916, 1110093, 18477781, 11028262, 39697101, 26006320,
+ 62128346, 10843781, 59151264, 19118701}},
+ {{2814918, 7836403, 27519878, 25686276, 46214848, 22000742,
+ 45614304, 8550129, 28346258, 1994730}},
+ },
+ {
+ {{47530565, 8085544, 53108345, 29605809, 2785837, 17323125,
+ 47591912, 7174893, 22628102, 8115180}},
+ {{36703732, 955510, 55975026, 18476362, 34661776, 20276352,
+ 41457285, 3317159, 57165847, 930271}},
+ {{51805164, 26720662, 28856489, 1357446, 23421993, 1057177,
+ 24091212, 32165462, 44343487, 22903716}},
+ },
+ {
+ {{44357633, 28250434, 54201256, 20785565, 51297352, 25757378,
+ 52269845, 17000211, 65241845, 8398969}},
+ {{35139535, 2106402, 62372504, 1362500, 12813763, 16200670,
+ 22981545, 27263159, 18009407, 17781660}},
+ {{49887941, 24009210, 39324209, 14166834, 29815394, 7444469,
+ 29551787, 29827013, 19288548, 1325865}},
+ },
+ {
+ {{15100138, 17718680, 43184885, 32549333, 40658671, 15509407,
+ 12376730, 30075286, 33166106, 25511682}},
+ {{20909212, 13023121, 57899112, 16251777, 61330449, 25459517,
+ 12412150, 10018715, 2213263, 19676059}},
+ {{32529814, 22479743, 30361438, 16864679, 57972923, 1513225,
+ 22922121, 6382134, 61341936, 8371347}},
+ },
+ },
+ {
+ {
+ {{9923462, 11271500, 12616794, 3544722, 37110496, 31832805,
+ 12891686, 25361300, 40665920, 10486143}},
+ {{44511638, 26541766, 8587002, 25296571, 4084308, 20584370, 361725,
+ 2610596, 43187334, 22099236}},
+ {{5408392, 32417741, 62139741, 10561667, 24145918, 14240566,
+ 31319731, 29318891, 19985174, 30118346}},
+ },
+ {
+ {{53114407, 16616820, 14549246, 3341099, 32155958, 13648976,
+ 49531796, 8849296, 65030, 8370684}},
+ {{58787919, 21504805, 31204562, 5839400, 46481576, 32497154,
+ 47665921, 6922163, 12743482, 23753914}},
+ {{64747493, 12678784, 28815050, 4759974, 43215817, 4884716,
+ 23783145, 11038569, 18800704, 255233}},
+ },
+ {
+ {{61839187, 31780545, 13957885, 7990715, 23132995, 728773, 13393847,
+ 9066957, 19258688, 18800639}},
+ {{64172210, 22726896, 56676774, 14516792, 63468078, 4372540,
+ 35173943, 2209389, 65584811, 2055793}},
+ {{580882, 16705327, 5468415, 30871414, 36182444, 18858431,
+ 59905517, 24560042, 37087844, 7394434}},
+ },
+ {
+ {{23838809, 1822728, 51370421, 15242726, 8318092, 29821328,
+ 45436683, 30062226, 62287122, 14799920}},
+ {{13345610, 9759151, 3371034, 17416641, 16353038, 8577942, 31129804,
+ 13496856, 58052846, 7402517}},
+ {{2286874, 29118501, 47066405, 31546095, 53412636, 5038121,
+ 11006906, 17794080, 8205060, 1607563}},
+ },
+ {
+ {{14414067, 25552300, 3331829, 30346215, 22249150, 27960244,
+ 18364660, 30647474, 30019586, 24525154}},
+ {{39420813, 1585952, 56333811, 931068, 37988643, 22552112,
+ 52698034, 12029092, 9944378, 8024}},
+ {{4368715, 29844802, 29874199, 18531449, 46878477, 22143727,
+ 50994269, 32555346, 58966475, 5640029}},
+ },
+ {
+ {{10299591, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887,
+ 16859868, 15219797, 19226649}},
+ {{27425505, 27835351, 3055005, 10660664, 23458024, 595578, 51710259,
+ 32381236, 48766680, 9742716}},
+ {{6744077, 2427284, 26042789, 2720740, 66260958, 1118973, 32324614,
+ 7406442, 12420155, 1994844}},
+ },
+ {
+ {{14012502, 28529712, 48724410, 23975962, 40623521, 29617992,
+ 54075385, 22644628, 24319928, 27108099}},
+ {{16412671, 29047065, 10772640, 15929391, 50040076, 28895810,
+ 10555944, 23070383, 37006495, 28815383}},
+ {{22397363, 25786748, 57815702, 20761563, 17166286, 23799296,
+ 39775798, 6199365, 21880021, 21303672}},
+ },
+ {
+ {{62825557, 5368522, 35991846, 8163388, 36785801, 3209127,
+ 16557151, 8890729, 8840445, 4957760}},
+ {{51661137, 709326, 60189418, 22684253, 37330941, 6522331,
+ 45388683, 12130071, 52312361, 5005756}},
+ {{64994094, 19246303, 23019041, 15765735, 41839181, 6002751,
+ 10183197, 20315106, 50713577, 31378319}},
+ },
+ },
+ {
+ {
+ {{48083108, 1632004, 13466291, 25559332, 43468412, 16573536,
+ 35094956, 30497327, 22208661, 2000468}},
+ {{3065054, 32141671, 41510189, 33192999, 49425798, 27851016,
+ 58944651, 11248526, 63417650, 26140247}},
+ {{10379208, 27508878, 8877318, 1473647, 37817580, 21046851,
+ 16690914, 2553332, 63976176, 16400288}},
+ },
+ {
+ {{15716668, 1254266, 48636174, 7446273, 58659946, 6344163,
+ 45011593, 26268851, 26894936, 9132066}},
+ {{24158868, 12938817, 11085297, 25376834, 39045385, 29097348,
+ 36532400, 64451, 60291780, 30861549}},
+ {{13488534, 7794716, 22236231, 5989356, 25426474, 20976224, 2350709,
+ 30135921, 62420857, 2364225}},
+ },
+ {
+ {{16335033, 9132434, 25640582, 6678888, 1725628, 8517937, 55301840,
+ 21856974, 15445874, 25756331}},
+ {{29004188, 25687351, 28661401, 32914020, 54314860, 25611345,
+ 31863254, 29418892, 66830813, 17795152}},
+ {{60986784, 18687766, 38493958, 14569918, 56250865, 29962602,
+ 10343411, 26578142, 37280576, 22738620}},
+ },
+ {
+ {{27081650, 3463984, 14099042, 29036828, 1616302, 27348828, 29542635,
+ 15372179, 17293797, 960709}},
+ {{20263915, 11434237, 61343429, 11236809, 13505955, 22697330,
+ 50997518, 6493121, 47724353, 7639713}},
+ {{64278047, 18715199, 25403037, 25339236, 58791851, 17380732,
+ 18006286, 17510682, 29994676, 17746311}},
+ },
+ {
+ {{9769828, 5202651, 42951466, 19923039, 39057860, 21992807,
+ 42495722, 19693649, 35924288, 709463}},
+ {{12286395, 13076066, 45333675, 32377809, 42105665, 4057651,
+ 35090736, 24663557, 16102006, 13205847}},
+ {{13733362, 5599946, 10557076, 3195751, 61550873, 8536969, 41568694,
+ 8525971, 10151379, 10394400}},
+ },
+ {
+ {{4024660, 17416881, 22436261, 12276534, 58009849, 30868332,
+ 19698228, 11743039, 33806530, 8934413}},
+ {{51229064, 29029191, 58528116, 30620370, 14634844, 32856154,
+ 57659786, 3137093, 55571978, 11721157}},
+ {{17555920, 28540494, 8268605, 2331751, 44370049, 9761012, 9319229,
+ 8835153, 57903375, 32274386}},
+ },
+ {
+ {{66647436, 25724417, 20614117, 16688288, 59594098, 28747312,
+ 22300303, 505429, 6108462, 27371017}},
+ {{62038564, 12367916, 36445330, 3234472, 32617080, 25131790,
+ 29880582, 20071101, 40210373, 25686972}},
+ {{35133562, 5726538, 26934134, 10237677, 63935147, 32949378,
+ 24199303, 3795095, 7592688, 18562353}},
+ },
+ {
+ {{21594432, 18590204, 17466407, 29477210, 32537083, 2739898,
+ 6407723, 12018833, 38852812, 4298411}},
+ {{46458361, 21592935, 39872588, 570497, 3767144, 31836892,
+ 13891941, 31985238, 13717173, 10805743}},
+ {{52432215, 17910135, 15287173, 11927123, 24177847, 25378864,
+ 66312432, 14860608, 40169934, 27690595}},
+ },
+ },
+ {
+ {
+ {{12962541, 5311799, 57048096, 11658279, 18855286, 25600231,
+ 13286262, 20745728, 62727807, 9882021}},
+ {{18512060, 11319350, 46985740, 15090308, 18818594, 5271736,
+ 44380960, 3666878, 43141434, 30255002}},
+ {{60319844, 30408388, 16192428, 13241070, 15898607, 19348318,
+ 57023983, 26893321, 64705764, 5276064}},
+ },
+ {
+ {{30169808, 28236784, 26306205, 21803573, 27814963, 7069267,
+ 7152851, 3684982, 1449224, 13082861}},
+ {{10342807, 3098505, 2119311, 193222, 25702612, 12233820, 23697382,
+ 15056736, 46092426, 25352431}},
+ {{33958735, 3261607, 22745853, 7948688, 19370557, 18376767,
+ 40936887, 6482813, 56808784, 22494330}},
+ },
+ {
+ {{32869458, 28145887, 25609742, 15678670, 56421095, 18083360,
+ 26112420, 2521008, 44444576, 6904814}},
+ {{29506904, 4457497, 3377935, 23757988, 36598817, 12935079, 1561737,
+ 3841096, 38105225, 26896789}},
+ {{10340844, 26924055, 48452231, 31276001, 12621150, 20215377,
+ 30878496, 21730062, 41524312, 5181965}},
+ },
+ {
+ {{25940096, 20896407, 17324187, 23247058, 58437395, 15029093,
+ 24396252, 17103510, 64786011, 21165857}},
+ {{45343161, 9916822, 65808455, 4079497, 66080518, 11909558, 1782390,
+ 12641087, 20603771, 26992690}},
+ {{48226577, 21881051, 24849421, 11501709, 13161720, 28785558,
+ 1925522, 11914390, 4662781, 7820689}},
+ },
+ {
+ {{12241050, 33128450, 8132690, 9393934, 32846760, 31954812, 29749455,
+ 12172924, 16136752, 15264020}},
+ {{56758909, 18873868, 58896884, 2330219, 49446315, 19008651,
+ 10658212, 6671822, 19012087, 3772772}},
+ {{3753511, 30133366, 10617073, 2028709, 14841030, 26832768, 28718731,
+ 17791548, 20527770, 12988982}},
+ },
+ {
+ {{52286360, 27757162, 63400876, 12689772, 66209881, 22639565,
+ 42925817, 22989488, 3299664, 21129479}},
+ {{50331161, 18301130, 57466446, 4978982, 3308785, 8755439, 6943197,
+ 6461331, 41525717, 8991217}},
+ {{49882601, 1816361, 65435576, 27467992, 31783887, 25378441,
+ 34160718, 7417949, 36866577, 1507264}},
+ },
+ {
+ {{29692644, 6829891, 56610064, 4334895, 20945975, 21647936,
+ 38221255, 8209390, 14606362, 22907359}},
+ {{63627275, 8707080, 32188102, 5672294, 22096700, 1711240, 34088169,
+ 9761486, 4170404, 31469107}},
+ {{55521375, 14855944, 62981086, 32022574, 40459774, 15084045,
+ 22186522, 16002000, 52832027, 25153633}},
+ },
+ {
+ {{62297408, 13761028, 35404987, 31070512, 63796392, 7869046,
+ 59995292, 23934339, 13240844, 10965870}},
+ {{59366301, 25297669, 52340529, 19898171, 43876480, 12387165,
+ 4498947, 14147411, 29514390, 4302863}},
+ {{53695440, 21146572, 20757301, 19752600, 14785142, 8976368,
+ 62047588, 31410058, 17846987, 19582505}},
+ },
+ },
+ {
+ {
+ {{64864412, 32799703, 62511833, 32488122, 60861691, 1455298,
+ 45461136, 24339642, 61886162, 12650266}},
+ {{57202067, 17484121, 21134159, 12198166, 40044289, 708125, 387813,
+ 13770293, 47974538, 10958662}},
+ {{22470984, 12369526, 23446014, 28113323, 45588061, 23855708,
+ 55336367, 21979976, 42025033, 4271861}},
+ },
+ {
+ {{41939299, 23500789, 47199531, 15361594, 61124506, 2159191,
+ 75375, 29275903, 34582642, 8469672}},
+ {{15854951, 4148314, 58214974, 7259001, 11666551, 13824734,
+ 36577666, 2697371, 24154791, 24093489}},
+ {{15446137, 17747788, 29759746, 14019369, 30811221, 23944241,
+ 35526855, 12840103, 24913809, 9815020}},
+ },
+ {
+ {{62399578, 27940162, 35267365, 21265538, 52665326, 10799413,
+ 58005188, 13438768, 18735128, 9466238}},
+ {{11933045, 9281483, 5081055, 28370608, 64480701, 28648802, 59381042,
+ 22658328, 44380208, 16199063}},
+ {{14576810, 379472, 40322331, 25237195, 37682355, 22741457,
+ 67006097, 1876698, 30801119, 2164795}},
+ },
+ {
+ {{15995086, 3199873, 13672555, 13712240, 47730029, 28906785,
+ 54027253, 18058162, 53616056, 1268051}},
+ {{56818250, 29895392, 63822271, 10948817, 23037027, 3794475,
+ 63638526, 20954210, 50053494, 3565903}},
+ {{29210069, 24135095, 61189071, 28601646, 10834810, 20226706,
+ 50596761, 22733718, 39946641, 19523900}},
+ },
+ {
+ {{53946955, 15508587, 16663704, 25398282, 38758921, 9019122,
+ 37925443, 29785008, 2244110, 19552453}},
+ {{61955989, 29753495, 57802388, 27482848, 16243068, 14684434,
+ 41435776, 17373631, 13491505, 4641841}},
+ {{10813398, 643330, 47920349, 32825515, 30292061, 16954354,
+ 27548446, 25833190, 14476988, 20787001}},
+ },
+ {
+ {{10292079, 9984945, 6481436, 8279905, 59857350, 7032742, 27282937,
+ 31910173, 39196053, 12651323}},
+ {{35923332, 32741048, 22271203, 11835308, 10201545, 15351028,
+ 17099662, 3988035, 21721536, 30405492}},
+ {{10202177, 27008593, 35735631, 23979793, 34958221, 25434748,
+ 54202543, 3852693, 13216206, 14842320}},
+ },
+ {
+ {{51293224, 22953365, 60569911, 26295436, 60124204, 26972653,
+ 35608016, 13765823, 39674467, 9900183}},
+ {{14465486, 19721101, 34974879, 18815558, 39665676, 12990491,
+ 33046193, 15796406, 60056998, 25514317}},
+ {{30924398, 25274812, 6359015, 20738097, 16508376, 9071735,
+ 41620263, 15413634, 9524356, 26535554}},
+ },
+ {
+ {{12274201, 20378885, 32627640, 31769106, 6736624, 13267305,
+ 5237659, 28444949, 15663515, 4035784}},
+ {{64157555, 8903984, 17349946, 601635, 50676049, 28941875,
+ 53376124, 17665097, 44850385, 4659090}},
+ {{50192582, 28601458, 36715152, 18395610, 20774811, 15897498,
+ 5736189, 15026997, 64930608, 20098846}},
+ },
+ },
+ {
+ {
+ {{58249865, 31335375, 28571665, 23398914, 66634396, 23448733,
+ 63307367, 278094, 23440562, 33264224}},
+ {{10226222, 27625730, 15139955, 120818, 52241171, 5218602, 32937275,
+ 11551483, 50536904, 26111567}},
+ {{17932739, 21117156, 43069306, 10749059, 11316803, 7535897,
+ 22503767, 5561594, 63462240, 3898660}},
+ },
+ {
+ {{7749907, 32584865, 50769132, 33537967, 42090752, 15122142, 65535333,
+ 7152529, 21831162, 1245233}},
+ {{26958440, 18896406, 4314585, 8346991, 61431100, 11960071,
+ 34519569, 32934396, 36706772, 16838219}},
+ {{54942968, 9166946, 33491384, 13673479, 29787085, 13096535,
+ 6280834, 14587357, 44770839, 13987524}},
+ },
+ {
+ {{42758936, 7778774, 21116000, 15572597, 62275598, 28196653,
+ 62807965, 28429792, 59639082, 30696363}},
+ {{9681908, 26817309, 35157219, 13591837, 60225043, 386949, 31622781,
+ 6439245, 52527852, 4091396}},
+ {{58682418, 1470726, 38999185, 31957441, 3978626, 28430809,
+ 47486180, 12092162, 29077877, 18812444}},
+ },
+ {
+ {{5269168, 26694706, 53878652, 25533716, 25932562, 1763552,
+ 61502754, 28048550, 47091016, 2357888}},
+ {{32264008, 18146780, 61721128, 32394338, 65017541, 29607531,
+ 23104803, 20684524, 5727337, 189038}},
+ {{14609104, 24599962, 61108297, 16931650, 52531476, 25810533,
+ 40363694, 10942114, 41219933, 18669734}},
+ },
+ {
+ {{20513481, 5557931, 51504251, 7829530, 26413943, 31535028,
+ 45729895, 7471780, 13913677, 28416557}},
+ {{41534488, 11967825, 29233242, 12948236, 60354399, 4713226,
+ 58167894, 14059179, 12878652, 8511905}},
+ {{41452044, 3393630, 64153449, 26478905, 64858154, 9366907,
+ 36885446, 6812973, 5568676, 30426776}},
+ },
+ {
+ {{11630004, 12144454, 2116339, 13606037, 27378885, 15676917,
+ 49700111, 20050058, 52713667, 8070817}},
+ {{27117677, 23547054, 35826092, 27984343, 1127281, 12772488,
+ 37262958, 10483305, 55556115, 32525717}},
+ {{10637467, 27866368, 5674780, 1072708, 40765276, 26572129,
+ 65424888, 9177852, 39615702, 15431202}},
+ },
+ {
+ {{20525126, 10892566, 54366392, 12779442, 37615830, 16150074,
+ 38868345, 14943141, 52052074, 25618500}},
+ {{37084402, 5626925, 66557297, 23573344, 753597, 11981191, 25244767,
+ 30314666, 63752313, 9594023}},
+ {{43356201, 2636869, 61944954, 23450613, 585133, 7877383, 11345683,
+ 27062142, 13352334, 22577348}},
+ },
+ {
+ {{65177046, 28146973, 3304648, 20669563, 17015805, 28677341,
+ 37325013, 25801949, 53893326, 33235227}},
+ {{20239939, 6607058, 6203985, 3483793, 48721888, 32775202, 46385121,
+ 15077869, 44358105, 14523816}},
+ {{27406023, 27512775, 27423595, 29057038, 4996213, 10002360,
+ 38266833, 29008937, 36936121, 28748764}},
+ },
+ },
+ {
+ {
+ {{11374242, 12660715, 17861383, 21013599, 10935567, 1099227,
+ 53222788, 24462691, 39381819, 11358503}},
+ {{54378055, 10311866, 1510375, 10778093, 64989409, 24408729,
+ 32676002, 11149336, 40985213, 4985767}},
+ {{48012542, 341146, 60911379, 33315398, 15756972, 24757770, 66125820,
+ 13794113, 47694557, 17933176}},
+ },
+ {
+ {{6490062, 11940286, 25495923, 25828072, 8668372, 24803116, 3367602,
+ 6970005, 65417799, 24549641}},
+ {{1656478, 13457317, 15370807, 6364910, 13605745, 8362338, 47934242,
+ 28078708, 50312267, 28522993}},
+ {{44835530, 20030007, 67044178, 29220208, 48503227, 22632463,
+ 46537798, 26546453, 67009010, 23317098}},
+ },
+ {
+ {{17747446, 10039260, 19368299, 29503841, 46478228, 17513145,
+ 31992682, 17696456, 37848500, 28042460}},
+ {{31932008, 28568291, 47496481, 16366579, 22023614, 88450, 11371999,
+ 29810185, 4882241, 22927527}},
+ {{29796488, 37186, 19818052, 10115756, 55279832, 3352735, 18551198,
+ 3272828, 61917932, 29392022}},
+ },
+ {
+ {{12501267, 4044383, 58495907, 20162046, 34678811, 5136598,
+ 47878486, 30024734, 330069, 29895023}},
+ {{6384877, 2899513, 17807477, 7663917, 64749976, 12363164, 25366522,
+ 24980540, 66837568, 12071498}},
+ {{58743349, 29511910, 25133447, 29037077, 60897836, 2265926,
+ 34339246, 1936674, 61949167, 3829362}},
+ },
+ {
+ {{28425966, 27718999, 66531773, 28857233, 52891308, 6870929, 7921550,
+ 26986645, 26333139, 14267664}},
+ {{56041645, 11871230, 27385719, 22994888, 62522949, 22365119,
+ 10004785, 24844944, 45347639, 8930323}},
+ {{45911060, 17158396, 25654215, 31829035, 12282011, 11008919,
+ 1541940, 4757911, 40617363, 17145491}},
+ },
+ {
+ {{13537262, 25794942, 46504023, 10961926, 61186044, 20336366,
+ 53952279, 6217253, 51165165, 13814989}},
+ {{49686272, 15157789, 18705543, 29619, 24409717, 33293956, 27361680,
+ 9257833, 65152338, 31777517}},
+ {{42063564, 23362465, 15366584, 15166509, 54003778, 8423555,
+ 37937324, 12361134, 48422886, 4578289}},
+ },
+ {
+ {{24579768, 3711570, 1342322, 22374306, 40103728, 14124955,
+ 44564335, 14074918, 21964432, 8235257}},
+ {{60580251, 31142934, 9442965, 27628844, 12025639, 32067012,
+ 64127349, 31885225, 13006805, 2355433}},
+ {{50803946, 19949172, 60476436, 28412082, 16974358, 22643349,
+ 27202043, 1719366, 1141648, 20758196}},
+ },
+ {
+ {{54244920, 20334445, 58790597, 22536340, 60298718, 28710537,
+ 13475065, 30420460, 32674894, 13715045}},
+ {{11423316, 28086373, 32344215, 8962751, 24989809, 9241752,
+ 53843611, 16086211, 38367983, 17912338}},
+ {{65699196, 12530727, 60740138, 10847386, 19531186, 19422272,
+ 55399715, 7791793, 39862921, 4383346}},
+ },
+ },
+ {
+ {
+ {{38137966, 5271446, 65842855, 23817442, 54653627, 16732598,
+ 62246457, 28647982, 27193556, 6245191}},
+ {{51914908, 5362277, 65324971, 2695833, 4960227, 12840725, 23061898,
+ 3260492, 22510453, 8577507}},
+ {{54476394, 11257345, 34415870, 13548176, 66387860, 10879010,
+ 31168030, 13952092, 37537372, 29918525}},
+ },
+ {
+ {{3877321, 23981693, 32416691, 5405324, 56104457, 19897796,
+ 3759768, 11935320, 5611860, 8164018}},
+ {{50833043, 14667796, 15906460, 12155291, 44997715, 24514713,
+ 32003001, 24722143, 5773084, 25132323}},
+ {{43320746, 25300131, 1950874, 8937633, 18686727, 16459170, 66203139,
+ 12376319, 31632953, 190926}},
+ },
+ {
+ {{42515238, 17415546, 58684872, 13378745, 14162407, 6901328,
+ 58820115, 4508563, 41767309, 29926903}},
+ {{8884438, 27670423, 6023973, 10104341, 60227295, 28612898, 18722940,
+ 18768427, 65436375, 827624}},
+ {{34388281, 17265135, 34605316, 7101209, 13354605, 2659080,
+ 65308289, 19446395, 42230385, 1541285}},
+ },
+ {
+ {{2901328, 32436745, 3880375, 23495044, 49487923, 29941650,
+ 45306746, 29986950, 20456844, 31669399}},
+ {{27019610, 12299467, 53450576, 31951197, 54247203, 28692960,
+ 47568713, 28538373, 29439640, 15138866}},
+ {{21536104, 26928012, 34661045, 22864223, 44700786, 5175813,
+ 61688824, 17193268, 7779327, 109896}},
+ },
+ {
+ {{30279725, 14648750, 59063993, 6425557, 13639621, 32810923, 28698389,
+ 12180118, 23177719, 33000357}},
+ {{26572828, 3405927, 35407164, 12890904, 47843196, 5335865,
+ 60615096, 2378491, 4439158, 20275085}},
+ {{44392139, 3489069, 57883598, 33221678, 18875721, 32414337,
+ 14819433, 20822905, 49391106, 28092994}},
+ },
+ {
+ {{62052362, 16566550, 15953661, 3767752, 56672365, 15627059,
+ 66287910, 2177224, 8550082, 18440267}},
+ {{48635543, 16596774, 66727204, 15663610, 22860960, 15585581,
+ 39264755, 29971692, 43848403, 25125843}},
+ {{34628313, 15707274, 58902952, 27902350, 29464557, 2713815,
+ 44383727, 15860481, 45206294, 1494192}},
+ },
+ {
+ {{47546773, 19467038, 41524991, 24254879, 13127841, 759709,
+ 21923482, 16529112, 8742704, 12967017}},
+ {{38643965, 1553204, 32536856, 23080703, 42417258, 33148257,
+ 58194238, 30620535, 37205105, 15553882}},
+ {{21877890, 3230008, 9881174, 10539357, 62311749, 2841331, 11543572,
+ 14513274, 19375923, 20906471}},
+ },
+ {
+ {{8832269, 19058947, 13253510, 5137575, 5037871, 4078777, 24880818,
+ 27331716, 2862652, 9455043}},
+ {{29306751, 5123106, 20245049, 19404543, 9592565, 8447059, 65031740,
+ 30564351, 15511448, 4789663}},
+ {{46429108, 7004546, 8824831, 24119455, 63063159, 29803695,
+ 61354101, 108892, 23513200, 16652362}},
+ },
+ },
+ {
+ {
+ {{33852691, 4144781, 62632835, 26975308, 10770038, 26398890,
+ 60458447, 20618131, 48789665, 10212859}},
+ {{2756062, 8598110, 7383731, 26694540, 22312758, 32449420, 21179800,
+ 2600940, 57120566, 21047965}},
+ {{42463153, 13317461, 36659605, 17900503, 21365573, 22684775,
+ 11344423, 864440, 64609187, 16844368}},
+ },
+ {
+ {{40676061, 6148328, 49924452, 19080277, 18782928, 33278435,
+ 44547329, 211299, 2719757, 4940997}},
+ {{65784982, 3911312, 60160120, 14759764, 37081714, 7851206,
+ 21690126, 8518463, 26699843, 5276295}},
+ {{53958991, 27125364, 9396248, 365013, 24703301, 23065493, 1321585,
+ 149635, 51656090, 7159368}},
+ },
+ {
+ {{9987761, 30149673, 17507961, 9505530, 9731535, 31388918, 22356008,
+ 8312176, 22477218, 25151047}},
+ {{18155857, 17049442, 19744715, 9006923, 15154154, 23015456,
+ 24256459, 28689437, 44560690, 9334108}},
+ {{2986088, 28642539, 10776627, 30080588, 10620589, 26471229,
+ 45695018, 14253544, 44521715, 536905}},
+ },
+ {
+ {{4377737, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551,
+ 10589625, 10838060, 18134008}},
+ {{47766460, 867879, 9277171, 30335973, 52677291, 31567988,
+ 19295825, 17757482, 6378259, 699185}},
+ {{7895007, 4057113, 60027092, 20476675, 49222032, 33231305, 66392824,
+ 15693154, 62063800, 20180469}},
+ },
+ {
+ {{59371282, 27685029, 52542544, 26147512, 11385653, 13201616,
+ 31730678, 22591592, 63190227, 23885106}},
+ {{10188286, 17783598, 59772502, 13427542, 22223443, 14896287,
+ 30743455, 7116568, 45322357, 5427592}},
+ {{696102, 13206899, 27047647, 22922350, 15285304, 23701253,
+ 10798489, 28975712, 19236242, 12477404}},
+ },
+ {
+ {{55879425, 11243795, 50054594, 25513566, 66320635, 25386464,
+ 63211194, 11180503, 43939348, 7733643}},
+ {{17800790, 19518253, 40108434, 21787760, 23887826, 3149671,
+ 23466177, 23016261, 10322026, 15313801}},
+ {{26246234, 11968874, 32263343, 28085704, 6830754, 20231401,
+ 51314159, 33452449, 42659621, 10890803}},
+ },
+ {
+ {{35743198, 10271362, 54448239, 27287163, 16690206, 20491888,
+ 52126651, 16484930, 25180797, 28219548}},
+ {{66522290, 10376443, 34522450, 22268075, 19801892, 10997610,
+ 2276632, 9482883, 316878, 13820577}},
+ {{57226037, 29044064, 64993357, 16457135, 56008783, 11674995,
+ 30756178, 26039378, 30696929, 29841583}},
+ },
+ {
+ {{32988917, 23951020, 12499365, 7910787, 56491607, 21622917,
+ 59766047, 23569034, 34759346, 7392472}},
+ {{58253184, 15927860, 9866406, 29905021, 64711949, 16898650,
+ 36699387, 24419436, 25112946, 30627788}},
+ {{64604801, 33117465, 25621773, 27875660, 15085041, 28074555,
+ 42223985, 20028237, 5537437, 19640113}},
+ },
+ },
+ {
+ {
+ {{55883280, 2320284, 57524584, 10149186, 33664201, 5808647,
+ 52232613, 31824764, 31234589, 6090599}},
+ {{57475529, 116425, 26083934, 2897444, 60744427, 30866345, 609720,
+ 15878753, 60138459, 24519663}},
+ {{39351007, 247743, 51914090, 24551880, 23288160, 23542496,
+ 43239268, 6503645, 20650474, 1804084}},
+ },
+ {
+ {{39519059, 15456423, 8972517, 8469608, 15640622, 4439847, 3121995,
+ 23224719, 27842615, 33352104}},
+ {{51801891, 2839643, 22530074, 10026331, 4602058, 5048462, 28248656,
+ 5031932, 55733782, 12714368}},
+ {{20807691, 26283607, 29286140, 11421711, 39232341, 19686201,
+ 45881388, 1035545, 47375635, 12796919}},
+ },
+ {
+ {{12076880, 19253146, 58323862, 21705509, 42096072, 16400683,
+ 49517369, 20654993, 3480664, 18371617}},
+ {{34747315, 5457596, 28548107, 7833186, 7303070, 21600887,
+ 42745799, 17632556, 33734809, 2771024}},
+ {{45719598, 421931, 26597266, 6860826, 22486084, 26817260,
+ 49971378, 29344205, 42556581, 15673396}},
+ },
+ {
+ {{46924223, 2338215, 19788685, 23933476, 63107598, 24813538,
+ 46837679, 4733253, 3727144, 20619984}},
+ {{6120100, 814863, 55314462, 32931715, 6812204, 17806661, 2019593,
+ 7975683, 31123697, 22595451}},
+ {{30069250, 22119100, 30434653, 2958439, 18399564, 32578143,
+ 12296868, 9204260, 50676426, 9648164}},
+ },
+ {
+ {{32705413, 32003455, 30705657, 7451065, 55303258, 9631812, 3305266,
+ 5248604, 41100532, 22176930}},
+ {{17219846, 2375039, 35537917, 27978816, 47649184, 9219902, 294711,
+ 15298639, 2662509, 17257359}},
+ {{65935918, 25995736, 62742093, 29266687, 45762450, 25120105,
+ 32087528, 32331655, 32247247, 19164571}},
+ },
+ {
+ {{14312609, 1221556, 17395390, 24854289, 62163122, 24869796,
+ 38911119, 23916614, 51081240, 20175586}},
+ {{65680039, 23875441, 57873182, 6549686, 59725795, 33085767, 23046501,
+ 9803137, 17597934, 2346211}},
+ {{18510781, 15337574, 26171504, 981392, 44867312, 7827555,
+ 43617730, 22231079, 3059832, 21771562}},
+ },
+ {
+ {{10141598, 6082907, 17829293, 31606789, 9830091, 13613136,
+ 41552228, 28009845, 33606651, 3592095}},
+ {{33114149, 17665080, 40583177, 20211034, 33076704, 8716171,
+ 1151462, 1521897, 66126199, 26716628}},
+ {{34169699, 29298616, 23947180, 33230254, 34035889, 21248794,
+ 50471177, 3891703, 26353178, 693168}},
+ },
+ {
+ {{30374239, 1595580, 50224825, 13186930, 4600344, 406904, 9585294,
+ 33153764, 31375463, 14369965}},
+ {{52738210, 25781902, 1510300, 6434173, 48324075, 27291703,
+ 32732229, 20445593, 17901440, 16011505}},
+ {{18171223, 21619806, 54608461, 15197121, 56070717, 18324396,
+ 47936623, 17508055, 8764034, 12309598}},
+ },
+ },
+ {
+ {
+ {{5975889, 28311244, 47649501, 23872684, 55567586, 14015781,
+ 43443107, 1228318, 17544096, 22960650}},
+ {{5811932, 31839139, 3442886, 31285122, 48741515, 25194890,
+ 49064820, 18144304, 61543482, 12348899}},
+ {{35709185, 11407554, 25755363, 6891399, 63851926, 14872273,
+ 42259511, 8141294, 56476330, 32968952}},
+ },
+ {
+ {{54433560, 694025, 62032719, 13300343, 14015258, 19103038,
+ 57410191, 22225381, 30944592, 1130208}},
+ {{8247747, 26843490, 40546482, 25845122, 52706924, 18905521,
+ 4652151, 2488540, 23550156, 33283200}},
+ {{17294297, 29765994, 7026747, 15626851, 22990044, 113481, 2267737,
+ 27646286, 66700045, 33416712}},
+ },
+ {
+ {{16091066, 17300506, 18599251, 7340678, 2137637, 32332775,
+ 63744702, 14550935, 3260525, 26388161}},
+ {{62198760, 20221544, 18550886, 10864893, 50649539, 26262835,
+ 44079994, 20349526, 54360141, 2701325}},
+ {{58534169, 16099414, 4629974, 17213908, 46322650, 27548999,
+ 57090500, 9276970, 11329923, 1862132}},
+ },
+ {
+ {{14763057, 17650824, 36190593, 3689866, 3511892, 10313526,
+ 45157776, 12219230, 58070901, 32614131}},
+ {{8894987, 30108338, 6150752, 3013931, 301220, 15693451, 35127648,
+ 30644714, 51670695, 11595569}},
+ {{15214943, 3537601, 40870142, 19495559, 4418656, 18323671,
+ 13947275, 10730794, 53619402, 29190761}},
+ },
+ {
+ {{64570558, 7682792, 32759013, 263109, 37124133, 25598979,
+ 44776739, 23365796, 977107, 699994}},
+ {{54642373, 4195083, 57897332, 550903, 51543527, 12917919,
+ 19118110, 33114591, 36574330, 19216518}},
+ {{31788442, 19046775, 4799988, 7372237, 8808585, 18806489, 9408236,
+ 23502657, 12493931, 28145115}},
+ },
+ {
+ {{41428258, 5260743, 47873055, 27269961, 63412921, 16566086,
+ 27218280, 2607121, 29375955, 6024730}},
+ {{842132, 30759739, 62345482, 24831616, 26332017, 21148791,
+ 11831879, 6985184, 57168503, 2854095}},
+ {{62261602, 25585100, 2516241, 27706719, 9695690, 26333246, 16512644,
+ 960770, 12121869, 16648078}},
+ },
+ {
+ {{51890212, 14667095, 53772635, 2013716, 30598287, 33090295,
+ 35603941, 25672367, 20237805, 2838411}},
+ {{47820798, 4453151, 15298546, 17376044, 22115042, 17581828,
+ 12544293, 20083975, 1068880, 21054527}},
+ {{57549981, 17035596, 33238497, 13506958, 30505848, 32439836,
+ 58621956, 30924378, 12521377, 4845654}},
+ },
+ {
+ {{38910324, 10744107, 64150484, 10199663, 7759311, 20465832,
+ 3409347, 32681032, 60626557, 20668561}},
+ {{43547042, 6230155, 46726851, 10655313, 43068279, 21933259,
+ 10477733, 32314216, 63995636, 13974497}},
+ {{12966261, 15550616, 35069916, 31939085, 21025979, 32924988,
+ 5642324, 7188737, 18895762, 12629579}},
+ },
+ },
+ {
+ {
+ {{14741879, 18607545, 22177207, 21833195, 1279740, 8058600,
+ 11758140, 789443, 32195181, 3895677}},
+ {{10758205, 15755439, 62598914, 9243697, 62229442, 6879878, 64904289,
+ 29988312, 58126794, 4429646}},
+ {{64654951, 15725972, 46672522, 23143759, 61304955, 22514211,
+ 59972993, 21911536, 18047435, 18272689}},
+ },
+ {
+ {{41935844, 22247266, 29759955, 11776784, 44846481, 17733976,
+ 10993113, 20703595, 49488162, 24145963}},
+ {{21987233, 700364, 42603816, 14972007, 59334599, 27836036,
+ 32155025, 2581431, 37149879, 8773374}},
+ {{41540495, 454462, 53896929, 16126714, 25240068, 8594567,
+ 20656846, 12017935, 59234475, 19634276}},
+ },
+ {
+ {{6028163, 6263078, 36097058, 22252721, 66289944, 2461771,
+ 35267690, 28086389, 65387075, 30777706}},
+ {{54829870, 16624276, 987579, 27631834, 32908202, 1248608, 7719845,
+ 29387734, 28408819, 6816612}},
+ {{56750770, 25316602, 19549650, 21385210, 22082622, 16147817,
+ 20613181, 13982702, 56769294, 5067942}},
+ },
+ {
+ {{36602878, 29732664, 12074680, 13582412, 47230892, 2443950,
+ 47389578, 12746131, 5331210, 23448488}},
+ {{30528792, 3601899, 65151774, 4619784, 39747042, 18118043,
+ 24180792, 20984038, 27679907, 31905504}},
+ {{9402385, 19597367, 32834042, 10838634, 40528714, 20317236,
+ 26653273, 24868867, 22611443, 20839026}},
+ },
+ {
+ {{22190590, 1118029, 22736441, 15130463, 36648172, 27563110,
+ 19189624, 28905490, 4854858, 6622139}},
+ {{58798126, 30600981, 58846284, 30166382, 56707132, 33282502,
+ 13424425, 29987205, 26404408, 13001963}},
+ {{35867026, 18138731, 64114613, 8939345, 11562230, 20713762,
+ 41044498, 21932711, 51703708, 11020692}},
+ },
+ {
+ {{1866042, 25604943, 59210214, 23253421, 12483314, 13477547,
+ 3175636, 21130269, 28761761, 1406734}},
+ {{66660290, 31776765, 13018550, 3194501, 57528444, 22392694,
+ 24760584, 29207344, 25577410, 20175752}},
+ {{42818486, 4759344, 66418211, 31701615, 2066746, 10693769,
+ 37513074, 9884935, 57739938, 4745409}},
+ },
+ {
+ {{57967561, 6049713, 47577803, 29213020, 35848065, 9944275,
+ 51646856, 22242579, 10931923, 21622501}},
+ {{50547351, 14112679, 59096219, 4817317, 59068400, 22139825,
+ 44255434, 10856640, 46638094, 13434653}},
+ {{22759470, 23480998, 50342599, 31683009, 13637441, 23386341,
+ 1765143, 20900106, 28445306, 28189722}},
+ },
+ {
+ {{29875063, 12493613, 2795536, 29768102, 1710619, 15181182,
+ 56913147, 24765756, 9074233, 1167180}},
+ {{40903181, 11014232, 57266213, 30918946, 40200743, 7532293,
+ 48391976, 24018933, 3843902, 9367684}},
+ {{56139269, 27150720, 9591133, 9582310, 11349256, 108879, 16235123,
+ 8601684, 66969667, 4242894}},
+ },
+ },
+ {
+ {
+ {{22092954, 20363309, 65066070, 21585919, 32186752, 22037044,
+ 60534522, 2470659, 39691498, 16625500}},
+ {{56051142, 3042015, 13770083, 24296510, 584235, 33009577, 59338006,
+ 2602724, 39757248, 14247412}},
+ {{6314156, 23289540, 34336361, 15957556, 56951134, 168749,
+ 58490057, 14290060, 27108877, 32373552}},
+ },
+ {
+ {{58522267, 26383465, 13241781, 10960156, 34117849, 19759835,
+ 33547975, 22495543, 39960412, 981873}},
+ {{22833421, 9293594, 34459416, 19935764, 57971897, 14756818,
+ 44180005, 19583651, 56629059, 17356469}},
+ {{59340277, 3326785, 38997067, 10783823, 19178761, 14905060,
+ 22680049, 13906969, 51175174, 3797898}},
+ },
+ {
+ {{21721337, 29341686, 54902740, 9310181, 63226625, 19901321,
+ 23740223, 30845200, 20491982, 25512280}},
+ {{9209251, 18419377, 53852306, 27386633, 66377847, 15289672,
+ 25947805, 15286587, 30997318, 26851369}},
+ {{7392013, 16618386, 23946583, 25514540, 53843699, 32020573,
+ 52911418, 31232855, 17649997, 33304352}},
+ },
+ {
+ {{57807776, 19360604, 30609525, 30504889, 41933794, 32270679,
+ 51867297, 24028707, 64875610, 7662145}},
+ {{49550191, 1763593, 33994528, 15908609, 37067994, 21380136,
+ 7335079, 25082233, 63934189, 3440182}},
+ {{47219164, 27577423, 42997570, 23865561, 10799742, 16982475,
+ 40449, 29122597, 4862399, 1133}},
+ },
+ {
+ {{34252636, 25680474, 61686474, 14860949, 50789833, 7956141,
+ 7258061, 311861, 36513873, 26175010}},
+ {{63335436, 31988495, 28985339, 7499440, 24445838, 9325937, 29727763,
+ 16527196, 18278453, 15405622}},
+ {{62726958, 8508651, 47210498, 29880007, 61124410, 15149969,
+ 53795266, 843522, 45233802, 13626196}},
+ },
+ {
+ {{2281448, 20067377, 56193445, 30944521, 1879357, 16164207,
+ 56324982, 3953791, 13340839, 15928663}},
+ {{31727126, 26374577, 48671360, 25270779, 2875792, 17164102,
+ 41838969, 26539605, 43656557, 5964752}},
+ {{4100401, 27594980, 49929526, 6017713, 48403027, 12227140,
+ 40424029, 11344143, 2538215, 25983677}},
+ },
+ {
+ {{57675240, 6123112, 11159803, 31397824, 30016279, 14966241,
+ 46633881, 1485420, 66479608, 17595569}},
+ {{40304287, 4260918, 11851389, 9658551, 35091757, 16367491,
+ 46903439, 20363143, 11659921, 22439314}},
+ {{26180377, 10015009, 36264640, 24973138, 5418196, 9480663, 2231568,
+ 23384352, 33100371, 32248261}},
+ },
+ {
+ {{15121094, 28352561, 56718958, 15427820, 39598927, 17561924,
+ 21670946, 4486675, 61177054, 19088051}},
+ {{16166467, 24070699, 56004733, 6023907, 35182066, 32189508,
+ 2340059, 17299464, 56373093, 23514607}},
+ {{28042865, 29997343, 54982337, 12259705, 63391366, 26608532,
+ 6766452, 24864833, 18036435, 5803270}},
+ },
+ },
+ {
+ {
+ {{66291264, 6763911, 11803561, 1585585, 10958447, 30883267, 23855390,
+ 4598332, 60949433, 19436993}},
+ {{36077558, 19298237, 17332028, 31170912, 31312681, 27587249,
+ 696308, 50292, 47013125, 11763583}},
+ {{66514282, 31040148, 34874710, 12643979, 12650761, 14811489, 665117,
+ 20940800, 47335652, 22840869}},
+ },
+ {
+ {{30464590, 22291560, 62981387, 20819953, 19835326, 26448819,
+ 42712688, 2075772, 50088707, 992470}},
+ {{18357166, 26559999, 7766381, 16342475, 37783946, 411173, 14578841,
+ 8080033, 55534529, 22952821}},
+ {{19598397, 10334610, 12555054, 2555664, 18821899, 23214652,
+ 21873262, 16014234, 26224780, 16452269}},
+ },
+ {
+ {{36884939, 5145195, 5944548, 16385966, 3976735, 2009897, 55731060,
+ 25936245, 46575034, 3698649}},
+ {{14187449, 3448569, 56472628, 22743496, 44444983, 30120835,
+ 7268409, 22663988, 27394300, 12015369}},
+ {{19695742, 16087646, 28032085, 12999827, 6817792, 11427614,
+ 20244189, 32241655, 53849736, 30151970}},
+ },
+ {
+ {{30860084, 12735208, 65220619, 28854697, 50133957, 2256939,
+ 58942851, 12298311, 58558340, 23160969}},
+ {{61389038, 22309106, 65198214, 15569034, 26642876, 25966672,
+ 61319509, 18435777, 62132699, 12651792}},
+ {{64260450, 9953420, 11531313, 28271553, 26895122, 20857343,
+ 53990043, 17036529, 9768697, 31021214}},
+ },
+ {
+ {{42389405, 1894650, 66821166, 28850346, 15348718, 25397902,
+ 32767512, 12765450, 4940095, 10678226}},
+ {{18860224, 15980149, 48121624, 31991861, 40875851, 22482575,
+ 59264981, 13944023, 42736516, 16582018}},
+ {{51604604, 4970267, 37215820, 4175592, 46115652, 31354675,
+ 55404809, 15444559, 56105103, 7989036}},
+ },
+ {
+ {{31490433, 5568061, 64696061, 2182382, 34772017, 4531685,
+ 35030595, 6200205, 47422751, 18754260}},
+ {{49800177, 17674491, 35586086, 33551600, 34221481, 16375548,
+ 8680158, 17182719, 28550067, 26697300}},
+ {{38981977, 27866340, 16837844, 31733974, 60258182, 12700015,
+ 37068883, 4364037, 1155602, 5988841}},
+ },
+ {
+ {{21890435, 20281525, 54484852, 12154348, 59276991, 15300495,
+ 23148983, 29083951, 24618406, 8283181}},
+ {{33972757, 23041680, 9975415, 6841041, 35549071, 16356535,
+ 3070187, 26528504, 1466168, 10740210}},
+ {{65599446, 18066246, 53605478, 22898515, 32799043, 909394,
+ 53169961, 27774712, 34944214, 18227391}},
+ },
+ {
+ {{3960804, 19286629, 39082773, 17636380, 47704005, 13146867,
+ 15567327, 951507, 63848543, 32980496}},
+ {{24740822, 5052253, 37014733, 8961360, 25877428, 6165135,
+ 42740684, 14397371, 59728495, 27410326}},
+ {{38220480, 3510802, 39005586, 32395953, 55870735, 22922977,
+ 51667400, 19101303, 65483377, 27059617}},
+ },
+ },
+ {
+ {
+ {{793280, 24323954, 8836301, 27318725, 39747955, 31184838, 33152842,
+ 28669181, 57202663, 32932579}},
+ {{5666214, 525582, 20782575, 25516013, 42570364, 14657739, 16099374,
+ 1468826, 60937436, 18367850}},
+ {{62249590, 29775088, 64191105, 26806412, 7778749, 11688288,
+ 36704511, 23683193, 65549940, 23690785}},
+ },
+ {
+ {{10896313, 25834728, 824274, 472601, 47648556, 3009586, 25248958,
+ 14783338, 36527388, 17796587}},
+ {{10566929, 12612572, 35164652, 11118702, 54475488, 12362878,
+ 21752402, 8822496, 24003793, 14264025}},
+ {{27713843, 26198459, 56100623, 9227529, 27050101, 2504721,
+ 23886875, 20436907, 13958494, 27821979}},
+ },
+ {
+ {{43627235, 4867225, 39861736, 3900520, 29838369, 25342141,
+ 35219464, 23512650, 7340520, 18144364}},
+ {{4646495, 25543308, 44342840, 22021777, 23184552, 8566613,
+ 31366726, 32173371, 52042079, 23179239}},
+ {{49838347, 12723031, 50115803, 14878793, 21619651, 27356856,
+ 27584816, 3093888, 58265170, 3849920}},
+ },
+ {
+ {{58043933, 2103171, 25561640, 18428694, 61869039, 9582957,
+ 32477045, 24536477, 5002293, 18004173}},
+ {{55051311, 22376525, 21115584, 20189277, 8808711, 21523724,
+ 16489529, 13378448, 41263148, 12741425}},
+ {{61162478, 10645102, 36197278, 15390283, 63821882, 26435754,
+ 24306471, 15852464, 28834118, 25908360}},
+ },
+ {
+ {{49773116, 24447374, 42577584, 9434952, 58636780, 32971069,
+ 54018092, 455840, 20461858, 5491305}},
+ {{13669229, 17458950, 54626889, 23351392, 52539093, 21661233,
+ 42112877, 11293806, 38520660, 24132599}},
+ {{28497909, 6272777, 34085870, 14470569, 8906179, 32328802,
+ 18504673, 19389266, 29867744, 24758489}},
+ },
+ {
+ {{50901822, 13517195, 39309234, 19856633, 24009063, 27180541,
+ 60741263, 20379039, 22853428, 29542421}},
+ {{24191359, 16712145, 53177067, 15217830, 14542237, 1646131,
+ 18603514, 22516545, 12876622, 31441985}},
+ {{17902668, 4518229, 66697162, 30725184, 26878216, 5258055, 54248111,
+ 608396, 16031844, 3723494}},
+ },
+ {
+ {{38476072, 12763727, 46662418, 7577503, 33001348, 20536687,
+ 17558841, 25681542, 23896953, 29240187}},
+ {{47103464, 21542479, 31520463, 605201, 2543521, 5991821, 64163800,
+ 7229063, 57189218, 24727572}},
+ {{28816026, 298879, 38943848, 17633493, 19000927, 31888542,
+ 54428030, 30605106, 49057085, 31471516}},
+ },
+ {
+ {{16000882, 33209536, 3493091, 22107234, 37604268, 20394642,
+ 12577739, 16041268, 47393624, 7847706}},
+ {{10151868, 10572098, 27312476, 7922682, 14825339, 4723128,
+ 34252933, 27035413, 57088296, 3852847}},
+ {{55678375, 15697595, 45987307, 29133784, 5386313, 15063598,
+ 16514493, 17622322, 29330898, 18478208}},
+ },
+ },
+ {
+ {
+ {{41609129, 29175637, 51885955, 26653220, 16615730, 2051784,
+ 3303702, 15490, 39560068, 12314390}},
+ {{15683501, 27551389, 18109119, 23573784, 15337967, 27556609,
+ 50391428, 15921865, 16103996, 29823217}},
+ {{43939021, 22773182, 13588191, 31925625, 63310306, 32479502,
+ 47835256, 5402698, 37293151, 23713330}},
+ },
+ {
+ {{23190676, 2384583, 34394524, 3462153, 37205209, 32025299,
+ 55842007, 8911516, 41903005, 2739712}},
+ {{21374101, 30000182, 33584214, 9874410, 15377179, 11831242,
+ 33578960, 6134906, 4931255, 11987849}},
+ {{67101132, 30575573, 50885377, 7277596, 105524, 33232381, 35628324,
+ 13861387, 37032554, 10117929}},
+ },
+ {
+ {{37607694, 22809559, 40945095, 13051538, 41483300, 5089642,
+ 60783361, 6704078, 12890019, 15728940}},
+ {{45136504, 21783052, 66157804, 29135591, 14704839, 2695116, 903376,
+ 23126293, 12885166, 8311031}},
+ {{49592363, 5352193, 10384213, 19742774, 7506450, 13453191,
+ 26423267, 4384730, 1888765, 28119028}},
+ },
+ {
+ {{41291507, 30447119, 53614264, 30371925, 30896458, 19632703,
+ 34857219, 20846562, 47644429, 30214188}},
+ {{43500868, 30888657, 66582772, 4651135, 5765089, 4618330, 6092245,
+ 14845197, 17151279, 23700316}},
+ {{42278406, 20820711, 51942885, 10367249, 37577956, 33289075,
+ 22825804, 26467153, 50242379, 16176524}},
+ },
+ {
+ {{43525589, 6564960, 20063689, 3798228, 62368686, 7359224, 2006182,
+ 23191006, 38362610, 23356922}},
+ {{56482264, 29068029, 53788301, 28429114, 3432135, 27161203,
+ 23632036, 31613822, 32808309, 1099883}},
+ {{15030958, 5768825, 39657628, 30667132, 60681485, 18193060,
+ 51830967, 26745081, 2051440, 18328567}},
+ },
+ {
+ {{63746541, 26315059, 7517889, 9824992, 23555850, 295369, 5148398,
+ 19400244, 44422509, 16633659}},
+ {{4577067, 16802144, 13249840, 18250104, 19958762, 19017158,
+ 18559669, 22794883, 8402477, 23690159}},
+ {{38702534, 32502850, 40318708, 32646733, 49896449, 22523642,
+ 9453450, 18574360, 17983009, 9967138}},
+ },
+ {
+ {{41346370, 6524721, 26585488, 9969270, 24709298, 1220360, 65430874,
+ 7806336, 17507396, 3651560}},
+ {{56688388, 29436320, 14584638, 15971087, 51340543, 8861009,
+ 26556809, 27979875, 48555541, 22197296}},
+ {{2839082, 14284142, 4029895, 3472686, 14402957, 12689363, 40466743,
+ 8459446, 61503401, 25932490}},
+ },
+ {
+ {{62269556, 30018987, 9744960, 2871048, 25113978, 3187018, 41998051,
+ 32705365, 17258083, 25576693}},
+ {{18164541, 22959256, 49953981, 32012014, 19237077, 23809137,
+ 23357532, 18337424, 26908269, 12150756}},
+ {{36843994, 25906566, 5112248, 26517760, 65609056, 26580174, 43167,
+ 28016731, 34806789, 16215818}},
+ },
+ },
+ {
+ {
+ {{60209940, 9824393, 54804085, 29153342, 35711722, 27277596,
+ 32574488, 12532905, 59605792, 24879084}},
+ {{39765323, 17038963, 39957339, 22831480, 946345, 16291093,
+ 254968, 7168080, 21676107, 31611404}},
+ {{21260942, 25129680, 50276977, 21633609, 43430902, 3968120,
+ 63456915, 27338965, 63552672, 25641356}},
+ },
+ {
+ {{16544735, 13250366, 50304436, 15546241, 62525861, 12757257,
+ 64646556, 24874095, 48201831, 23891632}},
+ {{64693606, 17976703, 18312302, 4964443, 51836334, 20900867,
+ 26820650, 16690659, 25459437, 28989823}},
+ {{41964155, 11425019, 28423002, 22533875, 60963942, 17728207,
+ 9142794, 31162830, 60676445, 31909614}},
+ },
+ {
+ {{44004212, 6253475, 16964147, 29785560, 41994891, 21257994,
+ 39651638, 17209773, 6335691, 7249989}},
+ {{36775618, 13979674, 7503222, 21186118, 55152142, 28932738,
+ 36836594, 2682241, 25993170, 21075909}},
+ {{4364628, 5930691, 32304656, 23509878, 59054082, 15091130,
+ 22857016, 22955477, 31820367, 15075278}},
+ },
+ {
+ {{31879134, 24635739, 17258760, 90626, 59067028, 28636722, 24162787,
+ 23903546, 49138625, 12833044}},
+ {{19073683, 14851414, 42705695, 21694263, 7625277, 11091125,
+ 47489674, 2074448, 57694925, 14905376}},
+ {{24483648, 21618865, 64589997, 22007013, 65555733, 15355505,
+ 41826784, 9253128, 27628530, 25998952}},
+ },
+ {
+ {{17597607, 8340603, 19355617, 552187, 26198470, 30377849, 4593323,
+ 24396850, 52997988, 15297015}},
+ {{510886, 14337390, 35323607, 16638631, 6328095, 2713355, 46891447,
+ 21690211, 8683220, 2921426}},
+ {{18606791, 11874196, 27155355, 28272950, 43077121, 6265445,
+ 41930624, 32275507, 4674689, 13890525}},
+ },
+ {
+ {{13609624, 13069022, 39736503, 20498523, 24360585, 9592974,
+ 14977157, 9835105, 4389687, 288396}},
+ {{9922506, 33035038, 13613106, 5883594, 48350519, 33120168, 54804801,
+ 8317627, 23388070, 16052080}},
+ {{12719997, 11937594, 35138804, 28525742, 26900119, 8561328,
+ 46953177, 21921452, 52354592, 22741539}},
+ },
+ {
+ {{15961858, 14150409, 26716931, 32888600, 44314535, 13603568,
+ 11829573, 7467844, 38286736, 929274}},
+ {{11038231, 21972036, 39798381, 26237869, 56610336, 17246600,
+ 43629330, 24182562, 45715720, 2465073}},
+ {{20017144, 29231206, 27915241, 1529148, 12396362, 15675764,
+ 13817261, 23896366, 2463390, 28932292}},
+ },
+ {
+ {{50749986, 20890520, 55043680, 4996453, 65852442, 1073571,
+ 9583558, 12851107, 4003896, 12673717}},
+ {{65377275, 18398561, 63845933, 16143081, 19294135, 13385325,
+ 14741514, 24450706, 7903885, 2348101}},
+ {{24536016, 17039225, 12715591, 29692277, 1511292, 10047386,
+ 63266518, 26425272, 38731325, 10048126}},
+ },
+ },
+ {
+ {
+ {{54486638, 27349611, 30718824, 2591312, 56491836, 12192839,
+ 18873298, 26257342, 34811107, 15221631}},
+ {{40630742, 22450567, 11546243, 31701949, 9180879, 7656409,
+ 45764914, 2095754, 29769758, 6593415}},
+ {{35114656, 30646970, 4176911, 3264766, 12538965, 32686321, 26312344,
+ 27435754, 30958053, 8292160}},
+ },
+ {
+ {{31429803, 19595316, 29173531, 15632448, 12174511, 30794338,
+ 32808830, 3977186, 26143136, 30405556}},
+ {{22648882, 1402143, 44308880, 13746058, 7936347, 365344, 58440231,
+ 31879998, 63350620, 31249806}},
+ {{51616947, 8012312, 64594134, 20851969, 43143017, 23300402,
+ 65496150, 32018862, 50444388, 8194477}},
+ },
+ {
+ {{27338066, 26047012, 59694639, 10140404, 48082437, 26964542,
+ 27277190, 8855376, 28572286, 3005164}},
+ {{26287105, 4821776, 25476601, 29408529, 63344350, 17765447,
+ 49100281, 1182478, 41014043, 20474836}},
+ {{59937691, 3178079, 23970071, 6201893, 49913287, 29065239,
+ 45232588, 19571804, 32208682, 32356184}},
+ },
+ {
+ {{50451143, 2817642, 56822502, 14811297, 6024667, 13349505,
+ 39793360, 23056589, 39436278, 22014573}},
+ {{15941010, 24148500, 45741813, 8062054, 31876073, 33315803,
+ 51830470, 32110002, 15397330, 29424239}},
+ {{8934485, 20068965, 43822466, 20131190, 34662773, 14047985,
+ 31170398, 32113411, 39603297, 15087183}},
+ },
+ {
+ {{48751602, 31397940, 24524912, 16876564, 15520426, 27193656,
+ 51606457, 11461895, 16788528, 27685490}},
+ {{65161459, 16013772, 21750665, 3714552, 49707082, 17498998,
+ 63338576, 23231111, 31322513, 21938797}},
+ {{21426636, 27904214, 53460576, 28206894, 38296674, 28633461,
+ 48833472, 18933017, 13040861, 21441484}},
+ },
+ {
+ {{11293895, 12478086, 39972463, 15083749, 37801443, 14748871,
+ 14555558, 20137329, 1613710, 4896935}},
+ {{41213962, 15323293, 58619073, 25496531, 25967125, 20128972,
+ 2825959, 28657387, 43137087, 22287016}},
+ {{51184079, 28324551, 49665331, 6410663, 3622847, 10243618,
+ 20615400, 12405433, 43355834, 25118015}},
+ },
+ {
+ {{60017550, 12556207, 46917512, 9025186, 50036385, 4333800,
+ 4378436, 2432030, 23097949, 32988414}},
+ {{4565804, 17528778, 20084411, 25711615, 1724998, 189254, 24767264,
+ 10103221, 48596551, 2424777}},
+ {{366633, 21577626, 8173089, 26664313, 30788633, 5745705, 59940186,
+ 1344108, 63466311, 12412658}},
+ },
+ {
+ {{43107073, 7690285, 14929416, 33386175, 34898028, 20141445,
+ 24162696, 18227928, 63967362, 11179384}},
+ {{18289503, 18829478, 8056944, 16430056, 45379140, 7842513,
+ 61107423, 32067534, 48424218, 22110928}},
+ {{476239, 6601091, 60956074, 23831056, 17503544, 28690532, 27672958,
+ 13403813, 11052904, 5219329}},
+ },
+ },
+ {
+ {
+ {{20678527, 25178694, 34436965, 8849122, 62099106, 14574751,
+ 31186971, 29580702, 9014761, 24975376}},
+ {{53464795, 23204192, 51146355, 5075807, 65594203, 22019831,
+ 34006363, 9160279, 8473550, 30297594}},
+ {{24900749, 14435722, 17209120, 18261891, 44516588, 9878982,
+ 59419555, 17218610, 42540382, 11788947}},
+ },
+ {
+ {{63990690, 22159237, 53306774, 14797440, 9652448, 26708528,
+ 47071426, 10410732, 42540394, 32095740}},
+ {{51449703, 16736705, 44641714, 10215877, 58011687, 7563910,
+ 11871841, 21049238, 48595538, 8464117}},
+ {{43708233, 8348506, 52522913, 32692717, 63158658, 27181012,
+ 14325288, 8628612, 33313881, 25183915}},
+ },
+ {
+ {{46921872, 28586496, 22367355, 5271547, 66011747, 28765593,
+ 42303196, 23317577, 58168128, 27736162}},
+ {{60160060, 31759219, 34483180, 17533252, 32635413, 26180187,
+ 15989196, 20716244, 28358191, 29300528}},
+ {{43547083, 30755372, 34757181, 31892468, 57961144, 10429266,
+ 50471180, 4072015, 61757200, 5596588}},
+ },
+ {
+ {{38872266, 30164383, 12312895, 6213178, 3117142, 16078565,
+ 29266239, 2557221, 1768301, 15373193}},
+ {{59865506, 30307471, 62515396, 26001078, 66980936, 32642186, 66017961,
+ 29049440, 42448372, 3442909}},
+ {{36898293, 5124042, 14181784, 8197961, 18964734, 21615339,
+ 22597930, 7176455, 48523386, 13365929}},
+ },
+ {
+ {{59231455, 32054473, 8324672, 4690079, 6261860, 890446, 24538107,
+ 24984246, 57419264, 30522764}},
+ {{25008885, 22782833, 62803832, 23916421, 16265035, 15721635,
+ 683793, 21730648, 15723478, 18390951}},
+ {{57448220, 12374378, 40101865, 26528283, 59384749, 21239917,
+ 11879681, 5400171, 519526, 32318556}},
+ },
+ {
+ {{22258397, 17222199, 59239046, 14613015, 44588609, 30603508,
+ 46754982, 7315966, 16648397, 7605640}},
+ {{59027556, 25089834, 58885552, 9719709, 19259459, 18206220,
+ 23994941, 28272877, 57640015, 4763277}},
+ {{45409620, 9220968, 51378240, 1084136, 41632757, 30702041,
+ 31088446, 25789909, 55752334, 728111}},
+ },
+ {
+ {{26047201, 21802961, 60208540, 17032633, 24092067, 9158119,
+ 62835319, 20998873, 37743427, 28056159}},
+ {{17510331, 33231575, 5854288, 8403524, 17133918, 30441820, 38997856,
+ 12327944, 10750447, 10014012}},
+ {{56796096, 3936951, 9156313, 24656749, 16498691, 32559785,
+ 39627812, 32887699, 3424690, 7540221}},
+ },
+ {
+ {{30322361, 26590322, 11361004, 29411115, 7433303, 4989748, 60037442,
+ 17237212, 57864598, 15258045}},
+ {{13054543, 30774935, 19155473, 469045, 54626067, 4566041, 5631406,
+ 2711395, 1062915, 28418087}},
+ {{47868616, 22299832, 37599834, 26054466, 61273100, 13005410,
+ 61042375, 12194496, 32960380, 1459310}},
+ },
+ },
+ {
+ {
+ {{19852015, 7027924, 23669353, 10020366, 8586503, 26896525, 394196,
+ 27452547, 18638002, 22379495}},
+ {{31395515, 15098109, 26581030, 8030562, 50580950, 28547297,
+ 9012485, 25970078, 60465776, 28111795}},
+ {{57916680, 31207054, 65111764, 4529533, 25766844, 607986, 67095642,
+ 9677542, 34813975, 27098423}},
+ },
+ {
+ {{64664349, 33404494, 29348901, 8186665, 1873760, 12489863, 36174285,
+ 25714739, 59256019, 25416002}},
+ {{51872508, 18120922, 7766469, 746860, 26346930, 23332670,
+ 39775412, 10754587, 57677388, 5203575}},
+ {{31834314, 14135496, 66338857, 5159117, 20917671, 16786336,
+ 59640890, 26216907, 31809242, 7347066}},
+ },
+ {
+ {{57502122, 21680191, 20414458, 13033986, 13716524, 21862551,
+ 19797969, 21343177, 15192875, 31466942}},
+ {{54445282, 31372712, 1168161, 29749623, 26747876, 19416341,
+ 10609329, 12694420, 33473243, 20172328}},
+ {{33184999, 11180355, 15832085, 22169002, 65475192, 225883,
+ 15089336, 22530529, 60973201, 14480052}},
+ },
+ {
+ {{31308717, 27934434, 31030839, 31657333, 15674546, 26971549,
+ 5496207, 13685227, 27595050, 8737275}},
+ {{46790012, 18404192, 10933842, 17376410, 8335351, 26008410,
+ 36100512, 20943827, 26498113, 66511}},
+ {{22644435, 24792703, 50437087, 4884561, 64003250, 19995065,
+ 30540765, 29267685, 53781076, 26039336}},
+ },
+ {
+ {{39091017, 9834844, 18617207, 30873120, 63706907, 20246925,
+ 8205539, 13585437, 49981399, 15115438}},
+ {{23711543, 32881517, 31206560, 25191721, 6164646, 23844445,
+ 33572981, 32128335, 8236920, 16492939}},
+ {{43198286, 20038905, 40809380, 29050590, 25005589, 25867162,
+ 19574901, 10071562, 6708380, 27332008}},
+ },
+ {
+ {{2101372, 28624378, 19702730, 2367575, 51681697, 1047674, 5301017,
+ 9328700, 29955601, 21876122}},
+ {{3096359, 9271816, 45488000, 18032587, 52260867, 25961494,
+ 41216721, 20918836, 57191288, 6216607}},
+ {{34493015, 338662, 41913253, 2510421, 37895298, 19734218,
+ 24822829, 27407865, 40341383, 7525078}},
+ },
+ {
+ {{44042215, 19568808, 16133486, 25658254, 63719298, 778787,
+ 66198528, 30771936, 47722230, 11994100}},
+ {{21691500, 19929806, 66467532, 19187410, 3285880, 30070836,
+ 42044197, 9718257, 59631427, 13381417}},
+ {{18445390, 29352196, 14979845, 11622458, 65381754, 29971451,
+ 23111647, 27179185, 28535281, 15779576}},
+ },
+ {
+ {{30098034, 3089662, 57874477, 16662134, 45801924, 11308410,
+ 53040410, 12021729, 9955285, 17251076}},
+ {{9734894, 18977602, 59635230, 24415696, 2060391, 11313496,
+ 48682835, 9924398, 20194861, 13380996}},
+ {{40730762, 25589224, 44941042, 15789296, 49053522, 27385639,
+ 65123949, 15707770, 26342023, 10146099}},
+ },
+ },
+ {
+ {
+ {{41091971, 33334488, 21339190, 33513044, 19745255, 30675732,
+ 37471583, 2227039, 21612326, 33008704}},
+ {{54031477, 1184227, 23562814, 27583990, 46757619, 27205717,
+ 25764460, 12243797, 46252298, 11649657}},
+ {{57077370, 11262625, 27384172, 2271902, 26947504, 17556661, 39943,
+ 6114064, 33514190, 2333242}},
+ },
+ {
+ {{45675257, 21132610, 8119781, 7219913, 45278342, 24538297,
+ 60429113, 20883793, 24350577, 20104431}},
+ {{62992557, 22282898, 43222677, 4843614, 37020525, 690622,
+ 35572776, 23147595, 8317859, 12352766}},
+ {{18200138, 19078521, 34021104, 30857812, 43406342, 24451920,
+ 43556767, 31266881, 20712162, 6719373}},
+ },
+ {
+ {{26656189, 6075253, 59250308, 1886071, 38764821, 4262325, 11117530,
+ 29791222, 26224234, 30256974}},
+ {{49939907, 18700334, 63713187, 17184554, 47154818, 14050419,
+ 21728352, 9493610, 18620611, 17125804}},
+ {{53785524, 13325348, 11432106, 5964811, 18609221, 6062965,
+ 61839393, 23828875, 36407290, 17074774}},
+ },
+ {
+ {{43248326, 22321272, 26961356, 1640861, 34695752, 16816491,
+ 12248508, 28313793, 13735341, 1934062}},
+ {{25089769, 6742589, 17081145, 20148166, 21909292, 17486451,
+ 51972569, 29789085, 45830866, 5473615}},
+ {{31883658, 25593331, 1083431, 21982029, 22828470, 13290673,
+ 59983779, 12469655, 29111212, 28103418}},
+ },
+ {
+ {{24244947, 18504025, 40845887, 2791539, 52111265, 16666677,
+ 24367466, 6388839, 56813277, 452382}},
+ {{41468082, 30136590, 5217915, 16224624, 19987036, 29472163,
+ 42872612, 27639183, 15766061, 8407814}},
+ {{46701865, 13990230, 15495425, 16395525, 5377168, 15166495,
+ 58191841, 29165478, 59040954, 2276717}},
+ },
+ {
+ {{30157899, 12924066, 49396814, 9245752, 19895028, 3368142,
+ 43281277, 5096218, 22740376, 26251015}},
+ {{2041139, 19298082, 7783686, 13876377, 41161879, 20201972,
+ 24051123, 13742383, 51471265, 13295221}},
+ {{33338218, 25048699, 12532112, 7977527, 9106186, 31839181,
+ 49388668, 28941459, 62657506, 18884987}},
+ },
+ {
+ {{47063583, 5454096, 52762316, 6447145, 28862071, 1883651,
+ 64639598, 29412551, 7770568, 9620597}},
+ {{23208049, 7979712, 33071466, 8149229, 1758231, 22719437, 30945527,
+ 31860109, 33606523, 18786461}},
+ {{1439939, 17283952, 66028874, 32760649, 4625401, 10647766, 62065063,
+ 1220117, 30494170, 22113633}},
+ },
+ {
+ {{62071265, 20526136, 64138304, 30492664, 15640973, 26852766,
+ 40369837, 926049, 65424525, 20220784}},
+ {{13908495, 30005160, 30919927, 27280607, 45587000, 7989038,
+ 9021034, 9078865, 3353509, 4033511}},
+ {{37445433, 18440821, 32259990, 33209950, 24295848, 20642309,
+ 23161162, 8839127, 27485041, 7356032}},
+ },
+ },
+ {
+ {
+ {{9661008, 705443, 11980065, 28184278, 65480320, 14661172, 60762722,
+ 2625014, 28431036, 16782598}},
+ {{43269631, 25243016, 41163352, 7480957, 49427195, 25200248,
+ 44562891, 14150564, 15970762, 4099461}},
+ {{29262576, 16756590, 26350592, 24760869, 8529670, 22346382,
+ 13617292, 23617289, 11465738, 8317062}},
+ },
+ {
+ {{41615764, 26591503, 32500199, 24135381, 44070139, 31252209,
+ 14898636, 3848455, 20969334, 28396916}},
+ {{46724414, 19206718, 48772458, 13884721, 34069410, 2842113,
+ 45498038, 29904543, 11177094, 14989547}},
+ {{42612143, 21838415, 16959895, 2278463, 12066309, 10137771,
+ 13515641, 2581286, 38621356, 9930239}},
+ },
+ {
+ {{49357223, 31456605, 16544299, 20545132, 51194056, 18605350,
+ 18345766, 20150679, 16291480, 28240394}},
+ {{33879670, 2553287, 32678213, 9875984, 8534129, 6889387, 57432090,
+ 6957616, 4368891, 9788741}},
+ {{16660737, 7281060, 56278106, 12911819, 20108584, 25452756,
+ 45386327, 24941283, 16250551, 22443329}},
+ },
+ {
+ {{47343357, 2390525, 50557833, 14161979, 1905286, 6414907, 4689584,
+ 10604807, 36918461, 4782746}},
+ {{65754325, 14736940, 59741422, 20261545, 7710541, 19398842,
+ 57127292, 4383044, 22546403, 437323}},
+ {{31665558, 21373968, 50922033, 1491338, 48740239, 3294681,
+ 27343084, 2786261, 36475274, 19457415}},
+ },
+ {
+ {{52641566, 32870716, 33734756, 7448551, 19294360, 14334329,
+ 47418233, 2355318, 47824193, 27440058}},
+ {{15121312, 17758270, 6377019, 27523071, 56310752, 20596586,
+ 18952176, 15496498, 37728731, 11754227}},
+ {{64471568, 20071356, 8488726, 19250536, 12728760, 31931939,
+ 7141595, 11724556, 22761615, 23420291}},
+ },
+ {
+ {{16918416, 11729663, 49025285, 3022986, 36093132, 20214772,
+ 38367678, 21327038, 32851221, 11717399}},
+ {{11166615, 7338049, 60386341, 4531519, 37640192, 26252376,
+ 31474878, 3483633, 65915689, 29523600}},
+ {{66923210, 9921304, 31456609, 20017994, 55095045, 13348922,
+ 33142652, 6546660, 47123585, 29606055}},
+ },
+ {
+ {{34648249, 11266711, 55911757, 25655328, 31703693, 3855903,
+ 58571733, 20721383, 36336829, 18068118}},
+ {{49102387, 12709067, 3991746, 27075244, 45617340, 23004006,
+ 35973516, 17504552, 10928916, 3011958}},
+ {{60151107, 17960094, 31696058, 334240, 29576716, 14796075,
+ 36277808, 20749251, 18008030, 10258577}},
+ },
+ {
+ {{44660220, 15655568, 7018479, 29144429, 36794597, 32352840,
+ 65255398, 1367119, 25127874, 6671743}},
+ {{29701166, 19180498, 56230743, 9279287, 67091296, 13127209,
+ 21382910, 11042292, 25838796, 4642684}},
+ {{46678630, 14955536, 42982517, 8124618, 61739576, 27563961,
+ 30468146, 19653792, 18423288, 4177476}},
+ },
+ },
+};
+
+static uint8_t negative(signed char b) {
+ uint32_t x = b;
+ x >>= 31; // 1: yes; 0: no
+ return x;
+}
+
+static void table_select(ge_precomp *t, int pos, signed char b) {
+ ge_precomp minust;
+ uint8_t bnegative = negative(b);
+ uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
+
+ ge_precomp_0(t);
+ cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
+ cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
+ cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
+ cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
+ cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
+ cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
+ cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
+ cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
+ fe_copy_ll(&minust.yplusx, &t->yminusx);
+ fe_copy_ll(&minust.yminusx, &t->yplusx);
+
+ // NOTE: the input table is canonical, but types don't encode it
+ fe tmp;
+ fe_carry(&tmp, &t->xy2d);
+ fe_neg(&minust.xy2d, &tmp);
+
+ cmov(t, &minust, bnegative);
+}
+
+// h = a * B
+// where a = a[0]+256*a[1]+...+256^31 a[31]
+// B is the Ed25519 base point (x,4/5) with x positive.
+//
+// Preconditions:
+// a[31] <= 127
+void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) {
+ signed char e[64];
+ signed char carry;
+ ge_p1p1 r;
+ ge_p2 s;
+ ge_precomp t;
+ int i;
+
+ for (i = 0; i < 32; ++i) {
+ e[2 * i + 0] = (a[i] >> 0) & 15;
+ e[2 * i + 1] = (a[i] >> 4) & 15;
+ }
+ // each e[i] is between 0 and 15
+ // e[63] is between 0 and 7
+
+ carry = 0;
+ for (i = 0; i < 63; ++i) {
+ e[i] += carry;
+ carry = e[i] + 8;
+ carry >>= 4;
+ e[i] -= carry << 4;
+ }
+ e[63] += carry;
+ // each e[i] is between -8 and 8
+
+ ge_p3_0(h);
+ for (i = 1; i < 64; i += 2) {
+ table_select(&t, i / 2, e[i]);
+ ge_madd(&r, h, &t);
+ x25519_ge_p1p1_to_p3(h, &r);
+ }
+
+ ge_p3_dbl(&r, h);
+ x25519_ge_p1p1_to_p2(&s, &r);
+ ge_p2_dbl(&r, &s);
+ x25519_ge_p1p1_to_p2(&s, &r);
+ ge_p2_dbl(&r, &s);
+ x25519_ge_p1p1_to_p2(&s, &r);
+ ge_p2_dbl(&r, &s);
+ x25519_ge_p1p1_to_p3(h, &r);
+
+ for (i = 0; i < 64; i += 2) {
+ table_select(&t, i / 2, e[i]);
+ ge_madd(&r, h, &t);
+ x25519_ge_p1p1_to_p3(h, &r);
+ }
+}
+
+#endif
+
+static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
+ fe_cmov(&t->YplusX, &u->YplusX, b);
+ fe_cmov(&t->YminusX, &u->YminusX, b);
+ fe_cmov(&t->Z, &u->Z, b);
+ fe_cmov(&t->T2d, &u->T2d, b);
+}
+
+// r = scalar * A.
+// where a = a[0]+256*a[1]+...+256^31 a[31].
+void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) {
+ ge_p2 Ai_p2[8];
+ ge_cached Ai[16];
+ ge_p1p1 t;
+
+ ge_cached_0(&Ai[0]);
+ x25519_ge_p3_to_cached(&Ai[1], A);
+ ge_p3_to_p2(&Ai_p2[1], A);
+
+ unsigned i;
+ for (i = 2; i < 16; i += 2) {
+ ge_p2_dbl(&t, &Ai_p2[i / 2]);
+ ge_p1p1_to_cached(&Ai[i], &t);
+ if (i < 8) {
+ x25519_ge_p1p1_to_p2(&Ai_p2[i], &t);
+ }
+ x25519_ge_add(&t, A, &Ai[i]);
+ ge_p1p1_to_cached(&Ai[i + 1], &t);
+ if (i < 7) {
+ x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t);
+ }
+ }
+
+ ge_p2_0(r);
+ ge_p3 u;
+
+ for (i = 0; i < 256; i += 4) {
+ ge_p2_dbl(&t, r);
+ x25519_ge_p1p1_to_p2(r, &t);
+ ge_p2_dbl(&t, r);
+ x25519_ge_p1p1_to_p2(r, &t);
+ ge_p2_dbl(&t, r);
+ x25519_ge_p1p1_to_p2(r, &t);
+ ge_p2_dbl(&t, r);
+ x25519_ge_p1p1_to_p3(&u, &t);
+
+ uint8_t index = scalar[31 - i/8];
+ index >>= 4 - (i & 4);
+ index &= 0xf;
+
+ unsigned j;
+ ge_cached selected;
+ ge_cached_0(&selected);
+ for (j = 0; j < 16; j++) {
+ cmov_cached(&selected, &Ai[j], equal(j, index));
+ }
+
+ x25519_ge_add(&t, &u, &selected);
+ x25519_ge_p1p1_to_p2(r, &t);
+ }
+}
+
+static void slide(signed char *r, const uint8_t *a) {
+ int i;
+ int b;
+ int k;
+
+ for (i = 0; i < 256; ++i) {
+ r[i] = 1 & (a[i >> 3] >> (i & 7));
+ }
+
+ for (i = 0; i < 256; ++i) {
+ if (r[i]) {
+ for (b = 1; b <= 6 && i + b < 256; ++b) {
+ if (r[i + b]) {
+ if (r[i] + (r[i + b] << b) <= 15) {
+ r[i] += r[i + b] << b;
+ r[i + b] = 0;
+ } else if (r[i] - (r[i + b] << b) >= -15) {
+ r[i] -= r[i + b] << b;
+ for (k = i + b; k < 256; ++k) {
+ if (!r[k]) {
+ r[k] = 1;
+ break;
+ }
+ r[k] = 0;
+ }
+ } else {
+ break;
+ }
+ }
+ }
+ }
+ }
+}
+
+static const ge_precomp Bi[8] = {
+ {
+ {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786, 27544626,
+ 21800161, 61029707, 2047604}},
+ {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
+ 5043384, 19500929, 18085054}},
+ {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918,
+ 11864899, 42594502, 29115885}},
+ },
+ {
+ {{15636272, 23865875, 24204772, 25642034, 616976, 16869170, 27787599,
+ 18782243, 28944399, 32004408}},
+ {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576,
+ 21778470, 7689661, 11199574}},
+ {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774,
+ 10017326, 49359771, 23634074}},
+ },
+ {
+ {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860, 32867885,
+ 14515107, 51670560, 10819379}},
+ {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
+ 12483687, 54440373, 5581305}},
+ {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349,
+ 13850243, 43430843, 17738489}},
+ },
+ {
+ {{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
+ 5230134, 43156425, 18378665}},
+ {{36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025,
+ 16520125, 30598449, 7715701}},
+ {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204,
+ 1370707, 29794553, 32145132}},
+ },
+ {
+ {{44589871, 26862249, 14201701, 24808930, 43598457, 8844725, 18474211,
+ 32192982, 54046167, 13821876}},
+ {{60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027,
+ 26342105, 18853321, 19333481}},
+ {{4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505,
+ 23123294, 2207752, 30344648}},
+ },
+ {
+ {{41954014, 29368610, 29681143, 7868801, 60254203, 24130566, 54671499,
+ 32891431, 35997400, 17421995}},
+ {{25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789,
+ 15725684, 171356, 6466918}},
+ {{23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338,
+ 19466374, 36393951, 16193876}},
+ },
+ {
+ {{33587053, 3180712, 64714734, 14003686, 50205390, 17283591, 17238397,
+ 4729455, 49034351, 9256799}},
+ {{41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405,
+ 9761698, 47281666, 630304}},
+ {{53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312,
+ 17593437, 64659607, 19263131}},
+ },
+ {
+ {{63957664, 28508356, 9282713, 6866145, 35201802, 32691408, 48168288,
+ 15033783, 25105118, 25659556}},
+ {{42782475, 15950225, 35307649, 18961608, 55446126, 28463506,
+ 1573891, 30928545, 2198789, 17749813}},
+ {{64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841,
+ 17317989, 34647629, 21263748}},
+ },
+};
+
+// r = a * A + b * B
+// where a = a[0]+256*a[1]+...+256^31 a[31].
+// and b = b[0]+256*b[1]+...+256^31 b[31].
+// B is the Ed25519 base point (x,4/5) with x positive.
+static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
+ const ge_p3 *A, const uint8_t *b) {
+ signed char aslide[256];
+ signed char bslide[256];
+ ge_cached Ai[8]; // A,3A,5A,7A,9A,11A,13A,15A
+ ge_p1p1 t;
+ ge_p3 u;
+ ge_p3 A2;
+ int i;
+
+ slide(aslide, a);
+ slide(bslide, b);
+
+ x25519_ge_p3_to_cached(&Ai[0], A);
+ ge_p3_dbl(&t, A);
+ x25519_ge_p1p1_to_p3(&A2, &t);
+ x25519_ge_add(&t, &A2, &Ai[0]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[1], &u);
+ x25519_ge_add(&t, &A2, &Ai[1]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[2], &u);
+ x25519_ge_add(&t, &A2, &Ai[2]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[3], &u);
+ x25519_ge_add(&t, &A2, &Ai[3]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[4], &u);
+ x25519_ge_add(&t, &A2, &Ai[4]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[5], &u);
+ x25519_ge_add(&t, &A2, &Ai[5]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[6], &u);
+ x25519_ge_add(&t, &A2, &Ai[6]);
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_p3_to_cached(&Ai[7], &u);
+
+ ge_p2_0(r);
+
+ for (i = 255; i >= 0; --i) {
+ if (aslide[i] || bslide[i]) {
+ break;
+ }
+ }
+
+ for (; i >= 0; --i) {
+ ge_p2_dbl(&t, r);
+
+ if (aslide[i] > 0) {
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]);
+ } else if (aslide[i] < 0) {
+ x25519_ge_p1p1_to_p3(&u, &t);
+ x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+ }
+
+ if (bslide[i] > 0) {
+ x25519_ge_p1p1_to_p3(&u, &t);
+ ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+ } else if (bslide[i] < 0) {
+ x25519_ge_p1p1_to_p3(&u, &t);
+ ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+ }
+
+ x25519_ge_p1p1_to_p2(r, &t);
+ }
+}
+
+// The set of scalars is \Z/l
+// where l = 2^252 + 27742317777372353535851937790883648493.
+
+// Input:
+// s[0]+256*s[1]+...+256^63*s[63] = s
+//
+// Output:
+// s[0]+256*s[1]+...+256^31*s[31] = s mod l
+// where l = 2^252 + 27742317777372353535851937790883648493.
+// Overwrites s in place.
+void x25519_sc_reduce(uint8_t *s) {
+ int64_t s0 = 2097151 & load_3(s);
+ int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+ int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+ int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+ int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+ int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+ int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+ int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+ int64_t s8 = 2097151 & load_3(s + 21);
+ int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+ int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+ int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+ int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+ int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+ int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+ int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+ int64_t s16 = 2097151 & load_3(s + 42);
+ int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+ int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+ int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+ int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+ int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+ int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+ int64_t s23 = (load_4(s + 60) >> 3);
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+ int64_t carry10;
+ int64_t carry11;
+ int64_t carry12;
+ int64_t carry13;
+ int64_t carry14;
+ int64_t carry15;
+ int64_t carry16;
+
+ s11 += s23 * 666643;
+ s12 += s23 * 470296;
+ s13 += s23 * 654183;
+ s14 -= s23 * 997805;
+ s15 += s23 * 136657;
+ s16 -= s23 * 683901;
+ s23 = 0;
+
+ s10 += s22 * 666643;
+ s11 += s22 * 470296;
+ s12 += s22 * 654183;
+ s13 -= s22 * 997805;
+ s14 += s22 * 136657;
+ s15 -= s22 * 683901;
+ s22 = 0;
+
+ s9 += s21 * 666643;
+ s10 += s21 * 470296;
+ s11 += s21 * 654183;
+ s12 -= s21 * 997805;
+ s13 += s21 * 136657;
+ s14 -= s21 * 683901;
+ s21 = 0;
+
+ s8 += s20 * 666643;
+ s9 += s20 * 470296;
+ s10 += s20 * 654183;
+ s11 -= s20 * 997805;
+ s12 += s20 * 136657;
+ s13 -= s20 * 683901;
+ s20 = 0;
+
+ s7 += s19 * 666643;
+ s8 += s19 * 470296;
+ s9 += s19 * 654183;
+ s10 -= s19 * 997805;
+ s11 += s19 * 136657;
+ s12 -= s19 * 683901;
+ s19 = 0;
+
+ s6 += s18 * 666643;
+ s7 += s18 * 470296;
+ s8 += s18 * 654183;
+ s9 -= s18 * 997805;
+ s10 += s18 * 136657;
+ s11 -= s18 * 683901;
+ s18 = 0;
+
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+ carry12 = (s12 + (1 << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 << 21;
+ carry14 = (s14 + (1 << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 << 21;
+ carry16 = (s16 + (1 << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 << 21;
+
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+ carry13 = (s13 + (1 << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 << 21;
+ carry15 = (s15 + (1 << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 << 21;
+
+ s5 += s17 * 666643;
+ s6 += s17 * 470296;
+ s7 += s17 * 654183;
+ s8 -= s17 * 997805;
+ s9 += s17 * 136657;
+ s10 -= s17 * 683901;
+ s17 = 0;
+
+ s4 += s16 * 666643;
+ s5 += s16 * 470296;
+ s6 += s16 * 654183;
+ s7 -= s16 * 997805;
+ s8 += s16 * 136657;
+ s9 -= s16 * 683901;
+ s16 = 0;
+
+ s3 += s15 * 666643;
+ s4 += s15 * 470296;
+ s5 += s15 * 654183;
+ s6 -= s15 * 997805;
+ s7 += s15 * 136657;
+ s8 -= s15 * 683901;
+ s15 = 0;
+
+ s2 += s14 * 666643;
+ s3 += s14 * 470296;
+ s4 += s14 * 654183;
+ s5 -= s14 * 997805;
+ s6 += s14 * 136657;
+ s7 -= s14 * 683901;
+ s14 = 0;
+
+ s1 += s13 * 666643;
+ s2 += s13 * 470296;
+ s3 += s13 * 654183;
+ s4 -= s13 * 997805;
+ s5 += s13 * 136657;
+ s6 -= s13 * 683901;
+ s13 = 0;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = (s0 + (1 << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry2 = (s2 + (1 << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry4 = (s4 + (1 << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+
+ carry1 = (s1 + (1 << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry3 = (s3 + (1 << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry5 = (s5 + (1 << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+ carry11 = s11 >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+
+ s[0] = s0 >> 0;
+ s[1] = s0 >> 8;
+ s[2] = (s0 >> 16) | (s1 << 5);
+ s[3] = s1 >> 3;
+ s[4] = s1 >> 11;
+ s[5] = (s1 >> 19) | (s2 << 2);
+ s[6] = s2 >> 6;
+ s[7] = (s2 >> 14) | (s3 << 7);
+ s[8] = s3 >> 1;
+ s[9] = s3 >> 9;
+ s[10] = (s3 >> 17) | (s4 << 4);
+ s[11] = s4 >> 4;
+ s[12] = s4 >> 12;
+ s[13] = (s4 >> 20) | (s5 << 1);
+ s[14] = s5 >> 7;
+ s[15] = (s5 >> 15) | (s6 << 6);
+ s[16] = s6 >> 2;
+ s[17] = s6 >> 10;
+ s[18] = (s6 >> 18) | (s7 << 3);
+ s[19] = s7 >> 5;
+ s[20] = s7 >> 13;
+ s[21] = s8 >> 0;
+ s[22] = s8 >> 8;
+ s[23] = (s8 >> 16) | (s9 << 5);
+ s[24] = s9 >> 3;
+ s[25] = s9 >> 11;
+ s[26] = (s9 >> 19) | (s10 << 2);
+ s[27] = s10 >> 6;
+ s[28] = (s10 >> 14) | (s11 << 7);
+ s[29] = s11 >> 1;
+ s[30] = s11 >> 9;
+ s[31] = s11 >> 17;
+}
+
+// Input:
+// a[0]+256*a[1]+...+256^31*a[31] = a
+// b[0]+256*b[1]+...+256^31*b[31] = b
+// c[0]+256*c[1]+...+256^31*c[31] = c
+//
+// Output:
+// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+// where l = 2^252 + 27742317777372353535851937790883648493.
+static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
+ const uint8_t *c) {
+ int64_t a0 = 2097151 & load_3(a);
+ int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+ int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+ int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+ int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+ int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+ int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+ int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+ int64_t a8 = 2097151 & load_3(a + 21);
+ int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+ int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+ int64_t a11 = (load_4(a + 28) >> 7);
+ int64_t b0 = 2097151 & load_3(b);
+ int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+ int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+ int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+ int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+ int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+ int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+ int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+ int64_t b8 = 2097151 & load_3(b + 21);
+ int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+ int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+ int64_t b11 = (load_4(b + 28) >> 7);
+ int64_t c0 = 2097151 & load_3(c);
+ int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+ int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+ int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+ int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+ int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+ int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+ int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+ int64_t c8 = 2097151 & load_3(c + 21);
+ int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+ int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+ int64_t c11 = (load_4(c + 28) >> 7);
+ int64_t s0;
+ int64_t s1;
+ int64_t s2;
+ int64_t s3;
+ int64_t s4;
+ int64_t s5;
+ int64_t s6;
+ int64_t s7;
+ int64_t s8;
+ int64_t s9;
+ int64_t s10;
+ int64_t s11;
+ int64_t s12;
+ int64_t s13;
+ int64_t s14;
+ int64_t s15;
+ int64_t s16;
+ int64_t s17;
+ int64_t s18;
+ int64_t s19;
+ int64_t s20;
+ int64_t s21;
+ int64_t s22;
+ int64_t s23;
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+ int64_t carry10;
+ int64_t carry11;
+ int64_t carry12;
+ int64_t carry13;
+ int64_t carry14;
+ int64_t carry15;
+ int64_t carry16;
+ int64_t carry17;
+ int64_t carry18;
+ int64_t carry19;
+ int64_t carry20;
+ int64_t carry21;
+ int64_t carry22;
+
+ s0 = c0 + a0 * b0;
+ s1 = c1 + a0 * b1 + a1 * b0;
+ s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+ s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+ s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+ s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+ s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+ s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
+ a6 * b1 + a7 * b0;
+ s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
+ a6 * b2 + a7 * b1 + a8 * b0;
+ s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
+ a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+ s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
+ a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+ s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
+ a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+ s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 +
+ a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+ s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 +
+ a9 * b4 + a10 * b3 + a11 * b2;
+ s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 +
+ a10 * b4 + a11 * b3;
+ s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 +
+ a11 * b4;
+ s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+ s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+ s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+ s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+ s20 = a9 * b11 + a10 * b10 + a11 * b9;
+ s21 = a10 * b11 + a11 * b10;
+ s22 = a11 * b11;
+ s23 = 0;
+
+ carry0 = (s0 + (1 << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry2 = (s2 + (1 << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry4 = (s4 + (1 << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+ carry12 = (s12 + (1 << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 << 21;
+ carry14 = (s14 + (1 << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 << 21;
+ carry16 = (s16 + (1 << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 << 21;
+ carry18 = (s18 + (1 << 20)) >> 21;
+ s19 += carry18;
+ s18 -= carry18 << 21;
+ carry20 = (s20 + (1 << 20)) >> 21;
+ s21 += carry20;
+ s20 -= carry20 << 21;
+ carry22 = (s22 + (1 << 20)) >> 21;
+ s23 += carry22;
+ s22 -= carry22 << 21;
+
+ carry1 = (s1 + (1 << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry3 = (s3 + (1 << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry5 = (s5 + (1 << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+ carry13 = (s13 + (1 << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 << 21;
+ carry15 = (s15 + (1 << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 << 21;
+ carry17 = (s17 + (1 << 20)) >> 21;
+ s18 += carry17;
+ s17 -= carry17 << 21;
+ carry19 = (s19 + (1 << 20)) >> 21;
+ s20 += carry19;
+ s19 -= carry19 << 21;
+ carry21 = (s21 + (1 << 20)) >> 21;
+ s22 += carry21;
+ s21 -= carry21 << 21;
+
+ s11 += s23 * 666643;
+ s12 += s23 * 470296;
+ s13 += s23 * 654183;
+ s14 -= s23 * 997805;
+ s15 += s23 * 136657;
+ s16 -= s23 * 683901;
+ s23 = 0;
+
+ s10 += s22 * 666643;
+ s11 += s22 * 470296;
+ s12 += s22 * 654183;
+ s13 -= s22 * 997805;
+ s14 += s22 * 136657;
+ s15 -= s22 * 683901;
+ s22 = 0;
+
+ s9 += s21 * 666643;
+ s10 += s21 * 470296;
+ s11 += s21 * 654183;
+ s12 -= s21 * 997805;
+ s13 += s21 * 136657;
+ s14 -= s21 * 683901;
+ s21 = 0;
+
+ s8 += s20 * 666643;
+ s9 += s20 * 470296;
+ s10 += s20 * 654183;
+ s11 -= s20 * 997805;
+ s12 += s20 * 136657;
+ s13 -= s20 * 683901;
+ s20 = 0;
+
+ s7 += s19 * 666643;
+ s8 += s19 * 470296;
+ s9 += s19 * 654183;
+ s10 -= s19 * 997805;
+ s11 += s19 * 136657;
+ s12 -= s19 * 683901;
+ s19 = 0;
+
+ s6 += s18 * 666643;
+ s7 += s18 * 470296;
+ s8 += s18 * 654183;
+ s9 -= s18 * 997805;
+ s10 += s18 * 136657;
+ s11 -= s18 * 683901;
+ s18 = 0;
+
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+ carry12 = (s12 + (1 << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 << 21;
+ carry14 = (s14 + (1 << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 << 21;
+ carry16 = (s16 + (1 << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 << 21;
+
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+ carry13 = (s13 + (1 << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 << 21;
+ carry15 = (s15 + (1 << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 << 21;
+
+ s5 += s17 * 666643;
+ s6 += s17 * 470296;
+ s7 += s17 * 654183;
+ s8 -= s17 * 997805;
+ s9 += s17 * 136657;
+ s10 -= s17 * 683901;
+ s17 = 0;
+
+ s4 += s16 * 666643;
+ s5 += s16 * 470296;
+ s6 += s16 * 654183;
+ s7 -= s16 * 997805;
+ s8 += s16 * 136657;
+ s9 -= s16 * 683901;
+ s16 = 0;
+
+ s3 += s15 * 666643;
+ s4 += s15 * 470296;
+ s5 += s15 * 654183;
+ s6 -= s15 * 997805;
+ s7 += s15 * 136657;
+ s8 -= s15 * 683901;
+ s15 = 0;
+
+ s2 += s14 * 666643;
+ s3 += s14 * 470296;
+ s4 += s14 * 654183;
+ s5 -= s14 * 997805;
+ s6 += s14 * 136657;
+ s7 -= s14 * 683901;
+ s14 = 0;
+
+ s1 += s13 * 666643;
+ s2 += s13 * 470296;
+ s3 += s13 * 654183;
+ s4 -= s13 * 997805;
+ s5 += s13 * 136657;
+ s6 -= s13 * 683901;
+ s13 = 0;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = (s0 + (1 << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry2 = (s2 + (1 << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry4 = (s4 + (1 << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry6 = (s6 + (1 << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry8 = (s8 + (1 << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry10 = (s10 + (1 << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+
+ carry1 = (s1 + (1 << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry3 = (s3 + (1 << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry5 = (s5 + (1 << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry7 = (s7 + (1 << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry9 = (s9 + (1 << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry11 = (s11 + (1 << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+ carry11 = s11 >> 21;
+ s12 += carry11;
+ s11 -= carry11 << 21;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 << 21;
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 << 21;
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 << 21;
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 << 21;
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 << 21;
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 << 21;
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 << 21;
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 << 21;
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 << 21;
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 << 21;
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 << 21;
+
+ s[0] = s0 >> 0;
+ s[1] = s0 >> 8;
+ s[2] = (s0 >> 16) | (s1 << 5);
+ s[3] = s1 >> 3;
+ s[4] = s1 >> 11;
+ s[5] = (s1 >> 19) | (s2 << 2);
+ s[6] = s2 >> 6;
+ s[7] = (s2 >> 14) | (s3 << 7);
+ s[8] = s3 >> 1;
+ s[9] = s3 >> 9;
+ s[10] = (s3 >> 17) | (s4 << 4);
+ s[11] = s4 >> 4;
+ s[12] = s4 >> 12;
+ s[13] = (s4 >> 20) | (s5 << 1);
+ s[14] = s5 >> 7;
+ s[15] = (s5 >> 15) | (s6 << 6);
+ s[16] = s6 >> 2;
+ s[17] = s6 >> 10;
+ s[18] = (s6 >> 18) | (s7 << 3);
+ s[19] = s7 >> 5;
+ s[20] = s7 >> 13;
+ s[21] = s8 >> 0;
+ s[22] = s8 >> 8;
+ s[23] = (s8 >> 16) | (s9 << 5);
+ s[24] = s9 >> 3;
+ s[25] = s9 >> 11;
+ s[26] = (s9 >> 19) | (s10 << 2);
+ s[27] = s10 >> 6;
+ s[28] = (s10 >> 14) | (s11 << 7);
+ s[29] = s11 >> 1;
+ s[30] = s11 >> 9;
+ s[31] = s11 >> 17;
+}
+
+void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) {
+ uint8_t seed[32];
+ RAND_bytes(seed, 32);
+ ED25519_keypair_from_seed(out_public_key, out_private_key, seed);
+}
+
+int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
+ const uint8_t private_key[64]) {
+ uint8_t az[SHA512_DIGEST_LENGTH];
+ SHA512(private_key, 32, az);
+
+ az[0] &= 248;
+ az[31] &= 63;
+ az[31] |= 64;
+
+ SHA512_CTX hash_ctx;
+ SHA512_Init(&hash_ctx);
+ SHA512_Update(&hash_ctx, az + 32, 32);
+ SHA512_Update(&hash_ctx, message, message_len);
+ uint8_t nonce[SHA512_DIGEST_LENGTH];
+ SHA512_Final(nonce, &hash_ctx);
+
+ x25519_sc_reduce(nonce);
+ ge_p3 R;
+ x25519_ge_scalarmult_base(&R, nonce);
+ ge_p3_tobytes(out_sig, &R);
+
+ SHA512_Init(&hash_ctx);
+ SHA512_Update(&hash_ctx, out_sig, 32);
+ SHA512_Update(&hash_ctx, private_key + 32, 32);
+ SHA512_Update(&hash_ctx, message, message_len);
+ uint8_t hram[SHA512_DIGEST_LENGTH];
+ SHA512_Final(hram, &hash_ctx);
+
+ x25519_sc_reduce(hram);
+ sc_muladd(out_sig + 32, hram, az, nonce);
+
+ return 1;
+}
+
+int ED25519_verify(const uint8_t *message, size_t message_len,
+ const uint8_t signature[64], const uint8_t public_key[32]) {
+ ge_p3 A;
+ if ((signature[63] & 224) != 0 ||
+ x25519_ge_frombytes_vartime(&A, public_key) != 0) {
+ return 0;
+ }
+
+ fe_loose t;
+ fe_neg(&t, &A.X);
+ fe_carry(&A.X, &t);
+ fe_neg(&t, &A.T);
+ fe_carry(&A.T, &t);
+
+ uint8_t pkcopy[32];
+ OPENSSL_memcpy(pkcopy, public_key, 32);
+ uint8_t rcopy[32];
+ OPENSSL_memcpy(rcopy, signature, 32);
+ uint8_t scopy[32];
+ OPENSSL_memcpy(scopy, signature + 32, 32);
+
+ SHA512_CTX hash_ctx;
+ SHA512_Init(&hash_ctx);
+ SHA512_Update(&hash_ctx, signature, 32);
+ SHA512_Update(&hash_ctx, public_key, 32);
+ SHA512_Update(&hash_ctx, message, message_len);
+ uint8_t h[SHA512_DIGEST_LENGTH];
+ SHA512_Final(h, &hash_ctx);
+
+ x25519_sc_reduce(h);
+
+ ge_p2 R;
+ ge_double_scalarmult_vartime(&R, h, &A, scopy);
+
+ uint8_t rcheck[32];
+ x25519_ge_tobytes(rcheck, &R);
+
+ return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;
+}
+
+void ED25519_keypair_from_seed(uint8_t out_public_key[32],
+ uint8_t out_private_key[64],
+ const uint8_t seed[32]) {
+ uint8_t az[SHA512_DIGEST_LENGTH];
+ SHA512(seed, 32, az);
+
+ az[0] &= 248;
+ az[31] &= 63;
+ az[31] |= 64;
+
+ ge_p3 A;
+ x25519_ge_scalarmult_base(&A, az);
+ ge_p3_tobytes(out_public_key, &A);
+
+ OPENSSL_memcpy(out_private_key, seed, 32);
+ OPENSSL_memcpy(out_private_key + 32, out_public_key, 32);
+}
+
+
+#if defined(BORINGSSL_X25519_X86_64)
+
+static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32]) {
+ x25519_x86_64(out, scalar, point);
+}
+
+#else
+
+// Replace (f,g) with (g,f) if b == 1;
+// replace (f,g) with (f,g) if b == 0.
+//
+// Preconditions: b in {0,1}.
+static void fe_cswap(fe *f, fe *g, unsigned int b) {
+ b = 0-b;
+ unsigned i;
+ for (i = 0; i < 10; i++) {
+ uint32_t x = f->v[i] ^ g->v[i];
+ x &= b;
+ f->v[i] ^= x;
+ g->v[i] ^= x;
+ }
+}
+
+// NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0..
+static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) {
+ assert_fe_loose(in1);
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = 0;
+ { const uint32_t x39 = 0;
+ { const uint32_t x37 = 0;
+ { const uint32_t x35 = 0;
+ { const uint32_t x33 = 0;
+ { const uint32_t x31 = 0;
+ { const uint32_t x29 = 0;
+ { const uint32_t x27 = 0;
+ { const uint32_t x25 = 0;
+ { const uint32_t x23 = 121666;
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
+}
+
+static void fe_mul121666(fe *h, const fe_loose *f) {
+ assert_fe_loose(f->v);
+ fe_mul_121666_impl(h->v, f->v);
+ assert_fe(h->v);
+}
+
+static void x25519_scalar_mult_generic(uint8_t out[32],
+ const uint8_t scalar[32],
+ const uint8_t point[32]) {
+ fe x1, x2, z2, x3, z3, tmp0, tmp1;
+ fe_loose x2l, z2l, x3l, tmp0l, tmp1l;
+
+ uint8_t e[32];
+ OPENSSL_memcpy(e, scalar, 32);
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+ fe_frombytes(&x1, point);
+ fe_1(&x2);
+ fe_0(&z2);
+ fe_copy(&x3, &x1);
+ fe_1(&z3);
+
+ unsigned swap = 0;
+ int pos;
+ for (pos = 254; pos >= 0; --pos) {
+ unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+ swap ^= b;
+ fe_cswap(&x2, &x3, swap);
+ fe_cswap(&z2, &z3, swap);
+ swap = b;
+ fe_sub(&tmp0l, &x3, &z3);
+ fe_sub(&tmp1l, &x2, &z2);
+ fe_add(&x2l, &x2, &z2);
+ fe_add(&z2l, &x3, &z3);
+ fe_mul_tll(&z3, &tmp0l, &x2l);
+ fe_mul_tll(&z2, &z2l, &tmp1l);
+ fe_sq_tl(&tmp0, &tmp1l);
+ fe_sq_tl(&tmp1, &x2l);
+ fe_add(&x3l, &z3, &z2);
+ fe_sub(&z2l, &z3, &z2);
+ fe_mul_ttt(&x2, &tmp1, &tmp0);
+ fe_sub(&tmp1l, &tmp1, &tmp0);
+ fe_sq_tl(&z2, &z2l);
+ fe_mul121666(&z3, &tmp1l);
+ fe_sq_tl(&x3, &x3l);
+ fe_add(&tmp0l, &tmp0, &z3);
+ fe_mul_ttt(&z3, &x1, &z2);
+ fe_mul_tll(&z2, &tmp1l, &tmp0l);
+ }
+ fe_cswap(&x2, &x3, swap);
+ fe_cswap(&z2, &z3, swap);
+
+ fe_invert(&z2, &z2);
+ fe_mul_ttt(&x2, &x2, &z2);
+ fe_tobytes(out, &x2);
+}
+
+static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32]) {
+#if defined(BORINGSSL_X25519_NEON)
+ if (CRYPTO_is_NEON_capable()) {
+ x25519_NEON(out, scalar, point);
+ return;
+ }
+#endif
+
+ x25519_scalar_mult_generic(out, scalar, point);
+}
+
+#endif // BORINGSSL_X25519_X86_64
+
+
+void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
+ RAND_bytes(out_private_key, 32);
+
+ // All X25519 implementations should decode scalars correctly (see
+ // https://tools.ietf.org/html/rfc7748#section-5). However, if an
+ // implementation doesn't then it might interoperate with random keys a
+ // fraction of the time because they'll, randomly, happen to be correctly
+ // formed.
+ //
+ // Thus we do the opposite of the masking here to make sure that our private
+ // keys are never correctly masked and so, hopefully, any incorrect
+ // implementations are deterministically broken.
+ //
+ // This does not affect security because, although we're throwing away
+ // entropy, a valid implementation of scalarmult should throw away the exact
+ // same bits anyway.
+ out_private_key[0] |= 7;
+ out_private_key[31] &= 63;
+ out_private_key[31] |= 128;
+
+ X25519_public_from_private(out_public_value, out_private_key);
+}
+
+int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
+ const uint8_t peer_public_value[32]) {
+ static const uint8_t kZeros[32] = {0};
+ x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
+ // The all-zero output results when the input is a point of small order.
+ return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
+}
+
+#if defined(BORINGSSL_X25519_X86_64)
+
+// When |BORINGSSL_X25519_X86_64| is set, base point multiplication is done with
+// the Montgomery ladder because it's faster. Otherwise it's done using the
+// Ed25519 tables.
+
+void X25519_public_from_private(uint8_t out_public_value[32],
+ const uint8_t private_key[32]) {
+ static const uint8_t kMongomeryBasePoint[32] = {9};
+ x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint);
+}
+
+#else
+
+void X25519_public_from_private(uint8_t out_public_value[32],
+ const uint8_t private_key[32]) {
+#if defined(BORINGSSL_X25519_NEON)
+ if (CRYPTO_is_NEON_capable()) {
+ static const uint8_t kMongomeryBasePoint[32] = {9};
+ x25519_NEON(out_public_value, private_key, kMongomeryBasePoint);
+ return;
+ }
+#endif
+
+ uint8_t e[32];
+ OPENSSL_memcpy(e, private_key, 32);
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+
+ ge_p3 A;
+ x25519_ge_scalarmult_base(&A, e);
+
+ // We only need the u-coordinate of the curve25519 point. The map is
+ // u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y).
+ fe_loose zplusy, zminusy;
+ fe zminusy_inv;
+ fe_add(&zplusy, &A.Z, &A.Y);
+ fe_sub(&zminusy, &A.Z, &A.Y);
+ fe_loose_invert(&zminusy_inv, &zminusy);
+ fe_mul_tlt(&zminusy_inv, &zplusy, &zminusy_inv);
+ fe_tobytes(out_public_value, &zminusy_inv);
+}
+
+#endif // BORINGSSL_X25519_X86_64
diff --git a/src/third_party/fiat/internal.h b/src/third_party/fiat/internal.h
new file mode 100644
index 0000000..10218e0
--- /dev/null
+++ b/src/third_party/fiat/internal.h
@@ -0,0 +1,142 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#ifndef OPENSSL_HEADER_CURVE25519_INTERNAL_H
+#define OPENSSL_HEADER_CURVE25519_INTERNAL_H
+
+#if defined(__cplusplus)
+extern "C" {
+#endif
+
+
+#if defined(OPENSSL_X86_64) && !defined(OPENSSL_SMALL) && \
+ !defined(OPENSSL_WINDOWS) && !defined(OPENSSL_NO_ASM)
+#define BORINGSSL_X25519_X86_64
+
+void x25519_x86_64(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32]);
+#endif
+
+
+#if defined(OPENSSL_ARM) && !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_APPLE)
+#define BORINGSSL_X25519_NEON
+
+// x25519_NEON is defined in asm/x25519-arm.S.
+void x25519_NEON(uint8_t out[32], const uint8_t scalar[32],
+ const uint8_t point[32]);
+#endif
+
+// fe means field element. Here the field is \Z/(2^255-19). An element t,
+// entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
+// t[3]+2^102 t[4]+...+2^230 t[9].
+// fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
+// Multiplication and carrying produce fe from fe_loose.
+typedef struct fe { uint32_t v[10]; } fe;
+
+// fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc.
+// Addition and subtraction produce fe_loose from (fe, fe).
+typedef struct fe_loose { uint32_t v[10]; } fe_loose;
+
+/* ge means group element.
+
+ * Here the group is the set of pairs (x,y) of field elements (see fe.h)
+ * satisfying -x^2 + y^2 = 1 + d x^2y^2
+ * where d = -121665/121666.
+ *
+ * Representations:
+ * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+ * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+ * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+ * ge_precomp (Duif): (y+x,y-x,2dxy) */
+
+typedef struct {
+ fe X;
+ fe Y;
+ fe Z;
+} ge_p2;
+
+typedef struct {
+ fe X;
+ fe Y;
+ fe Z;
+ fe T;
+} ge_p3;
+
+typedef struct {
+ fe_loose X;
+ fe_loose Y;
+ fe_loose Z;
+ fe_loose T;
+} ge_p1p1;
+
+typedef struct {
+ fe_loose yplusx;
+ fe_loose yminusx;
+ fe_loose xy2d;
+} ge_precomp;
+
+typedef struct {
+ fe_loose YplusX;
+ fe_loose YminusX;
+ fe_loose Z;
+ fe_loose T2d;
+} ge_cached;
+
+void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h);
+int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s);
+void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p);
+void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p);
+void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p);
+void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void x25519_ge_scalarmult_small_precomp(
+ ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]);
+void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]);
+void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A);
+void x25519_sc_reduce(uint8_t *s);
+
+enum spake2_state_t {
+ spake2_state_init = 0,
+ spake2_state_msg_generated,
+ spake2_state_key_generated,
+};
+
+struct spake2_ctx_st {
+ uint8_t private_key[32];
+ uint8_t my_msg[32];
+ uint8_t password_scalar[32];
+ uint8_t password_hash[64];
+ uint8_t *my_name;
+ size_t my_name_len;
+ uint8_t *their_name;
+ size_t their_name_len;
+ enum spake2_role_t my_role;
+ enum spake2_state_t state;
+ char disable_password_scalar_hack;
+};
+
+
+#if defined(__cplusplus)
+} // extern C
+#endif
+
+#endif // OPENSSL_HEADER_CURVE25519_INTERNAL_H
diff --git a/src/tool/client.cc b/src/tool/client.cc
index 2ec381f..873cea0 100644
--- a/src/tool/client.cc
+++ b/src/tool/client.cc
@@ -323,6 +323,10 @@
*out = tls13_default;
return true;
}
+ if (in == "draft21") {
+ *out = tls13_draft21;
+ return true;
+ }
if (in == "experiment") {
*out = tls13_experiment;
return true;
diff --git a/src/tool/server.cc b/src/tool/server.cc
index b6ed284..0061cb3 100644
--- a/src/tool/server.cc
+++ b/src/tool/server.cc
@@ -80,6 +80,10 @@
"Print debug information about the handshake",
},
{
+ "-require-any-client-cert", kBooleanArgument,
+ "The server will require a client certificate.",
+ },
+ {
"", kOptionalArgument, "",
},
};
@@ -320,6 +324,14 @@
SSL_CTX_set_info_callback(ctx.get(), InfoCallback);
}
+ if (args_map.count("-require-any-client-cert") != 0) {
+ SSL_CTX_set_verify(
+ ctx.get(), SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
+ SSL_CTX_set_cert_verify_callback(
+ ctx.get(), [](X509_STORE_CTX *store, void *arg) -> int { return 1; },
+ nullptr);
+ }
+
Listener listener;
if (!listener.Init(args_map["-accept"])) {
return false;
diff --git a/src/tool/transport_common.cc b/src/tool/transport_common.cc
index a7c2b36..1a80678 100644
--- a/src/tool/transport_common.cc
+++ b/src/tool/transport_common.cc
@@ -234,38 +234,6 @@
return false;
}
-static const char *SignatureAlgorithmToString(uint16_t version, uint16_t sigalg) {
- const bool is_tls12 = version == TLS1_2_VERSION || version == DTLS1_2_VERSION;
- switch (sigalg) {
- case SSL_SIGN_RSA_PKCS1_SHA1:
- return "rsa_pkcs1_sha1";
- case SSL_SIGN_RSA_PKCS1_SHA256:
- return "rsa_pkcs1_sha256";
- case SSL_SIGN_RSA_PKCS1_SHA384:
- return "rsa_pkcs1_sha384";
- case SSL_SIGN_RSA_PKCS1_SHA512:
- return "rsa_pkcs1_sha512";
- case SSL_SIGN_ECDSA_SHA1:
- return "ecdsa_sha1";
- case SSL_SIGN_ECDSA_SECP256R1_SHA256:
- return is_tls12 ? "ecdsa_sha256" : "ecdsa_secp256r1_sha256";
- case SSL_SIGN_ECDSA_SECP384R1_SHA384:
- return is_tls12 ? "ecdsa_sha384" : "ecdsa_secp384r1_sha384";
- case SSL_SIGN_ECDSA_SECP521R1_SHA512:
- return is_tls12 ? "ecdsa_sha512" : "ecdsa_secp521r1_sha512";
- case SSL_SIGN_RSA_PSS_SHA256:
- return "rsa_pss_sha256";
- case SSL_SIGN_RSA_PSS_SHA384:
- return "rsa_pss_sha384";
- case SSL_SIGN_RSA_PSS_SHA512:
- return "rsa_pss_sha512";
- case SSL_SIGN_ED25519:
- return "ed25519";
- default:
- return "(unknown)";
- }
-}
-
void PrintConnectionInfo(BIO *bio, const SSL *ssl) {
const SSL_CIPHER *cipher = SSL_get_current_cipher(ssl);
@@ -280,7 +248,8 @@
uint16_t sigalg = SSL_get_peer_signature_algorithm(ssl);
if (sigalg != 0) {
BIO_printf(bio, " Signature algorithm: %s\n",
- SignatureAlgorithmToString(SSL_version(ssl), sigalg));
+ SSL_get_signature_algorithm_name(
+ sigalg, SSL_version(ssl) != TLS1_2_VERSION));
}
BIO_printf(bio, " Secure renegotiation: %s\n",
SSL_get_secure_renegotiation_support(ssl) ? "yes" : "no");
diff --git a/src/util/bot/DEPS b/src/util/bot/DEPS
index 0d67e3d..7b9f39e 100644
--- a/src/util/bot/DEPS
+++ b/src/util/bot/DEPS
@@ -22,7 +22,7 @@
deps = {
'boringssl/util/bot/android_tools': {
- 'url': Var('chromium_git') + '/android_tools.git' + '@' + 'ca9dc7245b888c75307f0619e4a39fb46a82de66',
+ 'url': Var('chromium_git') + '/android_tools.git' + '@' + 'ca0bd083872ad925881736fe2bedc3ff855e08f5',
'condition': 'checkout_android',
},
diff --git a/src/util/bot/go/bootstrap.py b/src/util/bot/go/bootstrap.py
index 86335aa..ec5aa3e 100755
--- a/src/util/bot/go/bootstrap.py
+++ b/src/util/bot/go/bootstrap.py
@@ -45,7 +45,7 @@
EXE_SFX = '.exe' if sys.platform == 'win32' else ''
# Pinned version of Go toolset to download.
-TOOLSET_VERSION = 'go1.9.1'
+TOOLSET_VERSION = 'go1.9.2'
# Platform dependent portion of a download URL. See http://golang.org/dl/.
TOOLSET_VARIANTS = {
diff --git a/src/util/bot/update_clang.py b/src/util/bot/update_clang.py
index 3164750..ee66153 100644
--- a/src/util/bot/update_clang.py
+++ b/src/util/bot/update_clang.py
@@ -19,8 +19,8 @@
# CLANG_REVISION and CLANG_SUB_REVISION determine the build of clang
# to use. These should be synced with tools/clang/scripts/update.py in
# Chromium.
-CLANG_REVISION = '313786'
-CLANG_SUB_REVISION=1
+CLANG_REVISION = '315613'
+CLANG_SUB_REVISION=2
PACKAGE_VERSION = "%s-%s" % (CLANG_REVISION, CLANG_SUB_REVISION)
diff --git a/src/util/bot/vs_toolchain.py b/src/util/bot/vs_toolchain.py
index 64da79a..153a6ed 100644
--- a/src/util/bot/vs_toolchain.py
+++ b/src/util/bot/vs_toolchain.py
@@ -87,8 +87,8 @@
# Update 3 final with 10.0.15063.468 SDK and no vctip.exe.
return ['f53e4598951162bad6330f7a167486c7ae5db1e5']
if env_version == '2017':
- # VS 2017 Update 3.2 with 10.0.15063.468 SDK and patched setenv.cmd.
- return ['a9e1098bba66d2acccc377d5ee81265910f29272']
+ # VS 2017 Update 4 with 10.0.15063.468 SDK.
+ return ['88c3b62e1eb0893b8cd57e3f4859c3af27907f64']
raise Exception('Unsupported VS version %s' % env_version)
diff --git a/src/util/generate_build_files.py b/src/util/generate_build_files.py
index 738484d..4b4a899 100644
--- a/src/util/generate_build_files.py
+++ b/src/util/generate_build_files.py
@@ -587,7 +587,8 @@
def main(platforms):
cmake = ExtractVariablesFromCMakeFile(os.path.join('src', 'sources.cmake'))
- crypto_c_files = FindCFiles(os.path.join('src', 'crypto'), NoTestsNorFIPSFragments)
+ crypto_c_files = (FindCFiles(os.path.join('src', 'crypto'), NoTestsNorFIPSFragments) +
+ FindCFiles(os.path.join('src', 'third_party', 'fiat'), NoTestsNorFIPSFragments))
fips_fragments = FindCFiles(os.path.join('src', 'crypto', 'fipsmodule'), OnlyFIPSFragments)
ssl_source_files = FindCFiles(os.path.join('src', 'ssl'), NoTests)
tool_c_files = FindCFiles(os.path.join('src', 'tool'), NoTests)
@@ -638,8 +639,9 @@
NotSSLHeaderFiles))
ssl_internal_h_files = FindHeaderFiles(os.path.join('src', 'ssl'), NoTests)
- crypto_internal_h_files = FindHeaderFiles(
- os.path.join('src', 'crypto'), NoTests)
+ crypto_internal_h_files = (
+ FindHeaderFiles(os.path.join('src', 'crypto'), NoTests) +
+ FindHeaderFiles(os.path.join('src', 'third_party', 'fiat'), NoTests))
files = {
'crypto': crypto_c_files,
diff --git a/src/util/make_errors.go b/src/util/make_errors.go
index 22fbd6a..2525a69 100644
--- a/src/util/make_errors.go
+++ b/src/util/make_errors.go
@@ -110,7 +110,7 @@
}
for _, name := range filenames {
- if !strings.HasSuffix(name, ".c") {
+ if !strings.HasSuffix(name, ".c") && !strings.HasSuffix(name, ".cc") {
continue
}
@@ -136,7 +136,12 @@
if err := writeHeaderFile(newHeaderFile, headerFile, prefix, reasons); err != nil {
return err
}
- os.Rename(headerPath+".tmp", headerPath)
+ // Windows forbids renaming an open file.
+ headerFile.Close()
+ newHeaderFile.Close()
+ if err := os.Rename(headerPath+".tmp", headerPath); err != nil {
+ return err
+ }
dataFile, err := os.OpenFile(dataPath, os.O_CREATE|os.O_WRONLY|os.O_TRUNC, 0644)
if err != nil {