Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 1 | /* Copyright (c) 2014, Intel Corporation. |
| 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 | /* Developers and authors: |
| 16 | * Shay Gueron (1, 2), and Vlad Krasnov (1) |
| 17 | * (1) Intel Corporation, Israel Development Center |
| 18 | * (2) University of Haifa |
| 19 | * Reference: |
| 20 | * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with |
| 21 | * 256 Bit Primes" */ |
| 22 | |
| 23 | #include <openssl/ec.h> |
| 24 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 25 | #include <assert.h> |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 26 | #include <stdint.h> |
| 27 | #include <string.h> |
| 28 | |
| 29 | #include <openssl/bn.h> |
| 30 | #include <openssl/crypto.h> |
| 31 | #include <openssl/err.h> |
| 32 | |
| 33 | #include "../bn/internal.h" |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame^] | 34 | #include "../delocate.h" |
| 35 | #include "../../internal.h" |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 36 | #include "internal.h" |
| 37 | #include "p256-x86_64.h" |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 38 | |
| 39 | |
| 40 | #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \ |
| 41 | !defined(OPENSSL_SMALL) |
| 42 | |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 43 | typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; |
| 44 | |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 45 | /* One converted into the Montgomery domain */ |
| 46 | static const BN_ULONG ONE[P256_LIMBS] = { |
| 47 | TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), |
| 48 | TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe), |
| 49 | }; |
| 50 | |
| 51 | /* Precomputed tables for the default generator */ |
| 52 | #include "p256-x86_64-table.h" |
| 53 | |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 54 | /* Recode window to a signed digit, see util-64.c for details */ |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 55 | static unsigned booth_recode_w5(unsigned in) { |
| 56 | unsigned s, d; |
| 57 | |
| 58 | s = ~((in >> 5) - 1); |
| 59 | d = (1 << 6) - in - 1; |
| 60 | d = (d & s) | (in & ~s); |
| 61 | d = (d >> 1) + (d & 1); |
| 62 | |
| 63 | return (d << 1) + (s & 1); |
| 64 | } |
| 65 | |
| 66 | static unsigned booth_recode_w7(unsigned in) { |
| 67 | unsigned s, d; |
| 68 | |
| 69 | s = ~((in >> 7) - 1); |
| 70 | d = (1 << 8) - in - 1; |
| 71 | d = (d & s) | (in & ~s); |
| 72 | d = (d >> 1) + (d & 1); |
| 73 | |
| 74 | return (d << 1) + (s & 1); |
| 75 | } |
| 76 | |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 77 | /* copy_conditional copies |src| to |dst| if |move| is one and leaves it as-is |
| 78 | * if |move| is zero. |
| 79 | * |
| 80 | * WARNING: this breaks the usual convention of constant-time functions |
| 81 | * returning masks. */ |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 82 | static void copy_conditional(BN_ULONG dst[P256_LIMBS], |
| 83 | const BN_ULONG src[P256_LIMBS], BN_ULONG move) { |
| 84 | BN_ULONG mask1 = ((BN_ULONG)0) - move; |
| 85 | BN_ULONG mask2 = ~mask1; |
| 86 | |
| 87 | dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); |
| 88 | dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); |
| 89 | dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); |
| 90 | dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); |
| 91 | if (P256_LIMBS == 8) { |
| 92 | dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); |
| 93 | dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); |
| 94 | dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); |
| 95 | dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); |
| 96 | } |
| 97 | } |
| 98 | |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 99 | /* is_not_zero returns one iff in != 0 and zero otherwise. |
| 100 | * |
| 101 | * WARNING: this breaks the usual convention of constant-time functions |
| 102 | * returning masks. |
| 103 | * |
| 104 | * (define-fun is_not_zero ((in (_ BitVec 64))) (_ BitVec 64) |
| 105 | * (bvlshr (bvor in (bvsub #x0000000000000000 in)) #x000000000000003f) |
| 106 | * ) |
| 107 | * |
| 108 | * (declare-fun x () (_ BitVec 64)) |
| 109 | * |
| 110 | * (assert (and (= x #x0000000000000000) (= (is_not_zero x) #x0000000000000001))) |
| 111 | * (check-sat) |
| 112 | * |
| 113 | * (assert (and (not (= x #x0000000000000000)) (= (is_not_zero x) #x0000000000000000))) |
| 114 | * (check-sat) |
| 115 | * */ |
| 116 | static BN_ULONG is_not_zero(BN_ULONG in) { |
| 117 | in |= (0 - in); |
| 118 | in >>= BN_BITS2 - 1; |
| 119 | return in; |
| 120 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 121 | |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 122 | /* ecp_nistz256_mod_inverse_mont sets |r| to (|in| * 2^-256)^-1 * 2^256 mod p. |
| 123 | * That is, |r| is the modular inverse of |in| for input and output in the |
| 124 | * Montgomery domain. */ |
| 125 | static void ecp_nistz256_mod_inverse_mont(BN_ULONG r[P256_LIMBS], |
| 126 | const BN_ULONG in[P256_LIMBS]) { |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 127 | /* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff |
| 128 | ffffffff |
| 129 | We use FLT and used poly-2 as exponent */ |
| 130 | BN_ULONG p2[P256_LIMBS]; |
| 131 | BN_ULONG p4[P256_LIMBS]; |
| 132 | BN_ULONG p8[P256_LIMBS]; |
| 133 | BN_ULONG p16[P256_LIMBS]; |
| 134 | BN_ULONG p32[P256_LIMBS]; |
| 135 | BN_ULONG res[P256_LIMBS]; |
| 136 | int i; |
| 137 | |
| 138 | ecp_nistz256_sqr_mont(res, in); |
| 139 | ecp_nistz256_mul_mont(p2, res, in); /* 3*p */ |
| 140 | |
| 141 | ecp_nistz256_sqr_mont(res, p2); |
| 142 | ecp_nistz256_sqr_mont(res, res); |
| 143 | ecp_nistz256_mul_mont(p4, res, p2); /* f*p */ |
| 144 | |
| 145 | ecp_nistz256_sqr_mont(res, p4); |
| 146 | ecp_nistz256_sqr_mont(res, res); |
| 147 | ecp_nistz256_sqr_mont(res, res); |
| 148 | ecp_nistz256_sqr_mont(res, res); |
| 149 | ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */ |
| 150 | |
| 151 | ecp_nistz256_sqr_mont(res, p8); |
| 152 | for (i = 0; i < 7; i++) { |
| 153 | ecp_nistz256_sqr_mont(res, res); |
| 154 | } |
| 155 | ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */ |
| 156 | |
| 157 | ecp_nistz256_sqr_mont(res, p16); |
| 158 | for (i = 0; i < 15; i++) { |
| 159 | ecp_nistz256_sqr_mont(res, res); |
| 160 | } |
| 161 | ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */ |
| 162 | |
| 163 | ecp_nistz256_sqr_mont(res, p32); |
| 164 | for (i = 0; i < 31; i++) { |
| 165 | ecp_nistz256_sqr_mont(res, res); |
| 166 | } |
| 167 | ecp_nistz256_mul_mont(res, res, in); |
| 168 | |
| 169 | for (i = 0; i < 32 * 4; i++) { |
| 170 | ecp_nistz256_sqr_mont(res, res); |
| 171 | } |
| 172 | ecp_nistz256_mul_mont(res, res, p32); |
| 173 | |
| 174 | for (i = 0; i < 32; i++) { |
| 175 | ecp_nistz256_sqr_mont(res, res); |
| 176 | } |
| 177 | ecp_nistz256_mul_mont(res, res, p32); |
| 178 | |
| 179 | for (i = 0; i < 16; i++) { |
| 180 | ecp_nistz256_sqr_mont(res, res); |
| 181 | } |
| 182 | ecp_nistz256_mul_mont(res, res, p16); |
| 183 | |
| 184 | for (i = 0; i < 8; i++) { |
| 185 | ecp_nistz256_sqr_mont(res, res); |
| 186 | } |
| 187 | ecp_nistz256_mul_mont(res, res, p8); |
| 188 | |
| 189 | ecp_nistz256_sqr_mont(res, res); |
| 190 | ecp_nistz256_sqr_mont(res, res); |
| 191 | ecp_nistz256_sqr_mont(res, res); |
| 192 | ecp_nistz256_sqr_mont(res, res); |
| 193 | ecp_nistz256_mul_mont(res, res, p4); |
| 194 | |
| 195 | ecp_nistz256_sqr_mont(res, res); |
| 196 | ecp_nistz256_sqr_mont(res, res); |
| 197 | ecp_nistz256_mul_mont(res, res, p2); |
| 198 | |
| 199 | ecp_nistz256_sqr_mont(res, res); |
| 200 | ecp_nistz256_sqr_mont(res, res); |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 201 | ecp_nistz256_mul_mont(r, res, in); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 202 | } |
| 203 | |
| 204 | /* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and |
| 205 | * returns one if it fits. Otherwise it returns zero. */ |
| 206 | static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], |
| 207 | const BIGNUM *in) { |
| 208 | if (in->top > P256_LIMBS) { |
| 209 | return 0; |
| 210 | } |
| 211 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 212 | OPENSSL_memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS); |
| 213 | OPENSSL_memcpy(out, in->d, sizeof(BN_ULONG) * in->top); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 214 | return 1; |
| 215 | } |
| 216 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 217 | /* r = p * p_scalar */ |
| 218 | static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r, |
| 219 | const EC_POINT *p, const BIGNUM *p_scalar, |
| 220 | BN_CTX *ctx) { |
| 221 | assert(p != NULL); |
| 222 | assert(p_scalar != NULL); |
| 223 | |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 224 | static const unsigned kWindowSize = 5; |
| 225 | static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1; |
| 226 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 227 | /* A |P256_POINT| is (3 * 32) = 96 bytes, and the 64-byte alignment should |
| 228 | * add no more than 63 bytes of overhead. Thus, |table| should require |
| 229 | * ~1599 ((96 * 16) + 63) bytes of stack space. */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 230 | alignas(64) P256_POINT table[16]; |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 231 | uint8_t p_str[33]; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 232 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 233 | |
| 234 | int ret = 0; |
| 235 | BN_CTX *new_ctx = NULL; |
| 236 | int ctx_started = 0; |
| 237 | |
| 238 | if (BN_num_bits(p_scalar) > 256 || BN_is_negative(p_scalar)) { |
| 239 | if (ctx == NULL) { |
| 240 | new_ctx = BN_CTX_new(); |
| 241 | if (new_ctx == NULL) { |
| 242 | OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| 243 | goto err; |
| 244 | } |
| 245 | ctx = new_ctx; |
| 246 | } |
| 247 | BN_CTX_start(ctx); |
| 248 | ctx_started = 1; |
| 249 | BIGNUM *mod = BN_CTX_get(ctx); |
| 250 | if (mod == NULL) { |
| 251 | OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| 252 | goto err; |
| 253 | } |
| 254 | if (!BN_nnmod(mod, p_scalar, &group->order, ctx)) { |
| 255 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 256 | goto err; |
| 257 | } |
| 258 | p_scalar = mod; |
| 259 | } |
| 260 | |
| 261 | int j; |
| 262 | for (j = 0; j < p_scalar->top * BN_BYTES; j += BN_BYTES) { |
| 263 | BN_ULONG d = p_scalar->d[j / BN_BYTES]; |
| 264 | |
| 265 | p_str[j + 0] = d & 0xff; |
| 266 | p_str[j + 1] = (d >> 8) & 0xff; |
| 267 | p_str[j + 2] = (d >> 16) & 0xff; |
| 268 | p_str[j + 3] = (d >>= 24) & 0xff; |
| 269 | if (BN_BYTES == 8) { |
| 270 | d >>= 8; |
| 271 | p_str[j + 4] = d & 0xff; |
| 272 | p_str[j + 5] = (d >> 8) & 0xff; |
| 273 | p_str[j + 6] = (d >> 16) & 0xff; |
| 274 | p_str[j + 7] = (d >> 24) & 0xff; |
| 275 | } |
| 276 | } |
| 277 | |
| 278 | for (; j < 33; j++) { |
| 279 | p_str[j] = 0; |
| 280 | } |
| 281 | |
| 282 | /* table[0] is implicitly (0,0,0) (the point at infinity), therefore it is |
| 283 | * not stored. All other values are actually stored with an offset of -1 in |
| 284 | * table. */ |
| 285 | P256_POINT *row = table; |
| 286 | |
| 287 | if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &p->X) || |
| 288 | !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &p->Y) || |
| 289 | !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &p->Z)) { |
| 290 | OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 291 | goto err; |
| 292 | } |
| 293 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 294 | ecp_nistz256_point_double(&row[2 - 1], &row[1 - 1]); |
| 295 | ecp_nistz256_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]); |
| 296 | ecp_nistz256_point_double(&row[4 - 1], &row[2 - 1]); |
| 297 | ecp_nistz256_point_double(&row[6 - 1], &row[3 - 1]); |
| 298 | ecp_nistz256_point_double(&row[8 - 1], &row[4 - 1]); |
| 299 | ecp_nistz256_point_double(&row[12 - 1], &row[6 - 1]); |
| 300 | ecp_nistz256_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]); |
| 301 | ecp_nistz256_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]); |
| 302 | ecp_nistz256_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]); |
| 303 | ecp_nistz256_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]); |
| 304 | ecp_nistz256_point_double(&row[14 - 1], &row[7 - 1]); |
| 305 | ecp_nistz256_point_double(&row[10 - 1], &row[5 - 1]); |
| 306 | ecp_nistz256_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]); |
| 307 | ecp_nistz256_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]); |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 308 | ecp_nistz256_point_double(&row[16 - 1], &row[8 - 1]); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 309 | |
| 310 | BN_ULONG tmp[P256_LIMBS]; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 311 | alignas(32) P256_POINT h; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 312 | unsigned index = 255; |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 313 | unsigned wvalue = p_str[(index - 1) / 8]; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 314 | wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| 315 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 316 | ecp_nistz256_select_w5(r, table, booth_recode_w5(wvalue) >> 1); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 317 | |
| 318 | while (index >= 5) { |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 319 | if (index != 255) { |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 320 | unsigned off = (index - 1) / 8; |
| 321 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 322 | wvalue = p_str[off] | p_str[off + 1] << 8; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 323 | wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| 324 | |
| 325 | wvalue = booth_recode_w5(wvalue); |
| 326 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 327 | ecp_nistz256_select_w5(&h, table, wvalue >> 1); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 328 | |
| 329 | ecp_nistz256_neg(tmp, h.Y); |
| 330 | copy_conditional(h.Y, tmp, (wvalue & 1)); |
| 331 | |
| 332 | ecp_nistz256_point_add(r, r, &h); |
| 333 | } |
| 334 | |
| 335 | index -= kWindowSize; |
| 336 | |
| 337 | ecp_nistz256_point_double(r, r); |
| 338 | ecp_nistz256_point_double(r, r); |
| 339 | ecp_nistz256_point_double(r, r); |
| 340 | ecp_nistz256_point_double(r, r); |
| 341 | ecp_nistz256_point_double(r, r); |
| 342 | } |
| 343 | |
| 344 | /* Final window */ |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 345 | wvalue = p_str[0]; |
| 346 | wvalue = (wvalue << 1) & kMask; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 347 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 348 | wvalue = booth_recode_w5(wvalue); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 349 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 350 | ecp_nistz256_select_w5(&h, table, wvalue >> 1); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 351 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 352 | ecp_nistz256_neg(tmp, h.Y); |
| 353 | copy_conditional(h.Y, tmp, wvalue & 1); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 354 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 355 | ecp_nistz256_point_add(r, r, &h); |
| 356 | |
| 357 | ret = 1; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 358 | |
| 359 | err: |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 360 | if (ctx_started) { |
| 361 | BN_CTX_end(ctx); |
| 362 | } |
| 363 | BN_CTX_free(new_ctx); |
| 364 | return ret; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 365 | } |
| 366 | |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 367 | static int ecp_nistz256_points_mul( |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 368 | const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, |
| 369 | const EC_POINT *p_, const BIGNUM *p_scalar, BN_CTX *ctx) { |
| 370 | assert((p_ != NULL) == (p_scalar != NULL)); |
| 371 | |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 372 | static const unsigned kWindowSize = 7; |
| 373 | static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1; |
| 374 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 375 | alignas(32) union { |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 376 | P256_POINT p; |
| 377 | P256_POINT_AFFINE a; |
| 378 | } t, p; |
| 379 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 380 | int ret = 0; |
| 381 | BN_CTX *new_ctx = NULL; |
| 382 | int ctx_started = 0; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 383 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 384 | if (g_scalar != NULL) { |
| 385 | if (BN_num_bits(g_scalar) > 256 || BN_is_negative(g_scalar)) { |
| 386 | if (ctx == NULL) { |
| 387 | new_ctx = BN_CTX_new(); |
| 388 | if (new_ctx == NULL) { |
| 389 | goto err; |
| 390 | } |
| 391 | ctx = new_ctx; |
| 392 | } |
| 393 | BN_CTX_start(ctx); |
| 394 | ctx_started = 1; |
| 395 | BIGNUM *tmp_scalar = BN_CTX_get(ctx); |
| 396 | if (tmp_scalar == NULL) { |
| 397 | goto err; |
| 398 | } |
| 399 | |
| 400 | if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) { |
| 401 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| 402 | goto err; |
| 403 | } |
| 404 | g_scalar = tmp_scalar; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 405 | } |
| 406 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 407 | uint8_t p_str[33] = {0}; |
| 408 | int i; |
| 409 | for (i = 0; i < g_scalar->top * BN_BYTES; i += BN_BYTES) { |
| 410 | BN_ULONG d = g_scalar->d[i / BN_BYTES]; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 411 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 412 | p_str[i + 0] = d & 0xff; |
| 413 | p_str[i + 1] = (d >> 8) & 0xff; |
| 414 | p_str[i + 2] = (d >> 16) & 0xff; |
| 415 | p_str[i + 3] = (d >>= 24) & 0xff; |
| 416 | if (BN_BYTES == 8) { |
| 417 | d >>= 8; |
| 418 | p_str[i + 4] = d & 0xff; |
| 419 | p_str[i + 5] = (d >> 8) & 0xff; |
| 420 | p_str[i + 6] = (d >> 16) & 0xff; |
| 421 | p_str[i + 7] = (d >> 24) & 0xff; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 422 | } |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 423 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 424 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 425 | for (; i < (int) sizeof(p_str); i++) { |
| 426 | p_str[i] = 0; |
| 427 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 428 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 429 | /* First window */ |
| 430 | unsigned wvalue = (p_str[0] << 1) & kMask; |
| 431 | unsigned index = kWindowSize; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 432 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 433 | wvalue = booth_recode_w7(wvalue); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 434 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 435 | const PRECOMP256_ROW *const precomputed_table = |
| 436 | (const PRECOMP256_ROW *)ecp_nistz256_precomputed; |
| 437 | ecp_nistz256_select_w7(&p.a, precomputed_table[0], wvalue >> 1); |
| 438 | |
| 439 | ecp_nistz256_neg(p.p.Z, p.p.Y); |
| 440 | copy_conditional(p.p.Y, p.p.Z, wvalue & 1); |
| 441 | |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 442 | /* Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p| |
| 443 | * is infinity and |ONE| otherwise. |p| was computed from the table, so it |
| 444 | * is infinity iff |wvalue >> 1| is zero. */ |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 445 | OPENSSL_memset(p.p.Z, 0, sizeof(p.p.Z)); |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 446 | copy_conditional(p.p.Z, ONE, is_not_zero(wvalue >> 1)); |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 447 | |
| 448 | for (i = 1; i < 37; i++) { |
| 449 | unsigned off = (index - 1) / 8; |
| 450 | wvalue = p_str[off] | p_str[off + 1] << 8; |
| 451 | wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| 452 | index += kWindowSize; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 453 | |
| 454 | wvalue = booth_recode_w7(wvalue); |
| 455 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 456 | ecp_nistz256_select_w7(&t.a, precomputed_table[i], wvalue >> 1); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 457 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 458 | ecp_nistz256_neg(t.p.Z, t.a.Y); |
| 459 | copy_conditional(t.a.Y, t.p.Z, wvalue & 1); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 460 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 461 | ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 462 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 463 | } |
| 464 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 465 | const int p_is_infinity = g_scalar == NULL; |
| 466 | if (p_scalar != NULL) { |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 467 | P256_POINT *out = &t.p; |
| 468 | if (p_is_infinity) { |
| 469 | out = &p.p; |
| 470 | } |
| 471 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 472 | if (!ecp_nistz256_windowed_mul(group, out, p_, p_scalar, ctx)) { |
| 473 | goto err; |
| 474 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 475 | |
| 476 | if (!p_is_infinity) { |
| 477 | ecp_nistz256_point_add(&p.p, &p.p, out); |
| 478 | } |
| 479 | } |
| 480 | |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 481 | /* Not constant-time, but we're only operating on the public output. */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 482 | if (!bn_set_words(&r->X, p.p.X, P256_LIMBS) || |
| 483 | !bn_set_words(&r->Y, p.p.Y, P256_LIMBS) || |
| 484 | !bn_set_words(&r->Z, p.p.Z, P256_LIMBS)) { |
| 485 | return 0; |
| 486 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 487 | |
| 488 | ret = 1; |
| 489 | |
| 490 | err: |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 491 | if (ctx_started) { |
| 492 | BN_CTX_end(ctx); |
| 493 | } |
| 494 | BN_CTX_free(new_ctx); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 495 | return ret; |
| 496 | } |
| 497 | |
| 498 | static int ecp_nistz256_get_affine(const EC_GROUP *group, const EC_POINT *point, |
| 499 | BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { |
| 500 | BN_ULONG z_inv2[P256_LIMBS]; |
| 501 | BN_ULONG z_inv3[P256_LIMBS]; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 502 | BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS]; |
| 503 | |
| 504 | if (EC_POINT_is_at_infinity(group, point)) { |
| 505 | OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); |
| 506 | return 0; |
| 507 | } |
| 508 | |
| 509 | if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) || |
| 510 | !ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) || |
| 511 | !ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) { |
| 512 | OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE); |
| 513 | return 0; |
| 514 | } |
| 515 | |
Steven Valdez | 909b19f | 2016-11-21 15:35:44 -0500 | [diff] [blame] | 516 | ecp_nistz256_mod_inverse_mont(z_inv3, point_z); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 517 | ecp_nistz256_sqr_mont(z_inv2, z_inv3); |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 518 | |
Steven Valdez | b0b45c6 | 2017-01-17 16:23:54 -0500 | [diff] [blame] | 519 | /* Instead of using |ecp_nistz256_from_mont| to convert the |x| coordinate |
| 520 | * and then calling |ecp_nistz256_from_mont| again to convert the |y| |
| 521 | * coordinate below, convert the common factor |z_inv2| once now, saving one |
| 522 | * reduction. */ |
| 523 | ecp_nistz256_from_mont(z_inv2, z_inv2); |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 524 | |
| 525 | if (x != NULL) { |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 526 | BN_ULONG x_aff[P256_LIMBS]; |
| 527 | ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 528 | if (!bn_set_words(x, x_aff, P256_LIMBS)) { |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 529 | OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| 530 | return 0; |
| 531 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 532 | } |
| 533 | |
| 534 | if (y != NULL) { |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 535 | BN_ULONG y_aff[P256_LIMBS]; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 536 | ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 537 | ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 538 | if (!bn_set_words(y, y_aff, P256_LIMBS)) { |
Adam Langley | 4139edb | 2016-01-13 15:00:54 -0800 | [diff] [blame] | 539 | OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| 540 | return 0; |
| 541 | } |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 542 | } |
| 543 | |
| 544 | return 1; |
| 545 | } |
| 546 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame^] | 547 | DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistz256_method) { |
| 548 | out->group_init = ec_GFp_mont_group_init; |
| 549 | out->group_finish = ec_GFp_mont_group_finish; |
| 550 | out->group_copy = ec_GFp_mont_group_copy; |
| 551 | out->group_set_curve = ec_GFp_mont_group_set_curve; |
| 552 | out->point_get_affine_coordinates = ecp_nistz256_get_affine; |
| 553 | out->mul = ecp_nistz256_points_mul; |
| 554 | out->field_mul = ec_GFp_mont_field_mul; |
| 555 | out->field_sqr = ec_GFp_mont_field_sqr; |
| 556 | out->field_encode = ec_GFp_mont_field_encode; |
| 557 | out->field_decode = ec_GFp_mont_field_decode; |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 558 | }; |
Adam Langley | fad6327 | 2015-11-12 12:15:39 -0800 | [diff] [blame] | 559 | |
| 560 | #endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \ |
| 561 | !defined(OPENSSL_SMALL) */ |