Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1 | /* Copyright (c) 2015, Google Inc. |
| 2 | * |
| 3 | * Permission to use, copy, modify, and/or distribute this software for any |
| 4 | * purpose with or without fee is hereby granted, provided that the above |
| 5 | * copyright notice and this permission notice appear in all copies. |
| 6 | * |
| 7 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 8 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| 9 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
| 10 | * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| 11 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
| 12 | * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
| 13 | * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ |
| 14 | |
| 15 | /* A 64-bit implementation of the NIST P-224 elliptic curve point multiplication |
| 16 | * |
| 17 | * Inspired by Daniel J. Bernstein's public domain nistp224 implementation |
| 18 | * and Adam Langley's public domain 64-bit C implementation of curve25519. */ |
| 19 | |
| 20 | #include <openssl/base.h> |
| 21 | |
| 22 | #if defined(OPENSSL_64_BIT) && !defined(OPENSSL_WINDOWS) && \ |
| 23 | !defined(OPENSSL_SMALL) |
| 24 | |
| 25 | #include <openssl/bn.h> |
| 26 | #include <openssl/ec.h> |
| 27 | #include <openssl/err.h> |
| 28 | #include <openssl/mem.h> |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 29 | |
| 30 | #include <string.h> |
| 31 | |
| 32 | #include "internal.h" |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 33 | #include "../internal.h" |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 34 | |
| 35 | |
| 36 | typedef uint8_t u8; |
| 37 | typedef uint64_t u64; |
| 38 | typedef int64_t s64; |
| 39 | |
| 40 | /* Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 |
| 41 | * using 64-bit coefficients called 'limbs', and sometimes (for multiplication |
| 42 | * results) as b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + |
| 43 | * 2^336*b_6 using 128-bit coefficients called 'widelimbs'. A 4-limb |
| 44 | * representation is an 'felem'; a 7-widelimb representation is a 'widefelem'. |
| 45 | * Even within felems, bits of adjacent limbs overlap, and we don't always |
| 46 | * reduce the representations: we ensure that inputs to each felem |
| 47 | * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, and |
| 48 | * fit into a 128-bit word without overflow. The coefficients are then again |
| 49 | * partially reduced to obtain an felem satisfying a_i < 2^57. We only reduce |
| 50 | * to the unique minimal representation at the end of the computation. */ |
| 51 | |
| 52 | typedef uint64_t limb; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 53 | typedef uint128_t widelimb; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 54 | |
| 55 | typedef limb felem[4]; |
| 56 | typedef widelimb widefelem[7]; |
| 57 | |
| 58 | /* Field element represented as a byte arrary. 28*8 = 224 bits is also the |
| 59 | * group order size for the elliptic curve, and we also use this type for |
| 60 | * scalars for point multiplication. */ |
| 61 | typedef u8 felem_bytearray[28]; |
| 62 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 63 | /* Precomputed multiples of the standard generator |
| 64 | * Points are given in coordinates (X, Y, Z) where Z normally is 1 |
| 65 | * (0 for the point at infinity). |
| 66 | * For each field element, slice a_0 is word 0, etc. |
| 67 | * |
| 68 | * The table has 2 * 16 elements, starting with the following: |
| 69 | * index | bits | point |
| 70 | * ------+---------+------------------------------ |
| 71 | * 0 | 0 0 0 0 | 0G |
| 72 | * 1 | 0 0 0 1 | 1G |
| 73 | * 2 | 0 0 1 0 | 2^56G |
| 74 | * 3 | 0 0 1 1 | (2^56 + 1)G |
| 75 | * 4 | 0 1 0 0 | 2^112G |
| 76 | * 5 | 0 1 0 1 | (2^112 + 1)G |
| 77 | * 6 | 0 1 1 0 | (2^112 + 2^56)G |
| 78 | * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G |
| 79 | * 8 | 1 0 0 0 | 2^168G |
| 80 | * 9 | 1 0 0 1 | (2^168 + 1)G |
| 81 | * 10 | 1 0 1 0 | (2^168 + 2^56)G |
| 82 | * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G |
| 83 | * 12 | 1 1 0 0 | (2^168 + 2^112)G |
| 84 | * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G |
| 85 | * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G |
| 86 | * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G |
| 87 | * followed by a copy of this with each element multiplied by 2^28. |
| 88 | * |
| 89 | * The reason for this is so that we can clock bits into four different |
| 90 | * locations when doing simple scalar multiplies against the base point, |
| 91 | * and then another four locations using the second 16 elements. */ |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 92 | static const felem g_pre_comp[2][16][3] = { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 93 | {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, |
| 94 | {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, |
| 95 | {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, |
| 96 | {1, 0, 0, 0}}, |
| 97 | {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, |
| 98 | {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, |
| 99 | {1, 0, 0, 0}}, |
| 100 | {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, |
| 101 | {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, |
| 102 | {1, 0, 0, 0}}, |
| 103 | {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, |
| 104 | {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, |
| 105 | {1, 0, 0, 0}}, |
| 106 | {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, |
| 107 | {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, |
| 108 | {1, 0, 0, 0}}, |
| 109 | {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, |
| 110 | {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, |
| 111 | {1, 0, 0, 0}}, |
| 112 | {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, |
| 113 | {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, |
| 114 | {1, 0, 0, 0}}, |
| 115 | {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, |
| 116 | {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, |
| 117 | {1, 0, 0, 0}}, |
| 118 | {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, |
| 119 | {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, |
| 120 | {1, 0, 0, 0}}, |
| 121 | {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, |
| 122 | {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, |
| 123 | {1, 0, 0, 0}}, |
| 124 | {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, |
| 125 | {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, |
| 126 | {1, 0, 0, 0}}, |
| 127 | {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, |
| 128 | {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, |
| 129 | {1, 0, 0, 0}}, |
| 130 | {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, |
| 131 | {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, |
| 132 | {1, 0, 0, 0}}, |
| 133 | {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, |
| 134 | {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, |
| 135 | {1, 0, 0, 0}}, |
| 136 | {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, |
| 137 | {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, |
| 138 | {1, 0, 0, 0}}}, |
| 139 | {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, |
| 140 | {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, |
| 141 | {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, |
| 142 | {1, 0, 0, 0}}, |
| 143 | {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, |
| 144 | {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, |
| 145 | {1, 0, 0, 0}}, |
| 146 | {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, |
| 147 | {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, |
| 148 | {1, 0, 0, 0}}, |
| 149 | {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, |
| 150 | {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, |
| 151 | {1, 0, 0, 0}}, |
| 152 | {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, |
| 153 | {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, |
| 154 | {1, 0, 0, 0}}, |
| 155 | {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, |
| 156 | {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, |
| 157 | {1, 0, 0, 0}}, |
| 158 | {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, |
| 159 | {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, |
| 160 | {1, 0, 0, 0}}, |
| 161 | {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, |
| 162 | {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, |
| 163 | {1, 0, 0, 0}}, |
| 164 | {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, |
| 165 | {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, |
| 166 | {1, 0, 0, 0}}, |
| 167 | {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, |
| 168 | {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, |
| 169 | {1, 0, 0, 0}}, |
| 170 | {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, |
| 171 | {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, |
| 172 | {1, 0, 0, 0}}, |
| 173 | {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, |
| 174 | {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, |
| 175 | {1, 0, 0, 0}}, |
| 176 | {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, |
| 177 | {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, |
| 178 | {1, 0, 0, 0}}, |
| 179 | {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, |
| 180 | {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, |
| 181 | {1, 0, 0, 0}}, |
| 182 | {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, |
| 183 | {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, |
| 184 | {1, 0, 0, 0}}}}; |
| 185 | |
| 186 | /* Helper functions to convert field elements to/from internal representation */ |
| 187 | static void bin28_to_felem(felem out, const u8 in[28]) { |
| 188 | out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; |
| 189 | out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; |
| 190 | out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; |
| 191 | out[3] = (*((const uint64_t *)(in + 20))) >> 8; |
| 192 | } |
| 193 | |
| 194 | static void felem_to_bin28(u8 out[28], const felem in) { |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 195 | for (size_t i = 0; i < 7; ++i) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 196 | out[i] = in[0] >> (8 * i); |
| 197 | out[i + 7] = in[1] >> (8 * i); |
| 198 | out[i + 14] = in[2] >> (8 * i); |
| 199 | out[i + 21] = in[3] >> (8 * i); |
| 200 | } |
| 201 | } |
| 202 | |
| 203 | /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 204 | static void flip_endian(u8 *out, const u8 *in, size_t len) { |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 205 | for (size_t i = 0; i < len; ++i) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 206 | out[i] = in[len - 1 - i]; |
| 207 | } |
| 208 | } |
| 209 | |
| 210 | /* From OpenSSL BIGNUM to internal representation */ |
| 211 | static int BN_to_felem(felem out, const BIGNUM *bn) { |
| 212 | /* BN_bn2bin eats leading zeroes */ |
| 213 | felem_bytearray b_out; |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 214 | OPENSSL_memset(b_out, 0, sizeof(b_out)); |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 215 | size_t num_bytes = BN_num_bytes(bn); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 216 | if (num_bytes > sizeof(b_out) || |
| 217 | BN_is_negative(bn)) { |
| 218 | OPENSSL_PUT_ERROR(EC, EC_R_BIGNUM_OUT_OF_RANGE); |
| 219 | return 0; |
| 220 | } |
| 221 | |
| 222 | felem_bytearray b_in; |
| 223 | num_bytes = BN_bn2bin(bn, b_in); |
| 224 | flip_endian(b_out, b_in, num_bytes); |
| 225 | bin28_to_felem(out, b_out); |
| 226 | return 1; |
| 227 | } |
| 228 | |
| 229 | /* From internal representation to OpenSSL BIGNUM */ |
| 230 | static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) { |
| 231 | felem_bytearray b_in, b_out; |
| 232 | felem_to_bin28(b_in, in); |
| 233 | flip_endian(b_out, b_in, sizeof(b_out)); |
| 234 | return BN_bin2bn(b_out, sizeof(b_out), out); |
| 235 | } |
| 236 | |
| 237 | /* Field operations, using the internal representation of field elements. |
| 238 | * NB! These operations are specific to our point multiplication and cannot be |
| 239 | * expected to be correct in general - e.g., multiplication with a large scalar |
| 240 | * will cause an overflow. */ |
| 241 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 242 | static void felem_assign(felem out, const felem in) { |
| 243 | out[0] = in[0]; |
| 244 | out[1] = in[1]; |
| 245 | out[2] = in[2]; |
| 246 | out[3] = in[3]; |
| 247 | } |
| 248 | |
| 249 | /* Sum two field elements: out += in */ |
| 250 | static void felem_sum(felem out, const felem in) { |
| 251 | out[0] += in[0]; |
| 252 | out[1] += in[1]; |
| 253 | out[2] += in[2]; |
| 254 | out[3] += in[3]; |
| 255 | } |
| 256 | |
| 257 | /* Get negative value: out = -in */ |
| 258 | /* Assumes in[i] < 2^57 */ |
| 259 | static void felem_neg(felem out, const felem in) { |
| 260 | static const limb two58p2 = (((limb)1) << 58) + (((limb)1) << 2); |
| 261 | static const limb two58m2 = (((limb)1) << 58) - (((limb)1) << 2); |
| 262 | static const limb two58m42m2 = |
| 263 | (((limb)1) << 58) - (((limb)1) << 42) - (((limb)1) << 2); |
| 264 | |
| 265 | /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ |
| 266 | out[0] = two58p2 - in[0]; |
| 267 | out[1] = two58m42m2 - in[1]; |
| 268 | out[2] = two58m2 - in[2]; |
| 269 | out[3] = two58m2 - in[3]; |
| 270 | } |
| 271 | |
| 272 | /* Subtract field elements: out -= in */ |
| 273 | /* Assumes in[i] < 2^57 */ |
| 274 | static void felem_diff(felem out, const felem in) { |
| 275 | static const limb two58p2 = (((limb)1) << 58) + (((limb)1) << 2); |
| 276 | static const limb two58m2 = (((limb)1) << 58) - (((limb)1) << 2); |
| 277 | static const limb two58m42m2 = |
| 278 | (((limb)1) << 58) - (((limb)1) << 42) - (((limb)1) << 2); |
| 279 | |
| 280 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ |
| 281 | out[0] += two58p2; |
| 282 | out[1] += two58m42m2; |
| 283 | out[2] += two58m2; |
| 284 | out[3] += two58m2; |
| 285 | |
| 286 | out[0] -= in[0]; |
| 287 | out[1] -= in[1]; |
| 288 | out[2] -= in[2]; |
| 289 | out[3] -= in[3]; |
| 290 | } |
| 291 | |
| 292 | /* Subtract in unreduced 128-bit mode: out -= in */ |
| 293 | /* Assumes in[i] < 2^119 */ |
| 294 | static void widefelem_diff(widefelem out, const widefelem in) { |
| 295 | static const widelimb two120 = ((widelimb)1) << 120; |
| 296 | static const widelimb two120m64 = |
| 297 | (((widelimb)1) << 120) - (((widelimb)1) << 64); |
| 298 | static const widelimb two120m104m64 = |
| 299 | (((widelimb)1) << 120) - (((widelimb)1) << 104) - (((widelimb)1) << 64); |
| 300 | |
| 301 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ |
| 302 | out[0] += two120; |
| 303 | out[1] += two120m64; |
| 304 | out[2] += two120m64; |
| 305 | out[3] += two120; |
| 306 | out[4] += two120m104m64; |
| 307 | out[5] += two120m64; |
| 308 | out[6] += two120m64; |
| 309 | |
| 310 | out[0] -= in[0]; |
| 311 | out[1] -= in[1]; |
| 312 | out[2] -= in[2]; |
| 313 | out[3] -= in[3]; |
| 314 | out[4] -= in[4]; |
| 315 | out[5] -= in[5]; |
| 316 | out[6] -= in[6]; |
| 317 | } |
| 318 | |
| 319 | /* Subtract in mixed mode: out128 -= in64 */ |
| 320 | /* in[i] < 2^63 */ |
| 321 | static void felem_diff_128_64(widefelem out, const felem in) { |
| 322 | static const widelimb two64p8 = (((widelimb)1) << 64) + (((widelimb)1) << 8); |
| 323 | static const widelimb two64m8 = (((widelimb)1) << 64) - (((widelimb)1) << 8); |
| 324 | static const widelimb two64m48m8 = |
| 325 | (((widelimb)1) << 64) - (((widelimb)1) << 48) - (((widelimb)1) << 8); |
| 326 | |
| 327 | /* Add 0 mod 2^224-2^96+1 to ensure out > in */ |
| 328 | out[0] += two64p8; |
| 329 | out[1] += two64m48m8; |
| 330 | out[2] += two64m8; |
| 331 | out[3] += two64m8; |
| 332 | |
| 333 | out[0] -= in[0]; |
| 334 | out[1] -= in[1]; |
| 335 | out[2] -= in[2]; |
| 336 | out[3] -= in[3]; |
| 337 | } |
| 338 | |
| 339 | /* Multiply a field element by a scalar: out = out * scalar |
| 340 | * The scalars we actually use are small, so results fit without overflow */ |
| 341 | static void felem_scalar(felem out, const limb scalar) { |
| 342 | out[0] *= scalar; |
| 343 | out[1] *= scalar; |
| 344 | out[2] *= scalar; |
| 345 | out[3] *= scalar; |
| 346 | } |
| 347 | |
| 348 | /* Multiply an unreduced field element by a scalar: out = out * scalar |
| 349 | * The scalars we actually use are small, so results fit without overflow */ |
| 350 | static void widefelem_scalar(widefelem out, const widelimb scalar) { |
| 351 | out[0] *= scalar; |
| 352 | out[1] *= scalar; |
| 353 | out[2] *= scalar; |
| 354 | out[3] *= scalar; |
| 355 | out[4] *= scalar; |
| 356 | out[5] *= scalar; |
| 357 | out[6] *= scalar; |
| 358 | } |
| 359 | |
| 360 | /* Square a field element: out = in^2 */ |
| 361 | static void felem_square(widefelem out, const felem in) { |
| 362 | limb tmp0, tmp1, tmp2; |
| 363 | tmp0 = 2 * in[0]; |
| 364 | tmp1 = 2 * in[1]; |
| 365 | tmp2 = 2 * in[2]; |
| 366 | out[0] = ((widelimb)in[0]) * in[0]; |
| 367 | out[1] = ((widelimb)in[0]) * tmp1; |
| 368 | out[2] = ((widelimb)in[0]) * tmp2 + ((widelimb)in[1]) * in[1]; |
| 369 | out[3] = ((widelimb)in[3]) * tmp0 + ((widelimb)in[1]) * tmp2; |
| 370 | out[4] = ((widelimb)in[3]) * tmp1 + ((widelimb)in[2]) * in[2]; |
| 371 | out[5] = ((widelimb)in[3]) * tmp2; |
| 372 | out[6] = ((widelimb)in[3]) * in[3]; |
| 373 | } |
| 374 | |
| 375 | /* Multiply two field elements: out = in1 * in2 */ |
| 376 | static void felem_mul(widefelem out, const felem in1, const felem in2) { |
| 377 | out[0] = ((widelimb)in1[0]) * in2[0]; |
| 378 | out[1] = ((widelimb)in1[0]) * in2[1] + ((widelimb)in1[1]) * in2[0]; |
| 379 | out[2] = ((widelimb)in1[0]) * in2[2] + ((widelimb)in1[1]) * in2[1] + |
| 380 | ((widelimb)in1[2]) * in2[0]; |
| 381 | out[3] = ((widelimb)in1[0]) * in2[3] + ((widelimb)in1[1]) * in2[2] + |
| 382 | ((widelimb)in1[2]) * in2[1] + ((widelimb)in1[3]) * in2[0]; |
| 383 | out[4] = ((widelimb)in1[1]) * in2[3] + ((widelimb)in1[2]) * in2[2] + |
| 384 | ((widelimb)in1[3]) * in2[1]; |
| 385 | out[5] = ((widelimb)in1[2]) * in2[3] + ((widelimb)in1[3]) * in2[2]; |
| 386 | out[6] = ((widelimb)in1[3]) * in2[3]; |
| 387 | } |
| 388 | |
| 389 | /* Reduce seven 128-bit coefficients to four 64-bit coefficients. |
| 390 | * Requires in[i] < 2^126, |
| 391 | * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ |
| 392 | static void felem_reduce(felem out, const widefelem in) { |
| 393 | static const widelimb two127p15 = |
| 394 | (((widelimb)1) << 127) + (((widelimb)1) << 15); |
| 395 | static const widelimb two127m71 = |
| 396 | (((widelimb)1) << 127) - (((widelimb)1) << 71); |
| 397 | static const widelimb two127m71m55 = |
| 398 | (((widelimb)1) << 127) - (((widelimb)1) << 71) - (((widelimb)1) << 55); |
| 399 | widelimb output[5]; |
| 400 | |
| 401 | /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ |
| 402 | output[0] = in[0] + two127p15; |
| 403 | output[1] = in[1] + two127m71m55; |
| 404 | output[2] = in[2] + two127m71; |
| 405 | output[3] = in[3]; |
| 406 | output[4] = in[4]; |
| 407 | |
| 408 | /* Eliminate in[4], in[5], in[6] */ |
| 409 | output[4] += in[6] >> 16; |
| 410 | output[3] += (in[6] & 0xffff) << 40; |
| 411 | output[2] -= in[6]; |
| 412 | |
| 413 | output[3] += in[5] >> 16; |
| 414 | output[2] += (in[5] & 0xffff) << 40; |
| 415 | output[1] -= in[5]; |
| 416 | |
| 417 | output[2] += output[4] >> 16; |
| 418 | output[1] += (output[4] & 0xffff) << 40; |
| 419 | output[0] -= output[4]; |
| 420 | |
| 421 | /* Carry 2 -> 3 -> 4 */ |
| 422 | output[3] += output[2] >> 56; |
| 423 | output[2] &= 0x00ffffffffffffff; |
| 424 | |
| 425 | output[4] = output[3] >> 56; |
| 426 | output[3] &= 0x00ffffffffffffff; |
| 427 | |
| 428 | /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ |
| 429 | |
| 430 | /* Eliminate output[4] */ |
| 431 | output[2] += output[4] >> 16; |
| 432 | /* output[2] < 2^56 + 2^56 = 2^57 */ |
| 433 | output[1] += (output[4] & 0xffff) << 40; |
| 434 | output[0] -= output[4]; |
| 435 | |
| 436 | /* Carry 0 -> 1 -> 2 -> 3 */ |
| 437 | output[1] += output[0] >> 56; |
| 438 | out[0] = output[0] & 0x00ffffffffffffff; |
| 439 | |
| 440 | output[2] += output[1] >> 56; |
| 441 | /* output[2] < 2^57 + 2^72 */ |
| 442 | out[1] = output[1] & 0x00ffffffffffffff; |
| 443 | output[3] += output[2] >> 56; |
| 444 | /* output[3] <= 2^56 + 2^16 */ |
| 445 | out[2] = output[2] & 0x00ffffffffffffff; |
| 446 | |
| 447 | /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, |
| 448 | * out[3] <= 2^56 + 2^16 (due to final carry), |
| 449 | * so out < 2*p */ |
| 450 | out[3] = output[3]; |
| 451 | } |
| 452 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 453 | /* Reduce to unique minimal representation. |
| 454 | * Requires 0 <= in < 2*p (always call felem_reduce first) */ |
| 455 | static void felem_contract(felem out, const felem in) { |
| 456 | static const int64_t two56 = ((limb)1) << 56; |
| 457 | /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ |
| 458 | /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ |
| 459 | int64_t tmp[4], a; |
| 460 | tmp[0] = in[0]; |
| 461 | tmp[1] = in[1]; |
| 462 | tmp[2] = in[2]; |
| 463 | tmp[3] = in[3]; |
| 464 | /* Case 1: a = 1 iff in >= 2^224 */ |
| 465 | a = (in[3] >> 56); |
| 466 | tmp[0] -= a; |
| 467 | tmp[1] += a << 40; |
| 468 | tmp[3] &= 0x00ffffffffffffff; |
| 469 | /* Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 and |
| 470 | * the lower part is non-zero */ |
| 471 | a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | |
| 472 | (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); |
| 473 | a &= 0x00ffffffffffffff; |
| 474 | /* turn a into an all-one mask (if a = 0) or an all-zero mask */ |
| 475 | a = (a - 1) >> 63; |
| 476 | /* subtract 2^224 - 2^96 + 1 if a is all-one */ |
| 477 | tmp[3] &= a ^ 0xffffffffffffffff; |
| 478 | tmp[2] &= a ^ 0xffffffffffffffff; |
| 479 | tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; |
| 480 | tmp[0] -= 1 & a; |
| 481 | |
| 482 | /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must |
| 483 | * be non-zero, so we only need one step */ |
| 484 | a = tmp[0] >> 63; |
| 485 | tmp[0] += two56 & a; |
| 486 | tmp[1] -= 1 & a; |
| 487 | |
| 488 | /* carry 1 -> 2 -> 3 */ |
| 489 | tmp[2] += tmp[1] >> 56; |
| 490 | tmp[1] &= 0x00ffffffffffffff; |
| 491 | |
| 492 | tmp[3] += tmp[2] >> 56; |
| 493 | tmp[2] &= 0x00ffffffffffffff; |
| 494 | |
| 495 | /* Now 0 <= out < p */ |
| 496 | out[0] = tmp[0]; |
| 497 | out[1] = tmp[1]; |
| 498 | out[2] = tmp[2]; |
| 499 | out[3] = tmp[3]; |
| 500 | } |
| 501 | |
| 502 | /* Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field |
| 503 | * elements are reduced to in < 2^225, so we only need to check three cases: 0, |
| 504 | * 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 */ |
| 505 | static limb felem_is_zero(const felem in) { |
| 506 | limb zero = in[0] | in[1] | in[2] | in[3]; |
| 507 | zero = (((int64_t)(zero)-1) >> 63) & 1; |
| 508 | |
| 509 | limb two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) | |
| 510 | (in[2] ^ 0x00ffffffffffffff) | |
| 511 | (in[3] ^ 0x00ffffffffffffff); |
| 512 | two224m96p1 = (((int64_t)(two224m96p1)-1) >> 63) & 1; |
| 513 | limb two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) | |
| 514 | (in[2] ^ 0x00ffffffffffffff) | |
| 515 | (in[3] ^ 0x01ffffffffffffff); |
| 516 | two225m97p2 = (((int64_t)(two225m97p2)-1) >> 63) & 1; |
| 517 | return (zero | two224m96p1 | two225m97p2); |
| 518 | } |
| 519 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 520 | /* Invert a field element */ |
| 521 | /* Computation chain copied from djb's code */ |
| 522 | static void felem_inv(felem out, const felem in) { |
| 523 | felem ftmp, ftmp2, ftmp3, ftmp4; |
| 524 | widefelem tmp; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 525 | |
| 526 | felem_square(tmp, in); |
| 527 | felem_reduce(ftmp, tmp); /* 2 */ |
| 528 | felem_mul(tmp, in, ftmp); |
| 529 | felem_reduce(ftmp, tmp); /* 2^2 - 1 */ |
| 530 | felem_square(tmp, ftmp); |
| 531 | felem_reduce(ftmp, tmp); /* 2^3 - 2 */ |
| 532 | felem_mul(tmp, in, ftmp); |
| 533 | felem_reduce(ftmp, tmp); /* 2^3 - 1 */ |
| 534 | felem_square(tmp, ftmp); |
| 535 | felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ |
| 536 | felem_square(tmp, ftmp2); |
| 537 | felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ |
| 538 | felem_square(tmp, ftmp2); |
| 539 | felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ |
| 540 | felem_mul(tmp, ftmp2, ftmp); |
| 541 | felem_reduce(ftmp, tmp); /* 2^6 - 1 */ |
| 542 | felem_square(tmp, ftmp); |
| 543 | felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 544 | for (size_t i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 545 | felem_square(tmp, ftmp2); |
| 546 | felem_reduce(ftmp2, tmp); |
| 547 | } |
| 548 | felem_mul(tmp, ftmp2, ftmp); |
| 549 | felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ |
| 550 | felem_square(tmp, ftmp2); |
| 551 | felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 552 | for (size_t i = 0; i < 11; ++i) {/* 2^24 - 2^12 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 553 | felem_square(tmp, ftmp3); |
| 554 | felem_reduce(ftmp3, tmp); |
| 555 | } |
| 556 | felem_mul(tmp, ftmp3, ftmp2); |
| 557 | felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ |
| 558 | felem_square(tmp, ftmp2); |
| 559 | felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 560 | for (size_t i = 0; i < 23; ++i) {/* 2^48 - 2^24 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 561 | felem_square(tmp, ftmp3); |
| 562 | felem_reduce(ftmp3, tmp); |
| 563 | } |
| 564 | felem_mul(tmp, ftmp3, ftmp2); |
| 565 | felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ |
| 566 | felem_square(tmp, ftmp3); |
| 567 | felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 568 | for (size_t i = 0; i < 47; ++i) {/* 2^96 - 2^48 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 569 | felem_square(tmp, ftmp4); |
| 570 | felem_reduce(ftmp4, tmp); |
| 571 | } |
| 572 | felem_mul(tmp, ftmp3, ftmp4); |
| 573 | felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ |
| 574 | felem_square(tmp, ftmp3); |
| 575 | felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 576 | for (size_t i = 0; i < 23; ++i) {/* 2^120 - 2^24 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 577 | felem_square(tmp, ftmp4); |
| 578 | felem_reduce(ftmp4, tmp); |
| 579 | } |
| 580 | felem_mul(tmp, ftmp2, ftmp4); |
| 581 | felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 582 | for (size_t i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 583 | felem_square(tmp, ftmp2); |
| 584 | felem_reduce(ftmp2, tmp); |
| 585 | } |
| 586 | felem_mul(tmp, ftmp2, ftmp); |
| 587 | felem_reduce(ftmp, tmp); /* 2^126 - 1 */ |
| 588 | felem_square(tmp, ftmp); |
| 589 | felem_reduce(ftmp, tmp); /* 2^127 - 2 */ |
| 590 | felem_mul(tmp, ftmp, in); |
| 591 | felem_reduce(ftmp, tmp); /* 2^127 - 1 */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 592 | for (size_t i = 0; i < 97; ++i) {/* 2^224 - 2^97 */ |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 593 | felem_square(tmp, ftmp); |
| 594 | felem_reduce(ftmp, tmp); |
| 595 | } |
| 596 | felem_mul(tmp, ftmp, ftmp3); |
| 597 | felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ |
| 598 | } |
| 599 | |
| 600 | /* Copy in constant time: |
| 601 | * if icopy == 1, copy in to out, |
| 602 | * if icopy == 0, copy out to itself. */ |
| 603 | static void copy_conditional(felem out, const felem in, limb icopy) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 604 | /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ |
| 605 | const limb copy = -icopy; |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 606 | for (size_t i = 0; i < 4; ++i) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 607 | const limb tmp = copy & (in[i] ^ out[i]); |
| 608 | out[i] ^= tmp; |
| 609 | } |
| 610 | } |
| 611 | |
| 612 | /* ELLIPTIC CURVE POINT OPERATIONS |
| 613 | * |
| 614 | * Points are represented in Jacobian projective coordinates: |
| 615 | * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), |
| 616 | * or to the point at infinity if Z == 0. */ |
| 617 | |
| 618 | /* Double an elliptic curve point: |
| 619 | * (X', Y', Z') = 2 * (X, Y, Z), where |
| 620 | * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 |
| 621 | * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 |
| 622 | * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z |
| 623 | * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, |
| 624 | * while x_out == y_in is not (maybe this works, but it's not tested). */ |
| 625 | static void point_double(felem x_out, felem y_out, felem z_out, |
| 626 | const felem x_in, const felem y_in, const felem z_in) { |
| 627 | widefelem tmp, tmp2; |
| 628 | felem delta, gamma, beta, alpha, ftmp, ftmp2; |
| 629 | |
| 630 | felem_assign(ftmp, x_in); |
| 631 | felem_assign(ftmp2, x_in); |
| 632 | |
| 633 | /* delta = z^2 */ |
| 634 | felem_square(tmp, z_in); |
| 635 | felem_reduce(delta, tmp); |
| 636 | |
| 637 | /* gamma = y^2 */ |
| 638 | felem_square(tmp, y_in); |
| 639 | felem_reduce(gamma, tmp); |
| 640 | |
| 641 | /* beta = x*gamma */ |
| 642 | felem_mul(tmp, x_in, gamma); |
| 643 | felem_reduce(beta, tmp); |
| 644 | |
| 645 | /* alpha = 3*(x-delta)*(x+delta) */ |
| 646 | felem_diff(ftmp, delta); |
| 647 | /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ |
| 648 | felem_sum(ftmp2, delta); |
| 649 | /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ |
| 650 | felem_scalar(ftmp2, 3); |
| 651 | /* ftmp2[i] < 3 * 2^58 < 2^60 */ |
| 652 | felem_mul(tmp, ftmp, ftmp2); |
| 653 | /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ |
| 654 | felem_reduce(alpha, tmp); |
| 655 | |
| 656 | /* x' = alpha^2 - 8*beta */ |
| 657 | felem_square(tmp, alpha); |
| 658 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
| 659 | felem_assign(ftmp, beta); |
| 660 | felem_scalar(ftmp, 8); |
| 661 | /* ftmp[i] < 8 * 2^57 = 2^60 */ |
| 662 | felem_diff_128_64(tmp, ftmp); |
| 663 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
| 664 | felem_reduce(x_out, tmp); |
| 665 | |
| 666 | /* z' = (y + z)^2 - gamma - delta */ |
| 667 | felem_sum(delta, gamma); |
| 668 | /* delta[i] < 2^57 + 2^57 = 2^58 */ |
| 669 | felem_assign(ftmp, y_in); |
| 670 | felem_sum(ftmp, z_in); |
| 671 | /* ftmp[i] < 2^57 + 2^57 = 2^58 */ |
| 672 | felem_square(tmp, ftmp); |
| 673 | /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ |
| 674 | felem_diff_128_64(tmp, delta); |
| 675 | /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ |
| 676 | felem_reduce(z_out, tmp); |
| 677 | |
| 678 | /* y' = alpha*(4*beta - x') - 8*gamma^2 */ |
| 679 | felem_scalar(beta, 4); |
| 680 | /* beta[i] < 4 * 2^57 = 2^59 */ |
| 681 | felem_diff(beta, x_out); |
| 682 | /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ |
| 683 | felem_mul(tmp, alpha, beta); |
| 684 | /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ |
| 685 | felem_square(tmp2, gamma); |
| 686 | /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ |
| 687 | widefelem_scalar(tmp2, 8); |
| 688 | /* tmp2[i] < 8 * 2^116 = 2^119 */ |
| 689 | widefelem_diff(tmp, tmp2); |
| 690 | /* tmp[i] < 2^119 + 2^120 < 2^121 */ |
| 691 | felem_reduce(y_out, tmp); |
| 692 | } |
| 693 | |
| 694 | /* Add two elliptic curve points: |
| 695 | * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where |
| 696 | * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - |
| 697 | * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 |
| 698 | * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * |
| 699 | * X_1)^2 - X_3) - |
| 700 | * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 |
| 701 | * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) |
| 702 | * |
| 703 | * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. */ |
| 704 | |
| 705 | /* This function is not entirely constant-time: it includes a branch for |
| 706 | * checking whether the two input points are equal, (while not equal to the |
| 707 | * point at infinity). This case never happens during single point |
| 708 | * multiplication, so there is no timing leak for ECDH or ECDSA signing. */ |
| 709 | static void point_add(felem x3, felem y3, felem z3, const felem x1, |
| 710 | const felem y1, const felem z1, const int mixed, |
| 711 | const felem x2, const felem y2, const felem z2) { |
| 712 | felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; |
| 713 | widefelem tmp, tmp2; |
| 714 | limb z1_is_zero, z2_is_zero, x_equal, y_equal; |
| 715 | |
| 716 | if (!mixed) { |
| 717 | /* ftmp2 = z2^2 */ |
| 718 | felem_square(tmp, z2); |
| 719 | felem_reduce(ftmp2, tmp); |
| 720 | |
| 721 | /* ftmp4 = z2^3 */ |
| 722 | felem_mul(tmp, ftmp2, z2); |
| 723 | felem_reduce(ftmp4, tmp); |
| 724 | |
| 725 | /* ftmp4 = z2^3*y1 */ |
| 726 | felem_mul(tmp2, ftmp4, y1); |
| 727 | felem_reduce(ftmp4, tmp2); |
| 728 | |
| 729 | /* ftmp2 = z2^2*x1 */ |
| 730 | felem_mul(tmp2, ftmp2, x1); |
| 731 | felem_reduce(ftmp2, tmp2); |
| 732 | } else { |
| 733 | /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ |
| 734 | |
| 735 | /* ftmp4 = z2^3*y1 */ |
| 736 | felem_assign(ftmp4, y1); |
| 737 | |
| 738 | /* ftmp2 = z2^2*x1 */ |
| 739 | felem_assign(ftmp2, x1); |
| 740 | } |
| 741 | |
| 742 | /* ftmp = z1^2 */ |
| 743 | felem_square(tmp, z1); |
| 744 | felem_reduce(ftmp, tmp); |
| 745 | |
| 746 | /* ftmp3 = z1^3 */ |
| 747 | felem_mul(tmp, ftmp, z1); |
| 748 | felem_reduce(ftmp3, tmp); |
| 749 | |
| 750 | /* tmp = z1^3*y2 */ |
| 751 | felem_mul(tmp, ftmp3, y2); |
| 752 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
| 753 | |
| 754 | /* ftmp3 = z1^3*y2 - z2^3*y1 */ |
| 755 | felem_diff_128_64(tmp, ftmp4); |
| 756 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
| 757 | felem_reduce(ftmp3, tmp); |
| 758 | |
| 759 | /* tmp = z1^2*x2 */ |
| 760 | felem_mul(tmp, ftmp, x2); |
| 761 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
| 762 | |
| 763 | /* ftmp = z1^2*x2 - z2^2*x1 */ |
| 764 | felem_diff_128_64(tmp, ftmp2); |
| 765 | /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ |
| 766 | felem_reduce(ftmp, tmp); |
| 767 | |
| 768 | /* the formulae are incorrect if the points are equal |
| 769 | * so we check for this and do doubling if this happens */ |
| 770 | x_equal = felem_is_zero(ftmp); |
| 771 | y_equal = felem_is_zero(ftmp3); |
| 772 | z1_is_zero = felem_is_zero(z1); |
| 773 | z2_is_zero = felem_is_zero(z2); |
| 774 | /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ |
| 775 | if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { |
| 776 | point_double(x3, y3, z3, x1, y1, z1); |
| 777 | return; |
| 778 | } |
| 779 | |
| 780 | /* ftmp5 = z1*z2 */ |
| 781 | if (!mixed) { |
| 782 | felem_mul(tmp, z1, z2); |
| 783 | felem_reduce(ftmp5, tmp); |
| 784 | } else { |
| 785 | /* special case z2 = 0 is handled later */ |
| 786 | felem_assign(ftmp5, z1); |
| 787 | } |
| 788 | |
| 789 | /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ |
| 790 | felem_mul(tmp, ftmp, ftmp5); |
| 791 | felem_reduce(z_out, tmp); |
| 792 | |
| 793 | /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ |
| 794 | felem_assign(ftmp5, ftmp); |
| 795 | felem_square(tmp, ftmp); |
| 796 | felem_reduce(ftmp, tmp); |
| 797 | |
| 798 | /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ |
| 799 | felem_mul(tmp, ftmp, ftmp5); |
| 800 | felem_reduce(ftmp5, tmp); |
| 801 | |
| 802 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
| 803 | felem_mul(tmp, ftmp2, ftmp); |
| 804 | felem_reduce(ftmp2, tmp); |
| 805 | |
| 806 | /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ |
| 807 | felem_mul(tmp, ftmp4, ftmp5); |
| 808 | /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ |
| 809 | |
| 810 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ |
| 811 | felem_square(tmp2, ftmp3); |
| 812 | /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ |
| 813 | |
| 814 | /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ |
| 815 | felem_diff_128_64(tmp2, ftmp5); |
| 816 | /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ |
| 817 | |
| 818 | /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
| 819 | felem_assign(ftmp5, ftmp2); |
| 820 | felem_scalar(ftmp5, 2); |
| 821 | /* ftmp5[i] < 2 * 2^57 = 2^58 */ |
| 822 | |
| 823 | /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - |
| 824 | 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
| 825 | felem_diff_128_64(tmp2, ftmp5); |
| 826 | /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ |
| 827 | felem_reduce(x_out, tmp2); |
| 828 | |
| 829 | /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ |
| 830 | felem_diff(ftmp2, x_out); |
| 831 | /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ |
| 832 | |
| 833 | /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */ |
| 834 | felem_mul(tmp2, ftmp3, ftmp2); |
| 835 | /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ |
| 836 | |
| 837 | /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - |
| 838 | z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ |
| 839 | widefelem_diff(tmp2, tmp); |
| 840 | /* tmp2[i] < 2^118 + 2^120 < 2^121 */ |
| 841 | felem_reduce(y_out, tmp2); |
| 842 | |
| 843 | /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is |
| 844 | * the point at infinity, so we need to check for this separately */ |
| 845 | |
| 846 | /* if point 1 is at infinity, copy point 2 to output, and vice versa */ |
| 847 | copy_conditional(x_out, x2, z1_is_zero); |
| 848 | copy_conditional(x_out, x1, z2_is_zero); |
| 849 | copy_conditional(y_out, y2, z1_is_zero); |
| 850 | copy_conditional(y_out, y1, z2_is_zero); |
| 851 | copy_conditional(z_out, z2, z1_is_zero); |
| 852 | copy_conditional(z_out, z1, z2_is_zero); |
| 853 | felem_assign(x3, x_out); |
| 854 | felem_assign(y3, y_out); |
| 855 | felem_assign(z3, z_out); |
| 856 | } |
| 857 | |
| 858 | /* select_point selects the |idx|th point from a precomputation table and |
| 859 | * copies it to out. */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 860 | static void select_point(const u64 idx, size_t size, |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 861 | const felem pre_comp[/*size*/][3], felem out[3]) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 862 | limb *outlimbs = &out[0][0]; |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 863 | OPENSSL_memset(outlimbs, 0, 3 * sizeof(felem)); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 864 | |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 865 | for (size_t i = 0; i < size; i++) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 866 | const limb *inlimbs = &pre_comp[i][0][0]; |
| 867 | u64 mask = i ^ idx; |
| 868 | mask |= mask >> 4; |
| 869 | mask |= mask >> 2; |
| 870 | mask |= mask >> 1; |
| 871 | mask &= 1; |
| 872 | mask--; |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 873 | for (size_t j = 0; j < 4 * 3; j++) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 874 | outlimbs[j] |= inlimbs[j] & mask; |
| 875 | } |
| 876 | } |
| 877 | } |
| 878 | |
| 879 | /* get_bit returns the |i|th bit in |in| */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 880 | static char get_bit(const felem_bytearray in, size_t i) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 881 | if (i >= 224) { |
| 882 | return 0; |
| 883 | } |
| 884 | return (in[i >> 3] >> (i & 7)) & 1; |
| 885 | } |
| 886 | |
| 887 | /* Interleaved point multiplication using precomputed point multiples: |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 888 | * The small point multiples 0*P, 1*P, ..., 16*P are in p_pre_comp, the scalars |
| 889 | * in p_scalar, if non-NULL. If g_scalar is non-NULL, we also add this multiple |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 890 | * of the generator, using certain (large) precomputed multiples in g_pre_comp. |
| 891 | * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 892 | static void batch_mul(felem x_out, felem y_out, felem z_out, const u8 *p_scalar, |
| 893 | const u8 *g_scalar, const felem p_pre_comp[17][3]) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 894 | felem nq[3], tmp[4]; |
| 895 | u64 bits; |
| 896 | u8 sign, digit; |
| 897 | |
| 898 | /* set nq to the point at infinity */ |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 899 | OPENSSL_memset(nq, 0, 3 * sizeof(felem)); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 900 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 901 | /* Loop over both scalars msb-to-lsb, interleaving additions of multiples of |
| 902 | * the generator (two in each of the last 28 rounds) and additions of p (every |
| 903 | * 5th round). */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 904 | int skip = 1; /* save two point operations in the first round */ |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 905 | size_t i = p_scalar != NULL ? 220 : 27; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 906 | for (;;) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 907 | /* double */ |
| 908 | if (!skip) { |
| 909 | point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
| 910 | } |
| 911 | |
| 912 | /* add multiples of the generator */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 913 | if (g_scalar != NULL && i <= 27) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 914 | /* first, look 28 bits upwards */ |
| 915 | bits = get_bit(g_scalar, i + 196) << 3; |
| 916 | bits |= get_bit(g_scalar, i + 140) << 2; |
| 917 | bits |= get_bit(g_scalar, i + 84) << 1; |
| 918 | bits |= get_bit(g_scalar, i + 28); |
| 919 | /* select the point to add, in constant time */ |
| 920 | select_point(bits, 16, g_pre_comp[1], tmp); |
| 921 | |
| 922 | if (!skip) { |
| 923 | point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, |
| 924 | tmp[0], tmp[1], tmp[2]); |
| 925 | } else { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 926 | OPENSSL_memcpy(nq, tmp, 3 * sizeof(felem)); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 927 | skip = 0; |
| 928 | } |
| 929 | |
| 930 | /* second, look at the current position */ |
| 931 | bits = get_bit(g_scalar, i + 168) << 3; |
| 932 | bits |= get_bit(g_scalar, i + 112) << 2; |
| 933 | bits |= get_bit(g_scalar, i + 56) << 1; |
| 934 | bits |= get_bit(g_scalar, i); |
| 935 | /* select the point to add, in constant time */ |
| 936 | select_point(bits, 16, g_pre_comp[0], tmp); |
| 937 | point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0], |
| 938 | tmp[1], tmp[2]); |
| 939 | } |
| 940 | |
| 941 | /* do other additions every 5 doublings */ |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 942 | if (p_scalar != NULL && i % 5 == 0) { |
| 943 | bits = get_bit(p_scalar, i + 4) << 5; |
| 944 | bits |= get_bit(p_scalar, i + 3) << 4; |
| 945 | bits |= get_bit(p_scalar, i + 2) << 3; |
| 946 | bits |= get_bit(p_scalar, i + 1) << 2; |
| 947 | bits |= get_bit(p_scalar, i) << 1; |
| 948 | bits |= get_bit(p_scalar, i - 1); |
| 949 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 950 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 951 | /* select the point to add or subtract */ |
| 952 | select_point(digit, 17, p_pre_comp, tmp); |
| 953 | felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ |
| 954 | copy_conditional(tmp[1], tmp[3], sign); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 955 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 956 | if (!skip) { |
| 957 | point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, |
| 958 | tmp[0], tmp[1], tmp[2]); |
| 959 | } else { |
| 960 | OPENSSL_memcpy(nq, tmp, 3 * sizeof(felem)); |
| 961 | skip = 0; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 962 | } |
| 963 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 964 | |
| 965 | if (i == 0) { |
| 966 | break; |
| 967 | } |
| 968 | --i; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 969 | } |
| 970 | felem_assign(x_out, nq[0]); |
| 971 | felem_assign(y_out, nq[1]); |
| 972 | felem_assign(z_out, nq[2]); |
| 973 | } |
| 974 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 975 | /* Takes the Jacobian coordinates (X, Y, Z) of a point and returns |
| 976 | * (X', Y') = (X/Z^2, Y/Z^3) */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 977 | static int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, |
| 978 | const EC_POINT *point, |
| 979 | BIGNUM *x, BIGNUM *y, |
| 980 | BN_CTX *ctx) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 981 | felem z1, z2, x_in, y_in, x_out, y_out; |
| 982 | widefelem tmp; |
| 983 | |
| 984 | if (EC_POINT_is_at_infinity(group, point)) { |
| 985 | OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); |
| 986 | return 0; |
| 987 | } |
| 988 | |
| 989 | if (!BN_to_felem(x_in, &point->X) || |
| 990 | !BN_to_felem(y_in, &point->Y) || |
| 991 | !BN_to_felem(z1, &point->Z)) { |
| 992 | return 0; |
| 993 | } |
| 994 | |
| 995 | felem_inv(z2, z1); |
| 996 | felem_square(tmp, z2); |
| 997 | felem_reduce(z1, tmp); |
| 998 | felem_mul(tmp, x_in, z1); |
| 999 | felem_reduce(x_in, tmp); |
| 1000 | felem_contract(x_out, x_in); |
| 1001 | if (x != NULL && !felem_to_BN(x, x_out)) { |
| 1002 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 1003 | return 0; |
| 1004 | } |
| 1005 | |
| 1006 | felem_mul(tmp, z1, z2); |
| 1007 | felem_reduce(z1, tmp); |
| 1008 | felem_mul(tmp, y_in, z1); |
| 1009 | felem_reduce(y_in, tmp); |
| 1010 | felem_contract(y_out, y_in); |
| 1011 | if (y != NULL && !felem_to_BN(y, y_out)) { |
| 1012 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 1013 | return 0; |
| 1014 | } |
| 1015 | |
| 1016 | return 1; |
| 1017 | } |
| 1018 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1019 | static int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, |
| 1020 | const BIGNUM *g_scalar, const EC_POINT *p, |
| 1021 | const BIGNUM *p_scalar, BN_CTX *ctx) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1022 | int ret = 0; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1023 | BN_CTX *new_ctx = NULL; |
| 1024 | BIGNUM *x, *y, *z, *tmp_scalar; |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1025 | felem_bytearray g_secret, p_secret; |
| 1026 | felem p_pre_comp[17][3]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1027 | felem_bytearray tmp; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1028 | felem x_in, y_in, z_in, x_out, y_out, z_out; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1029 | |
| 1030 | if (ctx == NULL) { |
| 1031 | ctx = BN_CTX_new(); |
| 1032 | new_ctx = ctx; |
| 1033 | if (ctx == NULL) { |
| 1034 | return 0; |
| 1035 | } |
| 1036 | } |
| 1037 | |
| 1038 | BN_CTX_start(ctx); |
| 1039 | if ((x = BN_CTX_get(ctx)) == NULL || |
| 1040 | (y = BN_CTX_get(ctx)) == NULL || |
| 1041 | (z = BN_CTX_get(ctx)) == NULL || |
| 1042 | (tmp_scalar = BN_CTX_get(ctx)) == NULL) { |
| 1043 | goto err; |
| 1044 | } |
| 1045 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1046 | if (p != NULL && p_scalar != NULL) { |
| 1047 | /* We treat NULL scalars as 0, and NULL points as points at infinity, i.e., |
| 1048 | * they contribute nothing to the linear combination. */ |
| 1049 | OPENSSL_memset(&p_secret, 0, sizeof(p_secret)); |
| 1050 | OPENSSL_memset(&p_pre_comp, 0, sizeof(p_pre_comp)); |
| 1051 | size_t num_bytes; |
| 1052 | /* reduce g_scalar to 0 <= g_scalar < 2^224 */ |
| 1053 | if (BN_num_bits(p_scalar) > 224 || BN_is_negative(p_scalar)) { |
| 1054 | /* this is an unusual input, and we don't guarantee |
| 1055 | * constant-timeness */ |
| 1056 | if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { |
| 1057 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 1058 | goto err; |
| 1059 | } |
| 1060 | num_bytes = BN_bn2bin(tmp_scalar, tmp); |
| 1061 | } else { |
| 1062 | num_bytes = BN_bn2bin(p_scalar, tmp); |
| 1063 | } |
| 1064 | |
| 1065 | flip_endian(p_secret, tmp, num_bytes); |
| 1066 | /* precompute multiples */ |
| 1067 | if (!BN_to_felem(x_out, &p->X) || |
| 1068 | !BN_to_felem(y_out, &p->Y) || |
| 1069 | !BN_to_felem(z_out, &p->Z)) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1070 | goto err; |
| 1071 | } |
| 1072 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1073 | felem_assign(p_pre_comp[1][0], x_out); |
| 1074 | felem_assign(p_pre_comp[1][1], y_out); |
| 1075 | felem_assign(p_pre_comp[1][2], z_out); |
| 1076 | |
| 1077 | for (size_t j = 2; j <= 16; ++j) { |
| 1078 | if (j & 1) { |
| 1079 | point_add(p_pre_comp[j][0], p_pre_comp[j][1], p_pre_comp[j][2], |
| 1080 | p_pre_comp[1][0], p_pre_comp[1][1], p_pre_comp[1][2], |
| 1081 | 0, p_pre_comp[j - 1][0], p_pre_comp[j - 1][1], |
| 1082 | p_pre_comp[j - 1][2]); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1083 | } else { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1084 | point_double(p_pre_comp[j][0], p_pre_comp[j][1], |
| 1085 | p_pre_comp[j][2], p_pre_comp[j / 2][0], |
| 1086 | p_pre_comp[j / 2][1], p_pre_comp[j / 2][2]); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1087 | } |
| 1088 | } |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1089 | } |
| 1090 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 1091 | if (g_scalar != NULL) { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1092 | OPENSSL_memset(g_secret, 0, sizeof(g_secret)); |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1093 | size_t num_bytes; |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 1094 | /* reduce g_scalar to 0 <= g_scalar < 2^224 */ |
| 1095 | if (BN_num_bits(g_scalar) > 224 || BN_is_negative(g_scalar)) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1096 | /* this is an unusual input, and we don't guarantee constant-timeness */ |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 1097 | if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1098 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 1099 | goto err; |
| 1100 | } |
| 1101 | num_bytes = BN_bn2bin(tmp_scalar, tmp); |
| 1102 | } else { |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 1103 | num_bytes = BN_bn2bin(g_scalar, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1104 | } |
| 1105 | |
| 1106 | flip_endian(g_secret, tmp, num_bytes); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1107 | } |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 1108 | batch_mul(x_out, y_out, z_out, |
| 1109 | (p != NULL && p_scalar != NULL) ? p_secret : NULL, |
| 1110 | g_scalar != NULL ? g_secret : NULL, (const felem(*)[3])p_pre_comp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1111 | |
| 1112 | /* reduce the output to its unique minimal representation */ |
| 1113 | felem_contract(x_in, x_out); |
| 1114 | felem_contract(y_in, y_out); |
| 1115 | felem_contract(z_in, z_out); |
| 1116 | if (!felem_to_BN(x, x_in) || |
| 1117 | !felem_to_BN(y, y_in) || |
| 1118 | !felem_to_BN(z, z_in)) { |
| 1119 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 1120 | goto err; |
| 1121 | } |
| 1122 | ret = ec_point_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); |
| 1123 | |
| 1124 | err: |
| 1125 | BN_CTX_end(ctx); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1126 | BN_CTX_free(new_ctx); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1127 | return ret; |
| 1128 | } |
| 1129 | |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 1130 | const EC_METHOD EC_GFp_nistp224_method = { |
| 1131 | ec_GFp_simple_group_init, |
| 1132 | ec_GFp_simple_group_finish, |
| 1133 | ec_GFp_simple_group_copy, |
| 1134 | ec_GFp_simple_group_set_curve, |
| 1135 | ec_GFp_nistp224_point_get_affine_coordinates, |
| 1136 | ec_GFp_nistp224_points_mul, |
| 1137 | ec_GFp_simple_field_mul, |
| 1138 | ec_GFp_simple_field_sqr, |
| 1139 | NULL /* field_encode */, |
| 1140 | NULL /* field_decode */, |
| 1141 | }; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1142 | |
| 1143 | #endif /* 64_BIT && !WINDOWS && !SMALL */ |