Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 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 | |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 74 | |
| 75 | /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective |
| 76 | * coordinates. |
| 77 | * Uses algorithm Mdouble in appendix of |
| 78 | * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| 79 | * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| 80 | * modified to not require precomputation of c=b^{2^{m-1}}. |
| 81 | */ |
| 82 | static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) |
| 83 | { |
| 84 | BIGNUM *t1; |
| 85 | int ret = 0; |
| 86 | |
| 87 | /* Since Mdouble is static we can guarantee that ctx != NULL. */ |
| 88 | BN_CTX_start(ctx); |
| 89 | t1 = BN_CTX_get(ctx); |
| 90 | if (t1 == NULL) goto err; |
| 91 | |
| 92 | if (!group->meth->field_sqr(group, x, x, ctx)) goto err; |
| 93 | if (!group->meth->field_sqr(group, t1, z, ctx)) goto err; |
| 94 | if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err; |
| 95 | if (!group->meth->field_sqr(group, x, x, ctx)) goto err; |
| 96 | if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err; |
| 97 | if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err; |
| 98 | if (!BN_GF2m_add(x, x, t1)) goto err; |
| 99 | |
| 100 | ret = 1; |
| 101 | |
| 102 | err: |
| 103 | BN_CTX_end(ctx); |
| 104 | return ret; |
| 105 | } |
| 106 | |
| 107 | /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery |
| 108 | * projective coordinates. |
| 109 | * Uses algorithm Madd in appendix of |
| 110 | * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| 111 | * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| 112 | */ |
| 113 | static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, |
| 114 | const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) |
| 115 | { |
| 116 | BIGNUM *t1, *t2; |
| 117 | int ret = 0; |
| 118 | |
| 119 | /* Since Madd is static we can guarantee that ctx != NULL. */ |
| 120 | BN_CTX_start(ctx); |
| 121 | t1 = BN_CTX_get(ctx); |
| 122 | t2 = BN_CTX_get(ctx); |
| 123 | if (t2 == NULL) goto err; |
| 124 | |
| 125 | if (!BN_copy(t1, x)) goto err; |
| 126 | if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err; |
| 127 | if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err; |
| 128 | if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err; |
| 129 | if (!BN_GF2m_add(z1, z1, x1)) goto err; |
| 130 | if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err; |
| 131 | if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err; |
| 132 | if (!BN_GF2m_add(x1, x1, t2)) goto err; |
| 133 | |
| 134 | ret = 1; |
| 135 | |
| 136 | err: |
| 137 | BN_CTX_end(ctx); |
| 138 | return ret; |
| 139 | } |
| 140 | |
| 141 | /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) |
| 142 | * using Montgomery point multiplication algorithm Mxy() in appendix of |
| 143 | * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| 144 | * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| 145 | * Returns: |
| 146 | * 0 on error |
| 147 | * 1 if return value should be the point at infinity |
| 148 | * 2 otherwise |
| 149 | */ |
| 150 | static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, |
| 151 | BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) |
| 152 | { |
| 153 | BIGNUM *t3, *t4, *t5; |
| 154 | int ret = 0; |
| 155 | |
| 156 | if (BN_is_zero(z1)) |
| 157 | { |
| 158 | BN_zero(x2); |
| 159 | BN_zero(z2); |
| 160 | return 1; |
| 161 | } |
| 162 | |
| 163 | if (BN_is_zero(z2)) |
| 164 | { |
| 165 | if (!BN_copy(x2, x)) return 0; |
| 166 | if (!BN_GF2m_add(z2, x, y)) return 0; |
| 167 | return 2; |
| 168 | } |
| 169 | |
| 170 | /* Since Mxy is static we can guarantee that ctx != NULL. */ |
| 171 | BN_CTX_start(ctx); |
| 172 | t3 = BN_CTX_get(ctx); |
| 173 | t4 = BN_CTX_get(ctx); |
| 174 | t5 = BN_CTX_get(ctx); |
| 175 | if (t5 == NULL) goto err; |
| 176 | |
| 177 | if (!BN_one(t5)) goto err; |
| 178 | |
| 179 | if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err; |
| 180 | |
| 181 | if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err; |
| 182 | if (!BN_GF2m_add(z1, z1, x1)) goto err; |
| 183 | if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err; |
| 184 | if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err; |
| 185 | if (!BN_GF2m_add(z2, z2, x2)) goto err; |
| 186 | |
| 187 | if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err; |
| 188 | if (!group->meth->field_sqr(group, t4, x, ctx)) goto err; |
| 189 | if (!BN_GF2m_add(t4, t4, y)) goto err; |
| 190 | if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err; |
| 191 | if (!BN_GF2m_add(t4, t4, z2)) goto err; |
| 192 | |
| 193 | if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err; |
| 194 | if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err; |
| 195 | if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err; |
| 196 | if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err; |
| 197 | if (!BN_GF2m_add(z2, x2, x)) goto err; |
| 198 | |
| 199 | if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err; |
| 200 | if (!BN_GF2m_add(z2, z2, y)) goto err; |
| 201 | |
| 202 | ret = 2; |
| 203 | |
| 204 | err: |
| 205 | BN_CTX_end(ctx); |
| 206 | return ret; |
| 207 | } |
| 208 | |
| 209 | /* Computes scalar*point and stores the result in r. |
| 210 | * point can not equal r. |
| 211 | * Uses algorithm 2P of |
| 212 | * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over |
| 213 | * GF(2^m) without precomputation" (CHES '99, LNCS 1717). |
| 214 | */ |
| 215 | static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| 216 | const EC_POINT *point, BN_CTX *ctx) |
| 217 | { |
| 218 | BIGNUM *x1, *x2, *z1, *z2; |
| 219 | int ret = 0, i; |
| 220 | BN_ULONG mask,word; |
| 221 | |
| 222 | if (r == point) |
| 223 | { |
| 224 | ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); |
| 225 | return 0; |
| 226 | } |
| 227 | |
| 228 | /* if result should be point at infinity */ |
| 229 | if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || |
| 230 | EC_POINT_is_at_infinity(group, point)) |
| 231 | { |
| 232 | return EC_POINT_set_to_infinity(group, r); |
| 233 | } |
| 234 | |
| 235 | /* only support affine coordinates */ |
| 236 | if (!point->Z_is_one) return 0; |
| 237 | |
| 238 | /* Since point_multiply is static we can guarantee that ctx != NULL. */ |
| 239 | BN_CTX_start(ctx); |
| 240 | x1 = BN_CTX_get(ctx); |
| 241 | z1 = BN_CTX_get(ctx); |
| 242 | if (z1 == NULL) goto err; |
| 243 | |
| 244 | x2 = &r->X; |
| 245 | z2 = &r->Y; |
| 246 | |
| 247 | if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ |
| 248 | if (!BN_one(z1)) goto err; /* z1 = 1 */ |
| 249 | if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */ |
| 250 | if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err; |
| 251 | if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ |
| 252 | |
| 253 | /* find top most bit and go one past it */ |
| 254 | i = scalar->top - 1; |
| 255 | mask = BN_TBIT; |
| 256 | word = scalar->d[i]; |
| 257 | while (!(word & mask)) mask >>= 1; |
| 258 | mask >>= 1; |
| 259 | /* if top most bit was at word break, go to next word */ |
| 260 | if (!mask) |
| 261 | { |
| 262 | i--; |
| 263 | mask = BN_TBIT; |
| 264 | } |
| 265 | |
| 266 | for (; i >= 0; i--) |
| 267 | { |
| 268 | word = scalar->d[i]; |
| 269 | while (mask) |
| 270 | { |
| 271 | if (word & mask) |
| 272 | { |
| 273 | if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err; |
| 274 | if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err; |
| 275 | } |
| 276 | else |
| 277 | { |
| 278 | if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; |
| 279 | if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; |
| 280 | } |
| 281 | mask >>= 1; |
| 282 | } |
| 283 | mask = BN_TBIT; |
| 284 | } |
| 285 | |
| 286 | /* convert out of "projective" coordinates */ |
| 287 | i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); |
| 288 | if (i == 0) goto err; |
| 289 | else if (i == 1) |
| 290 | { |
| 291 | if (!EC_POINT_set_to_infinity(group, r)) goto err; |
| 292 | } |
| 293 | else |
| 294 | { |
| 295 | if (!BN_one(&r->Z)) goto err; |
| 296 | r->Z_is_one = 1; |
| 297 | } |
| 298 | |
| 299 | /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ |
| 300 | BN_set_negative(&r->X, 0); |
| 301 | BN_set_negative(&r->Y, 0); |
| 302 | |
| 303 | ret = 1; |
| 304 | |
| 305 | err: |
| 306 | BN_CTX_end(ctx); |
| 307 | return ret; |
| 308 | } |
| 309 | |
| 310 | |
| 311 | /* Computes the sum |
| 312 | * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] |
| 313 | * gracefully ignoring NULL scalar values. |
| 314 | */ |
| 315 | int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| 316 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) |
| 317 | { |
| 318 | BN_CTX *new_ctx = NULL; |
| 319 | int ret = 0; |
| 320 | size_t i; |
| 321 | EC_POINT *p=NULL; |
| 322 | EC_POINT *acc = NULL; |
| 323 | |
| 324 | if (ctx == NULL) |
| 325 | { |
| 326 | ctx = new_ctx = BN_CTX_new(); |
| 327 | if (ctx == NULL) |
| 328 | return 0; |
| 329 | } |
| 330 | |
| 331 | /* This implementation is more efficient than the wNAF implementation for 2 |
| 332 | * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points, |
| 333 | * or if we can perform a fast multiplication based on precomputation. |
| 334 | */ |
| 335 | if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group))) |
| 336 | { |
| 337 | ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); |
| 338 | goto err; |
| 339 | } |
| 340 | |
| 341 | if ((p = EC_POINT_new(group)) == NULL) goto err; |
| 342 | if ((acc = EC_POINT_new(group)) == NULL) goto err; |
| 343 | |
| 344 | if (!EC_POINT_set_to_infinity(group, acc)) goto err; |
| 345 | |
| 346 | if (scalar) |
| 347 | { |
| 348 | if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err; |
| 349 | if (BN_is_negative(scalar)) |
| 350 | if (!group->meth->invert(group, p, ctx)) goto err; |
| 351 | if (!group->meth->add(group, acc, acc, p, ctx)) goto err; |
| 352 | } |
| 353 | |
| 354 | for (i = 0; i < num; i++) |
| 355 | { |
| 356 | if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err; |
| 357 | if (BN_is_negative(scalars[i])) |
| 358 | if (!group->meth->invert(group, p, ctx)) goto err; |
| 359 | if (!group->meth->add(group, acc, acc, p, ctx)) goto err; |
| 360 | } |
| 361 | |
| 362 | if (!EC_POINT_copy(r, acc)) goto err; |
| 363 | |
| 364 | ret = 1; |
| 365 | |
| 366 | err: |
| 367 | if (p) EC_POINT_free(p); |
| 368 | if (acc) EC_POINT_free(acc); |
| 369 | if (new_ctx != NULL) |
| 370 | BN_CTX_free(new_ctx); |
| 371 | return ret; |
| 372 | } |
| 373 | |
| 374 | |
| 375 | /* Precomputation for point multiplication: fall back to wNAF methods |
| 376 | * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ |
| 377 | |
| 378 | int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
| 379 | { |
| 380 | return ec_wNAF_precompute_mult(group, ctx); |
| 381 | } |
| 382 | |
| 383 | int ec_GF2m_have_precompute_mult(const EC_GROUP *group) |
| 384 | { |
| 385 | return ec_wNAF_have_precompute_mult(group); |
| 386 | } |