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| 1 /* crypto/ec/ec2_mult.c */ | |
| 2 /* ==================================================================== | |
| 3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
| 4 * | |
| 5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included | |
| 6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed | |
| 7 * to the OpenSSL project. | |
| 8 * | |
| 9 * The ECC Code is licensed pursuant to the OpenSSL open source | |
| 10 * license provided below. | |
| 11 * | |
| 12 * The software is originally written by Sheueling Chang Shantz and | |
| 13 * Douglas Stebila of Sun Microsystems Laboratories. | |
| 14 * | |
| 15 */ | |
| 16 /* ==================================================================== | |
| 17 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. | |
| 18 * | |
| 19 * Redistribution and use in source and binary forms, with or without | |
| 20 * modification, are permitted provided that the following conditions | |
| 21 * are met: | |
| 22 * | |
| 23 * 1. Redistributions of source code must retain the above copyright | |
| 24 * notice, this list of conditions and the following disclaimer. | |
| 25 * | |
| 26 * 2. Redistributions in binary form must reproduce the above copyright | |
| 27 * notice, this list of conditions and the following disclaimer in | |
| 28 * the documentation and/or other materials provided with the | |
| 29 * distribution. | |
| 30 * | |
| 31 * 3. All advertising materials mentioning features or use of this | |
| 32 * software must display the following acknowledgment: | |
| 33 * "This product includes software developed by the OpenSSL Project | |
| 34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
| 35 * | |
| 36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
| 37 * endorse or promote products derived from this software without | |
| 38 * prior written permission. For written permission, please contact | |
| 39 * openssl-core@openssl.org. | |
| 40 * | |
| 41 * 5. Products derived from this software may not be called "OpenSSL" | |
| 42 * nor may "OpenSSL" appear in their names without prior written | |
| 43 * permission of the OpenSSL Project. | |
| 44 * | |
| 45 * 6. Redistributions of any form whatsoever must retain the following | |
| 46 * acknowledgment: | |
| 47 * "This product includes software developed by the OpenSSL Project | |
| 48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
| 49 * | |
| 50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
| 51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
| 52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
| 53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
| 54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
| 55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
| 56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
| 57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
| 58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
| 59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
| 60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
| 61 * OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 62 * ==================================================================== | |
| 63 * | |
| 64 * This product includes cryptographic software written by Eric Young | |
| 65 * (eay@cryptsoft.com). This product includes software written by Tim | |
| 66 * Hudson (tjh@cryptsoft.com). | |
| 67 * | |
| 68 */ | |
| 69 | |
| 70 #include <openssl/err.h> | |
| 71 | |
| 72 #include "ec_lcl.h" | |
| 73 | |
| 74 #ifndef OPENSSL_NO_EC2M | |
| 75 | |
| 76 | |
| 77 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective | |
| 78 * coordinates. | |
| 79 * Uses algorithm Mdouble in appendix of | |
| 80 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over | |
| 81 * GF(2^m) without precomputation" (CHES '99, LNCS 1717). | |
| 82 * modified to not require precomputation of c=b^{2^{m-1}}. | |
| 83 */ | |
| 84 static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx
) | |
| 85 { | |
| 86 BIGNUM *t1; | |
| 87 int ret = 0; | |
| 88 | |
| 89 /* Since Mdouble is static we can guarantee that ctx != NULL. */ | |
| 90 BN_CTX_start(ctx); | |
| 91 t1 = BN_CTX_get(ctx); | |
| 92 if (t1 == NULL) goto err; | |
| 93 | |
| 94 if (!group->meth->field_sqr(group, x, x, ctx)) goto err; | |
| 95 if (!group->meth->field_sqr(group, t1, z, ctx)) goto err; | |
| 96 if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err; | |
| 97 if (!group->meth->field_sqr(group, x, x, ctx)) goto err; | |
| 98 if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err; | |
| 99 if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err; | |
| 100 if (!BN_GF2m_add(x, x, t1)) goto err; | |
| 101 | |
| 102 ret = 1; | |
| 103 | |
| 104 err: | |
| 105 BN_CTX_end(ctx); | |
| 106 return ret; | |
| 107 } | |
| 108 | |
| 109 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery | |
| 110 * projective coordinates. | |
| 111 * Uses algorithm Madd in appendix of | |
| 112 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over | |
| 113 * GF(2^m) without precomputation" (CHES '99, LNCS 1717). | |
| 114 */ | |
| 115 static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM
*z1, | |
| 116 const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) | |
| 117 { | |
| 118 BIGNUM *t1, *t2; | |
| 119 int ret = 0; | |
| 120 | |
| 121 /* Since Madd is static we can guarantee that ctx != NULL. */ | |
| 122 BN_CTX_start(ctx); | |
| 123 t1 = BN_CTX_get(ctx); | |
| 124 t2 = BN_CTX_get(ctx); | |
| 125 if (t2 == NULL) goto err; | |
| 126 | |
| 127 if (!BN_copy(t1, x)) goto err; | |
| 128 if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err; | |
| 129 if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err; | |
| 130 if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err; | |
| 131 if (!BN_GF2m_add(z1, z1, x1)) goto err; | |
| 132 if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err; | |
| 133 if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err; | |
| 134 if (!BN_GF2m_add(x1, x1, t2)) goto err; | |
| 135 | |
| 136 ret = 1; | |
| 137 | |
| 138 err: | |
| 139 BN_CTX_end(ctx); | |
| 140 return ret; | |
| 141 } | |
| 142 | |
| 143 /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) | |
| 144 * using Montgomery point multiplication algorithm Mxy() in appendix of | |
| 145 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over | |
| 146 * GF(2^m) without precomputation" (CHES '99, LNCS 1717). | |
| 147 * Returns: | |
| 148 * 0 on error | |
| 149 * 1 if return value should be the point at infinity | |
| 150 * 2 otherwise | |
| 151 */ | |
| 152 static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIG
NUM *x1, | |
| 153 BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) | |
| 154 { | |
| 155 BIGNUM *t3, *t4, *t5; | |
| 156 int ret = 0; | |
| 157 | |
| 158 if (BN_is_zero(z1)) | |
| 159 { | |
| 160 BN_zero(x2); | |
| 161 BN_zero(z2); | |
| 162 return 1; | |
| 163 } | |
| 164 | |
| 165 if (BN_is_zero(z2)) | |
| 166 { | |
| 167 if (!BN_copy(x2, x)) return 0; | |
| 168 if (!BN_GF2m_add(z2, x, y)) return 0; | |
| 169 return 2; | |
| 170 } | |
| 171 | |
| 172 /* Since Mxy is static we can guarantee that ctx != NULL. */ | |
| 173 BN_CTX_start(ctx); | |
| 174 t3 = BN_CTX_get(ctx); | |
| 175 t4 = BN_CTX_get(ctx); | |
| 176 t5 = BN_CTX_get(ctx); | |
| 177 if (t5 == NULL) goto err; | |
| 178 | |
| 179 if (!BN_one(t5)) goto err; | |
| 180 | |
| 181 if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err; | |
| 182 | |
| 183 if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err; | |
| 184 if (!BN_GF2m_add(z1, z1, x1)) goto err; | |
| 185 if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err; | |
| 186 if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err; | |
| 187 if (!BN_GF2m_add(z2, z2, x2)) goto err; | |
| 188 | |
| 189 if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err; | |
| 190 if (!group->meth->field_sqr(group, t4, x, ctx)) goto err; | |
| 191 if (!BN_GF2m_add(t4, t4, y)) goto err; | |
| 192 if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err; | |
| 193 if (!BN_GF2m_add(t4, t4, z2)) goto err; | |
| 194 | |
| 195 if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err; | |
| 196 if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err; | |
| 197 if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err; | |
| 198 if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err; | |
| 199 if (!BN_GF2m_add(z2, x2, x)) goto err; | |
| 200 | |
| 201 if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err; | |
| 202 if (!BN_GF2m_add(z2, z2, y)) goto err; | |
| 203 | |
| 204 ret = 2; | |
| 205 | |
| 206 err: | |
| 207 BN_CTX_end(ctx); | |
| 208 return ret; | |
| 209 } | |
| 210 | |
| 211 /* Computes scalar*point and stores the result in r. | |
| 212 * point can not equal r. | |
| 213 * Uses algorithm 2P of | |
| 214 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over | |
| 215 * GF(2^m) without precomputation" (CHES '99, LNCS 1717). | |
| 216 */ | |
| 217 static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
const BIGNUM *scalar, | |
| 218 const EC_POINT *point, BN_CTX *ctx) | |
| 219 { | |
| 220 BIGNUM *x1, *x2, *z1, *z2; | |
| 221 int ret = 0, i; | |
| 222 BN_ULONG mask,word; | |
| 223 | |
| 224 if (r == point) | |
| 225 { | |
| 226 ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUM
ENT); | |
| 227 return 0; | |
| 228 } | |
| 229 | |
| 230 /* if result should be point at infinity */ | |
| 231 if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || | |
| 232 EC_POINT_is_at_infinity(group, point)) | |
| 233 { | |
| 234 return EC_POINT_set_to_infinity(group, r); | |
| 235 } | |
| 236 | |
| 237 /* only support affine coordinates */ | |
| 238 if (!point->Z_is_one) return 0; | |
| 239 | |
| 240 /* Since point_multiply is static we can guarantee that ctx != NULL. */ | |
| 241 BN_CTX_start(ctx); | |
| 242 x1 = BN_CTX_get(ctx); | |
| 243 z1 = BN_CTX_get(ctx); | |
| 244 if (z1 == NULL) goto err; | |
| 245 | |
| 246 x2 = &r->X; | |
| 247 z2 = &r->Y; | |
| 248 | |
| 249 if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ | |
| 250 if (!BN_one(z1)) goto err; /* z1 = 1 */ | |
| 251 if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2
= x^2 */ | |
| 252 if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err; | |
| 253 if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ | |
| 254 | |
| 255 /* find top most bit and go one past it */ | |
| 256 i = scalar->top - 1; | |
| 257 mask = BN_TBIT; | |
| 258 word = scalar->d[i]; | |
| 259 while (!(word & mask)) mask >>= 1; | |
| 260 mask >>= 1; | |
| 261 /* if top most bit was at word break, go to next word */ | |
| 262 if (!mask) | |
| 263 { | |
| 264 i--; | |
| 265 mask = BN_TBIT; | |
| 266 } | |
| 267 | |
| 268 for (; i >= 0; i--) | |
| 269 { | |
| 270 word = scalar->d[i]; | |
| 271 while (mask) | |
| 272 { | |
| 273 if (word & mask) | |
| 274 { | |
| 275 if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2,
ctx)) goto err; | |
| 276 if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err; | |
| 277 } | |
| 278 else | |
| 279 { | |
| 280 if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1,
ctx)) goto err; | |
| 281 if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; | |
| 282 } | |
| 283 mask >>= 1; | |
| 284 } | |
| 285 mask = BN_TBIT; | |
| 286 } | |
| 287 | |
| 288 /* convert out of "projective" coordinates */ | |
| 289 i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); | |
| 290 if (i == 0) goto err; | |
| 291 else if (i == 1) | |
| 292 { | |
| 293 if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
| 294 } | |
| 295 else | |
| 296 { | |
| 297 if (!BN_one(&r->Z)) goto err; | |
| 298 r->Z_is_one = 1; | |
| 299 } | |
| 300 | |
| 301 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ | |
| 302 BN_set_negative(&r->X, 0); | |
| 303 BN_set_negative(&r->Y, 0); | |
| 304 | |
| 305 ret = 1; | |
| 306 | |
| 307 err: | |
| 308 BN_CTX_end(ctx); | |
| 309 return ret; | |
| 310 } | |
| 311 | |
| 312 | |
| 313 /* Computes the sum | |
| 314 * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*poi
nts[num-1] | |
| 315 * gracefully ignoring NULL scalar values. | |
| 316 */ | |
| 317 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, | |
| 318 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *c
tx) | |
| 319 { | |
| 320 BN_CTX *new_ctx = NULL; | |
| 321 int ret = 0; | |
| 322 size_t i; | |
| 323 EC_POINT *p=NULL; | |
| 324 EC_POINT *acc = NULL; | |
| 325 | |
| 326 if (ctx == NULL) | |
| 327 { | |
| 328 ctx = new_ctx = BN_CTX_new(); | |
| 329 if (ctx == NULL) | |
| 330 return 0; | |
| 331 } | |
| 332 | |
| 333 /* This implementation is more efficient than the wNAF implementation fo
r 2 | |
| 334 * or fewer points. Use the ec_wNAF_mul implementation for 3 or more po
ints, | |
| 335 * or if we can perform a fast multiplication based on precomputation. | |
| 336 */ | |
| 337 if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_pre
compute_mult(group))) | |
| 338 { | |
| 339 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); | |
| 340 goto err; | |
| 341 } | |
| 342 | |
| 343 if ((p = EC_POINT_new(group)) == NULL) goto err; | |
| 344 if ((acc = EC_POINT_new(group)) == NULL) goto err; | |
| 345 | |
| 346 if (!EC_POINT_set_to_infinity(group, acc)) goto err; | |
| 347 | |
| 348 if (scalar) | |
| 349 { | |
| 350 if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->
generator, ctx)) goto err; | |
| 351 if (BN_is_negative(scalar)) | |
| 352 if (!group->meth->invert(group, p, ctx)) goto err; | |
| 353 if (!group->meth->add(group, acc, acc, p, ctx)) goto err; | |
| 354 } | |
| 355 | |
| 356 for (i = 0; i < num; i++) | |
| 357 { | |
| 358 if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], poi
nts[i], ctx)) goto err; | |
| 359 if (BN_is_negative(scalars[i])) | |
| 360 if (!group->meth->invert(group, p, ctx)) goto err; | |
| 361 if (!group->meth->add(group, acc, acc, p, ctx)) goto err; | |
| 362 } | |
| 363 | |
| 364 if (!EC_POINT_copy(r, acc)) goto err; | |
| 365 | |
| 366 ret = 1; | |
| 367 | |
| 368 err: | |
| 369 if (p) EC_POINT_free(p); | |
| 370 if (acc) EC_POINT_free(acc); | |
| 371 if (new_ctx != NULL) | |
| 372 BN_CTX_free(new_ctx); | |
| 373 return ret; | |
| 374 } | |
| 375 | |
| 376 | |
| 377 /* Precomputation for point multiplication: fall back to wNAF methods | |
| 378 * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ | |
| 379 | |
| 380 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) | |
| 381 { | |
| 382 return ec_wNAF_precompute_mult(group, ctx); | |
| 383 } | |
| 384 | |
| 385 int ec_GF2m_have_precompute_mult(const EC_GROUP *group) | |
| 386 { | |
| 387 return ec_wNAF_have_precompute_mult(group); | |
| 388 } | |
| 389 | |
| 390 #endif | |
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Chromium Code Reviews
Issue 2072073002:
Delete bundled copy of OpenSSL and replace with README. (Closed)
Base URL: https://chromium.googlesource.com/chromium/deps/openssl@master