1 /* crypto/ec/ec_mult.c */ 2 /* ==================================================================== 3 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in 14 * the documentation and/or other materials provided with the 15 * distribution. 16 * 17 * 3. All advertising materials mentioning features or use of this 18 * software must display the following acknowledgment: 19 * "This product includes software developed by the OpenSSL Project 20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 21 * 22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 23 * endorse or promote products derived from this software without 24 * prior written permission. For written permission, please contact 25 * openssl-core@openssl.org. 26 * 27 * 5. Products derived from this software may not be called "OpenSSL" 28 * nor may "OpenSSL" appear in their names without prior written 29 * permission of the OpenSSL Project. 30 * 31 * 6. Redistributions of any form whatsoever must retain the following 32 * acknowledgment: 33 * "This product includes software developed by the OpenSSL Project 34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 35 * 36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 47 * OF THE POSSIBILITY OF SUCH DAMAGE. 48 * ==================================================================== 49 * 50 * This product includes cryptographic software written by Eric Young 51 * (eay@cryptsoft.com). This product includes software written by Tim 52 * Hudson (tjh@cryptsoft.com). 53 * 54 */ 55 56 #include <openssl/err.h> 57 58 #include "ec_lcl.h" 59 60 61 /* TODO: optional precomputation of multiples of the generator */ 62 63 64 65 /* 66 * wNAF-based interleaving multi-exponentation method 67 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>) 68 */ 69 70 71 /* Determine the width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. 72 * This is an array r[] of values that are either zero or odd with an 73 * absolute value less than 2^w satisfying 74 * scalar = \sum_j r[j]*2^j 75 * where at most one of any w+1 consecutive digits is non-zero. 76 */ 77 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx) 78 { 79 BIGNUM *c; 80 int ok = 0; 81 signed char *r = NULL; 82 int sign = 1; 83 int bit, next_bit, mask; 84 size_t len = 0, j; 85 86 BN_CTX_start(ctx); 87 c = BN_CTX_get(ctx); 88 if (c == NULL) goto err; 89 90 if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ 91 { 92 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 93 goto err; 94 } 95 bit = 1 << w; /* at most 128 */ 96 next_bit = bit << 1; /* at most 256 */ 97 mask = next_bit - 1; /* at most 255 */ 98 99 if (!BN_copy(c, scalar)) goto err; 100 if (c->neg) 101 { 102 sign = -1; 103 c->neg = 0; 104 } 105 106 len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */ 107 r = OPENSSL_malloc(len); 108 if (r == NULL) goto err; 109 110 j = 0; 111 while (!BN_is_zero(c)) 112 { 113 int u = 0; 114 115 if (BN_is_odd(c)) 116 { 117 if (c->d == NULL || c->top == 0) 118 { 119 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 120 goto err; 121 } 122 u = c->d[0] & mask; 123 if (u & bit) 124 { 125 u -= next_bit; 126 /* u < 0 */ 127 if (!BN_add_word(c, -u)) goto err; 128 } 129 else 130 { 131 /* u > 0 */ 132 if (!BN_sub_word(c, u)) goto err; 133 } 134 135 if (u <= -bit || u >= bit || !(u & 1) || c->neg) 136 { 137 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 138 goto err; 139 } 140 } 141 142 r[j++] = sign * u; 143 144 if (BN_is_odd(c)) 145 { 146 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 147 goto err; 148 } 149 if (!BN_rshift1(c, c)) goto err; 150 } 151 152 if (j > len) 153 { 154 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 155 goto err; 156 } 157 len = j; 158 ok = 1; 159 160 err: 161 BN_CTX_end(ctx); 162 if (!ok) 163 { 164 OPENSSL_free(r); 165 r = NULL; 166 } 167 if (ok) 168 *ret_len = len; 169 return r; 170 } 171 172 173 /* TODO: table should be optimised for the wNAF-based implementation, 174 * sometimes smaller windows will give better performance 175 * (thus the boundaries should be increased) 176 */ 177 #define EC_window_bits_for_scalar_size(b) \ 178 ((b) >= 2000 ? 6 : \ 179 (b) >= 800 ? 5 : \ 180 (b) >= 300 ? 4 : \ 181 (b) >= 70 ? 3 : \ 182 (b) >= 20 ? 2 : \ 183 1) 184 185 /* Compute 186 * \sum scalars[i]*points[i], 187 * also including 188 * scalar*generator 189 * in the addition if scalar != NULL 190 */ 191 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 192 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) 193 { 194 BN_CTX *new_ctx = NULL; 195 EC_POINT *generator = NULL; 196 EC_POINT *tmp = NULL; 197 size_t totalnum; 198 size_t i, j; 199 int k; 200 int r_is_inverted = 0; 201 int r_is_at_infinity = 1; 202 size_t *wsize = NULL; /* individual window sizes */ 203 signed char **wNAF = NULL; /* individual wNAFs */ 204 size_t *wNAF_len = NULL; 205 size_t max_len = 0; 206 size_t num_val; 207 EC_POINT **val = NULL; /* precomputation */ 208 EC_POINT **v; 209 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */ 210 int ret = 0; 211 212 if (group->meth != r->meth) 213 { 214 ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); 215 return 0; 216 } 217 218 if ((scalar == NULL) && (num == 0)) 219 { 220 return EC_POINT_set_to_infinity(group, r); 221 } 222 223 if (scalar != NULL) 224 { 225 generator = EC_GROUP_get0_generator(group); 226 if (generator == NULL) 227 { 228 ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); 229 return 0; 230 } 231 } 232 233 for (i = 0; i < num; i++) 234 { 235 if (group->meth != points[i]->meth) 236 { 237 ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); 238 return 0; 239 } 240 } 241 242 totalnum = num + (scalar != NULL); 243 244 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); 245 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); 246 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); 247 if (wNAF != NULL) 248 { 249 wNAF[0] = NULL; /* preliminary pivot */ 250 } 251 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err; 252 253 /* num_val := total number of points to precompute */ 254 num_val = 0; 255 for (i = 0; i < totalnum; i++) 256 { 257 size_t bits; 258 259 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); 260 wsize[i] = EC_window_bits_for_scalar_size(bits); 261 num_val += 1u << (wsize[i] - 1); 262 } 263 264 /* all precomputed points go into a single array 'val', 265 * 'val_sub[i]' is a pointer to the subarray for the i-th point */ 266 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); 267 if (val == NULL) goto err; 268 val[num_val] = NULL; /* pivot element */ 269 270 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); 271 if (val_sub == NULL) goto err; 272 273 /* allocate points for precomputation */ 274 v = val; 275 for (i = 0; i < totalnum; i++) 276 { 277 val_sub[i] = v; 278 for (j = 0; j < (1u << (wsize[i] - 1)); j++) 279 { 280 *v = EC_POINT_new(group); 281 if (*v == NULL) goto err; 282 v++; 283 } 284 } 285 if (!(v == val + num_val)) 286 { 287 ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR); 288 goto err; 289 } 290 291 if (ctx == NULL) 292 { 293 ctx = new_ctx = BN_CTX_new(); 294 if (ctx == NULL) 295 goto err; 296 } 297 298 tmp = EC_POINT_new(group); 299 if (tmp == NULL) goto err; 300 301 /* prepare precomputed values: 302 * val_sub[i][0] := points[i] 303 * val_sub[i][1] := 3 * points[i] 304 * val_sub[i][2] := 5 * points[i] 305 * ... 306 */ 307 for (i = 0; i < totalnum; i++) 308 { 309 if (i < num) 310 { 311 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; 312 } 313 else 314 { 315 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; 316 } 317 318 if (wsize[i] > 1) 319 { 320 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; 321 for (j = 1; j < (1u << (wsize[i] - 1)); j++) 322 { 323 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; 324 } 325 } 326 327 wNAF[i + 1] = NULL; /* make sure we always have a pivot */ 328 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i], ctx); 329 if (wNAF[i] == NULL) goto err; 330 if (wNAF_len[i] > max_len) 331 max_len = wNAF_len[i]; 332 } 333 334 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ 335 if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; 336 #endif 337 338 r_is_at_infinity = 1; 339 340 for (k = max_len - 1; k >= 0; k--) 341 { 342 if (!r_is_at_infinity) 343 { 344 if (!EC_POINT_dbl(group, r, r, ctx)) goto err; 345 } 346 347 for (i = 0; i < totalnum; i++) 348 { 349 if (wNAF_len[i] > (size_t)k) 350 { 351 int digit = wNAF[i][k]; 352 int is_neg; 353 354 if (digit) 355 { 356 is_neg = digit < 0; 357 358 if (is_neg) 359 digit = -digit; 360 361 if (is_neg != r_is_inverted) 362 { 363 if (!r_is_at_infinity) 364 { 365 if (!EC_POINT_invert(group, r, ctx)) goto err; 366 } 367 r_is_inverted = !r_is_inverted; 368 } 369 370 /* digit > 0 */ 371 372 if (r_is_at_infinity) 373 { 374 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; 375 r_is_at_infinity = 0; 376 } 377 else 378 { 379 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; 380 } 381 } 382 } 383 } 384 } 385 386 if (r_is_at_infinity) 387 { 388 if (!EC_POINT_set_to_infinity(group, r)) goto err; 389 } 390 else 391 { 392 if (r_is_inverted) 393 if (!EC_POINT_invert(group, r, ctx)) goto err; 394 } 395 396 ret = 1; 397 398 err: 399 if (new_ctx != NULL) 400 BN_CTX_free(new_ctx); 401 if (tmp != NULL) 402 EC_POINT_free(tmp); 403 if (wsize != NULL) 404 OPENSSL_free(wsize); 405 if (wNAF_len != NULL) 406 OPENSSL_free(wNAF_len); 407 if (wNAF != NULL) 408 { 409 signed char **w; 410 411 for (w = wNAF; *w != NULL; w++) 412 OPENSSL_free(*w); 413 414 OPENSSL_free(wNAF); 415 } 416 if (val != NULL) 417 { 418 for (v = val; *v != NULL; v++) 419 EC_POINT_clear_free(*v); 420 421 OPENSSL_free(val); 422 } 423 if (val_sub != NULL) 424 { 425 OPENSSL_free(val_sub); 426 } 427 return ret; 428 } 429 430 431 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) 432 { 433 const EC_POINT *points[1]; 434 const BIGNUM *scalars[1]; 435 436 points[0] = point; 437 scalars[0] = p_scalar; 438 439 return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx); 440 } 441 442 443 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 444 { 445 const EC_POINT *generator; 446 BN_CTX *new_ctx = NULL; 447 BIGNUM *order; 448 int ret = 0; 449 450 generator = EC_GROUP_get0_generator(group); 451 if (generator == NULL) 452 { 453 ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); 454 return 0; 455 } 456 457 if (ctx == NULL) 458 { 459 ctx = new_ctx = BN_CTX_new(); 460 if (ctx == NULL) 461 return 0; 462 } 463 464 BN_CTX_start(ctx); 465 order = BN_CTX_get(ctx); 466 if (order == NULL) goto err; 467 468 if (!EC_GROUP_get_order(group, order, ctx)) return 0; 469 if (BN_is_zero(order)) 470 { 471 ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); 472 goto err; 473 } 474 475 /* TODO */ 476 477 ret = 1; 478 479 err: 480 BN_CTX_end(ctx); 481 if (new_ctx != NULL) 482 BN_CTX_free(new_ctx); 483 return ret; 484 } 485