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| 1 /* crypto/bn/bn_gcd.c */ | |
| 2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) | |
| 3 * All rights reserved. | |
| 4 * | |
| 5 * This package is an SSL implementation written | |
| 6 * by Eric Young (eay@cryptsoft.com). | |
| 7 * The implementation was written so as to conform with Netscapes SSL. | |
| 8 * | |
| 9 * This library is free for commercial and non-commercial use as long as | |
| 10 * the following conditions are aheared to. The following conditions | |
| 11 * apply to all code found in this distribution, be it the RC4, RSA, | |
| 12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation | |
| 13 * included with this distribution is covered by the same copyright terms | |
| 14 * except that the holder is Tim Hudson (tjh@cryptsoft.com). | |
| 15 * | |
| 16 * Copyright remains Eric Young's, and as such any Copyright notices in | |
| 17 * the code are not to be removed. | |
| 18 * If this package is used in a product, Eric Young should be given attribution | |
| 19 * as the author of the parts of the library used. | |
| 20 * This can be in the form of a textual message at program startup or | |
| 21 * in documentation (online or textual) provided with the package. | |
| 22 * | |
| 23 * Redistribution and use in source and binary forms, with or without | |
| 24 * modification, are permitted provided that the following conditions | |
| 25 * are met: | |
| 26 * 1. Redistributions of source code must retain the copyright | |
| 27 * notice, this list of conditions and the following disclaimer. | |
| 28 * 2. Redistributions in binary form must reproduce the above copyright | |
| 29 * notice, this list of conditions and the following disclaimer in the | |
| 30 * documentation and/or other materials provided with the distribution. | |
| 31 * 3. All advertising materials mentioning features or use of this software | |
| 32 * must display the following acknowledgement: | |
| 33 * "This product includes cryptographic software written by | |
| 34 * Eric Young (eay@cryptsoft.com)" | |
| 35 * The word 'cryptographic' can be left out if the rouines from the library | |
| 36 * being used are not cryptographic related :-). | |
| 37 * 4. If you include any Windows specific code (or a derivative thereof) from | |
| 38 * the apps directory (application code) you must include an acknowledgement: | |
| 39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" | |
| 40 * | |
| 41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND | |
| 42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
| 43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
| 44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | |
| 45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
| 46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
| 47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
| 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
| 49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
| 50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
| 51 * SUCH DAMAGE. | |
| 52 * | |
| 53 * The licence and distribution terms for any publically available version or | |
| 54 * derivative of this code cannot be changed. i.e. this code cannot simply be | |
| 55 * copied and put under another distribution licence | |
| 56 * [including the GNU Public Licence.] | |
| 57 */ | |
| 58 /* ==================================================================== | |
| 59 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. | |
| 60 * | |
| 61 * Redistribution and use in source and binary forms, with or without | |
| 62 * modification, are permitted provided that the following conditions | |
| 63 * are met: | |
| 64 * | |
| 65 * 1. Redistributions of source code must retain the above copyright | |
| 66 * notice, this list of conditions and the following disclaimer. | |
| 67 * | |
| 68 * 2. Redistributions in binary form must reproduce the above copyright | |
| 69 * notice, this list of conditions and the following disclaimer in | |
| 70 * the documentation and/or other materials provided with the | |
| 71 * distribution. | |
| 72 * | |
| 73 * 3. All advertising materials mentioning features or use of this | |
| 74 * software must display the following acknowledgment: | |
| 75 * "This product includes software developed by the OpenSSL Project | |
| 76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
| 77 * | |
| 78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
| 79 * endorse or promote products derived from this software without | |
| 80 * prior written permission. For written permission, please contact | |
| 81 * openssl-core@openssl.org. | |
| 82 * | |
| 83 * 5. Products derived from this software may not be called "OpenSSL" | |
| 84 * nor may "OpenSSL" appear in their names without prior written | |
| 85 * permission of the OpenSSL Project. | |
| 86 * | |
| 87 * 6. Redistributions of any form whatsoever must retain the following | |
| 88 * acknowledgment: | |
| 89 * "This product includes software developed by the OpenSSL Project | |
| 90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
| 91 * | |
| 92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
| 93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
| 94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
| 95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
| 96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
| 97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
| 98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
| 99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
| 100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
| 101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
| 102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
| 103 * OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 104 * ==================================================================== | |
| 105 * | |
| 106 * This product includes cryptographic software written by Eric Young | |
| 107 * (eay@cryptsoft.com). This product includes software written by Tim | |
| 108 * Hudson (tjh@cryptsoft.com). | |
| 109 * | |
| 110 */ | |
| 111 | |
| 112 #include "cryptlib.h" | |
| 113 #include "bn_lcl.h" | |
| 114 | |
| 115 static BIGNUM *euclid(BIGNUM *a, BIGNUM *b); | |
| 116 | |
| 117 int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx) | |
| 118 { | |
| 119 BIGNUM *a,*b,*t; | |
| 120 int ret=0; | |
| 121 | |
| 122 bn_check_top(in_a); | |
| 123 bn_check_top(in_b); | |
| 124 | |
| 125 BN_CTX_start(ctx); | |
| 126 a = BN_CTX_get(ctx); | |
| 127 b = BN_CTX_get(ctx); | |
| 128 if (a == NULL || b == NULL) goto err; | |
| 129 | |
| 130 if (BN_copy(a,in_a) == NULL) goto err; | |
| 131 if (BN_copy(b,in_b) == NULL) goto err; | |
| 132 a->neg = 0; | |
| 133 b->neg = 0; | |
| 134 | |
| 135 if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; } | |
| 136 t=euclid(a,b); | |
| 137 if (t == NULL) goto err; | |
| 138 | |
| 139 if (BN_copy(r,t) == NULL) goto err; | |
| 140 ret=1; | |
| 141 err: | |
| 142 BN_CTX_end(ctx); | |
| 143 bn_check_top(r); | |
| 144 return(ret); | |
| 145 } | |
| 146 | |
| 147 static BIGNUM *euclid(BIGNUM *a, BIGNUM *b) | |
| 148 { | |
| 149 BIGNUM *t; | |
| 150 int shifts=0; | |
| 151 | |
| 152 bn_check_top(a); | |
| 153 bn_check_top(b); | |
| 154 | |
| 155 /* 0 <= b <= a */ | |
| 156 while (!BN_is_zero(b)) | |
| 157 { | |
| 158 /* 0 < b <= a */ | |
| 159 | |
| 160 if (BN_is_odd(a)) | |
| 161 { | |
| 162 if (BN_is_odd(b)) | |
| 163 { | |
| 164 if (!BN_sub(a,a,b)) goto err; | |
| 165 if (!BN_rshift1(a,a)) goto err; | |
| 166 if (BN_cmp(a,b) < 0) | |
| 167 { t=a; a=b; b=t; } | |
| 168 } | |
| 169 else /* a odd - b even */ | |
| 170 { | |
| 171 if (!BN_rshift1(b,b)) goto err; | |
| 172 if (BN_cmp(a,b) < 0) | |
| 173 { t=a; a=b; b=t; } | |
| 174 } | |
| 175 } | |
| 176 else /* a is even */ | |
| 177 { | |
| 178 if (BN_is_odd(b)) | |
| 179 { | |
| 180 if (!BN_rshift1(a,a)) goto err; | |
| 181 if (BN_cmp(a,b) < 0) | |
| 182 { t=a; a=b; b=t; } | |
| 183 } | |
| 184 else /* a even - b even */ | |
| 185 { | |
| 186 if (!BN_rshift1(a,a)) goto err; | |
| 187 if (!BN_rshift1(b,b)) goto err; | |
| 188 shifts++; | |
| 189 } | |
| 190 } | |
| 191 /* 0 <= b <= a */ | |
| 192 } | |
| 193 | |
| 194 if (shifts) | |
| 195 { | |
| 196 if (!BN_lshift(a,a,shifts)) goto err; | |
| 197 } | |
| 198 bn_check_top(a); | |
| 199 return(a); | |
| 200 err: | |
| 201 return(NULL); | |
| 202 } | |
| 203 | |
| 204 | |
| 205 /* solves ax == 1 (mod n) */ | |
| 206 static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in, | |
| 207 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx); | |
| 208 | |
| 209 BIGNUM *BN_mod_inverse(BIGNUM *in, | |
| 210 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) | |
| 211 { | |
| 212 BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL; | |
| 213 BIGNUM *ret=NULL; | |
| 214 int sign; | |
| 215 | |
| 216 if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_
CONSTTIME) != 0)) | |
| 217 { | |
| 218 return BN_mod_inverse_no_branch(in, a, n, ctx); | |
| 219 } | |
| 220 | |
| 221 bn_check_top(a); | |
| 222 bn_check_top(n); | |
| 223 | |
| 224 BN_CTX_start(ctx); | |
| 225 A = BN_CTX_get(ctx); | |
| 226 B = BN_CTX_get(ctx); | |
| 227 X = BN_CTX_get(ctx); | |
| 228 D = BN_CTX_get(ctx); | |
| 229 M = BN_CTX_get(ctx); | |
| 230 Y = BN_CTX_get(ctx); | |
| 231 T = BN_CTX_get(ctx); | |
| 232 if (T == NULL) goto err; | |
| 233 | |
| 234 if (in == NULL) | |
| 235 R=BN_new(); | |
| 236 else | |
| 237 R=in; | |
| 238 if (R == NULL) goto err; | |
| 239 | |
| 240 BN_one(X); | |
| 241 BN_zero(Y); | |
| 242 if (BN_copy(B,a) == NULL) goto err; | |
| 243 if (BN_copy(A,n) == NULL) goto err; | |
| 244 A->neg = 0; | |
| 245 if (B->neg || (BN_ucmp(B, A) >= 0)) | |
| 246 { | |
| 247 if (!BN_nnmod(B, B, A, ctx)) goto err; | |
| 248 } | |
| 249 sign = -1; | |
| 250 /* From B = a mod |n|, A = |n| it follows that | |
| 251 * | |
| 252 * 0 <= B < A, | |
| 253 * -sign*X*a == B (mod |n|), | |
| 254 * sign*Y*a == A (mod |n|). | |
| 255 */ | |
| 256 | |
| 257 if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) | |
| 258 { | |
| 259 /* Binary inversion algorithm; requires odd modulus. | |
| 260 * This is faster than the general algorithm if the modulus | |
| 261 * is sufficiently small (about 400 .. 500 bits on 32-bit | |
| 262 * sytems, but much more on 64-bit systems) */ | |
| 263 int shift; | |
| 264 | |
| 265 while (!BN_is_zero(B)) | |
| 266 { | |
| 267 /* | |
| 268 * 0 < B < |n|, | |
| 269 * 0 < A <= |n|, | |
| 270 * (1) -sign*X*a == B (mod |n|), | |
| 271 * (2) sign*Y*a == A (mod |n|) | |
| 272 */ | |
| 273 | |
| 274 /* Now divide B by the maximum possible power of two i
n the integers, | |
| 275 * and divide X by the same value mod |n|. | |
| 276 * When we're done, (1) still holds. */ | |
| 277 shift = 0; | |
| 278 while (!BN_is_bit_set(B, shift)) /* note that 0 < B */ | |
| 279 { | |
| 280 shift++; | |
| 281 | |
| 282 if (BN_is_odd(X)) | |
| 283 { | |
| 284 if (!BN_uadd(X, X, n)) goto err; | |
| 285 } | |
| 286 /* now X is even, so we can easily divide it by
two */ | |
| 287 if (!BN_rshift1(X, X)) goto err; | |
| 288 } | |
| 289 if (shift > 0) | |
| 290 { | |
| 291 if (!BN_rshift(B, B, shift)) goto err; | |
| 292 } | |
| 293 | |
| 294 | |
| 295 /* Same for A and Y. Afterwards, (2) still holds. */ | |
| 296 shift = 0; | |
| 297 while (!BN_is_bit_set(A, shift)) /* note that 0 < A */ | |
| 298 { | |
| 299 shift++; | |
| 300 | |
| 301 if (BN_is_odd(Y)) | |
| 302 { | |
| 303 if (!BN_uadd(Y, Y, n)) goto err; | |
| 304 } | |
| 305 /* now Y is even */ | |
| 306 if (!BN_rshift1(Y, Y)) goto err; | |
| 307 } | |
| 308 if (shift > 0) | |
| 309 { | |
| 310 if (!BN_rshift(A, A, shift)) goto err; | |
| 311 } | |
| 312 | |
| 313 | |
| 314 /* We still have (1) and (2). | |
| 315 * Both A and B are odd. | |
| 316 * The following computations ensure that | |
| 317 * | |
| 318 * 0 <= B < |n|, | |
| 319 * 0 < A < |n|, | |
| 320 * (1) -sign*X*a == B (mod |n|), | |
| 321 * (2) sign*Y*a == A (mod |n|), | |
| 322 * | |
| 323 * and that either A or B is even in the next iterat
ion. | |
| 324 */ | |
| 325 if (BN_ucmp(B, A) >= 0) | |
| 326 { | |
| 327 /* -sign*(X + Y)*a == B - A (mod |n|) */ | |
| 328 if (!BN_uadd(X, X, Y)) goto err; | |
| 329 /* NB: we could use BN_mod_add_quick(X, X, Y, n)
, but that | |
| 330 * actually makes the algorithm slower */ | |
| 331 if (!BN_usub(B, B, A)) goto err; | |
| 332 } | |
| 333 else | |
| 334 { | |
| 335 /* sign*(X + Y)*a == A - B (mod |n|) */ | |
| 336 if (!BN_uadd(Y, Y, X)) goto err; | |
| 337 /* as above, BN_mod_add_quick(Y, Y, X, n) would
slow things down */ | |
| 338 if (!BN_usub(A, A, B)) goto err; | |
| 339 } | |
| 340 } | |
| 341 } | |
| 342 else | |
| 343 { | |
| 344 /* general inversion algorithm */ | |
| 345 | |
| 346 while (!BN_is_zero(B)) | |
| 347 { | |
| 348 BIGNUM *tmp; | |
| 349 | |
| 350 /* | |
| 351 * 0 < B < A, | |
| 352 * (*) -sign*X*a == B (mod |n|), | |
| 353 * sign*Y*a == A (mod |n|) | |
| 354 */ | |
| 355 | |
| 356 /* (D, M) := (A/B, A%B) ... */ | |
| 357 if (BN_num_bits(A) == BN_num_bits(B)) | |
| 358 { | |
| 359 if (!BN_one(D)) goto err; | |
| 360 if (!BN_sub(M,A,B)) goto err; | |
| 361 } | |
| 362 else if (BN_num_bits(A) == BN_num_bits(B) + 1) | |
| 363 { | |
| 364 /* A/B is 1, 2, or 3 */ | |
| 365 if (!BN_lshift1(T,B)) goto err; | |
| 366 if (BN_ucmp(A,T) < 0) | |
| 367 { | |
| 368 /* A < 2*B, so D=1 */ | |
| 369 if (!BN_one(D)) goto err; | |
| 370 if (!BN_sub(M,A,B)) goto err; | |
| 371 } | |
| 372 else | |
| 373 { | |
| 374 /* A >= 2*B, so D=2 or D=3 */ | |
| 375 if (!BN_sub(M,A,T)) goto err; | |
| 376 if (!BN_add(D,T,B)) goto err; /* use D (
:= 3*B) as temp */ | |
| 377 if (BN_ucmp(A,D) < 0) | |
| 378 { | |
| 379 /* A < 3*B, so D=2 */ | |
| 380 if (!BN_set_word(D,2)) goto err; | |
| 381 /* M (= A - 2*B) already has the
correct value */ | |
| 382 } | |
| 383 else | |
| 384 { | |
| 385 /* only D=3 remains */ | |
| 386 if (!BN_set_word(D,3)) goto err; | |
| 387 /* currently M = A - 2*B, but
we need M = A - 3*B */ | |
| 388 if (!BN_sub(M,M,B)) goto err; | |
| 389 } | |
| 390 } | |
| 391 } | |
| 392 else | |
| 393 { | |
| 394 if (!BN_div(D,M,A,B,ctx)) goto err; | |
| 395 } | |
| 396 | |
| 397 /* Now | |
| 398 * A = D*B + M; | |
| 399 * thus we have | |
| 400 * (**) sign*Y*a == D*B + M (mod |n|). | |
| 401 */ | |
| 402 | |
| 403 tmp=A; /* keep the BIGNUM object, the value does not mat
ter */ | |
| 404 | |
| 405 /* (A, B) := (B, A mod B) ... */ | |
| 406 A=B; | |
| 407 B=M; | |
| 408 /* ... so we have 0 <= B < A again */ | |
| 409 | |
| 410 /* Since the former M is now B and the former B is
now A, | |
| 411 * (**) translates into | |
| 412 * sign*Y*a == D*A + B (mod |n|), | |
| 413 * i.e. | |
| 414 * sign*Y*a - D*A == B (mod |n|). | |
| 415 * Similarly, (*) translates into | |
| 416 * -sign*X*a == A (mod |n|). | |
| 417 * | |
| 418 * Thus, | |
| 419 * sign*Y*a + D*sign*X*a == B (mod |n|), | |
| 420 * i.e. | |
| 421 * sign*(Y + D*X)*a == B (mod |n|). | |
| 422 * | |
| 423 * So if we set (X, Y, sign) := (Y + D*X, X, -sign), w
e arrive back at | |
| 424 * -sign*X*a == B (mod |n|), | |
| 425 * sign*Y*a == A (mod |n|). | |
| 426 * Note that X and Y stay non-negative all the time. | |
| 427 */ | |
| 428 | |
| 429 /* most of the time D is very small, so we can optimize
tmp := D*X+Y */ | |
| 430 if (BN_is_one(D)) | |
| 431 { | |
| 432 if (!BN_add(tmp,X,Y)) goto err; | |
| 433 } | |
| 434 else | |
| 435 { | |
| 436 if (BN_is_word(D,2)) | |
| 437 { | |
| 438 if (!BN_lshift1(tmp,X)) goto err; | |
| 439 } | |
| 440 else if (BN_is_word(D,4)) | |
| 441 { | |
| 442 if (!BN_lshift(tmp,X,2)) goto err; | |
| 443 } | |
| 444 else if (D->top == 1) | |
| 445 { | |
| 446 if (!BN_copy(tmp,X)) goto err; | |
| 447 if (!BN_mul_word(tmp,D->d[0])) goto err; | |
| 448 } | |
| 449 else | |
| 450 { | |
| 451 if (!BN_mul(tmp,D,X,ctx)) goto err; | |
| 452 } | |
| 453 if (!BN_add(tmp,tmp,Y)) goto err; | |
| 454 } | |
| 455 | |
| 456 M=Y; /* keep the BIGNUM object, the value does not matte
r */ | |
| 457 Y=X; | |
| 458 X=tmp; | |
| 459 sign = -sign; | |
| 460 } | |
| 461 } | |
| 462 | |
| 463 /* | |
| 464 * The while loop (Euclid's algorithm) ends when | |
| 465 * A == gcd(a,n); | |
| 466 * we have | |
| 467 * sign*Y*a == A (mod |n|), | |
| 468 * where Y is non-negative. | |
| 469 */ | |
| 470 | |
| 471 if (sign < 0) | |
| 472 { | |
| 473 if (!BN_sub(Y,n,Y)) goto err; | |
| 474 } | |
| 475 /* Now Y*a == A (mod |n|). */ | |
| 476 | |
| 477 | |
| 478 if (BN_is_one(A)) | |
| 479 { | |
| 480 /* Y*a == 1 (mod |n|) */ | |
| 481 if (!Y->neg && BN_ucmp(Y,n) < 0) | |
| 482 { | |
| 483 if (!BN_copy(R,Y)) goto err; | |
| 484 } | |
| 485 else | |
| 486 { | |
| 487 if (!BN_nnmod(R,Y,n,ctx)) goto err; | |
| 488 } | |
| 489 } | |
| 490 else | |
| 491 { | |
| 492 BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE); | |
| 493 goto err; | |
| 494 } | |
| 495 ret=R; | |
| 496 err: | |
| 497 if ((ret == NULL) && (in == NULL)) BN_free(R); | |
| 498 BN_CTX_end(ctx); | |
| 499 bn_check_top(ret); | |
| 500 return(ret); | |
| 501 } | |
| 502 | |
| 503 | |
| 504 /* BN_mod_inverse_no_branch is a special version of BN_mod_inverse. | |
| 505 * It does not contain branches that may leak sensitive information. | |
| 506 */ | |
| 507 static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in, | |
| 508 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) | |
| 509 { | |
| 510 BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL; | |
| 511 BIGNUM local_A, local_B; | |
| 512 BIGNUM *pA, *pB; | |
| 513 BIGNUM *ret=NULL; | |
| 514 int sign; | |
| 515 | |
| 516 bn_check_top(a); | |
| 517 bn_check_top(n); | |
| 518 | |
| 519 BN_CTX_start(ctx); | |
| 520 A = BN_CTX_get(ctx); | |
| 521 B = BN_CTX_get(ctx); | |
| 522 X = BN_CTX_get(ctx); | |
| 523 D = BN_CTX_get(ctx); | |
| 524 M = BN_CTX_get(ctx); | |
| 525 Y = BN_CTX_get(ctx); | |
| 526 T = BN_CTX_get(ctx); | |
| 527 if (T == NULL) goto err; | |
| 528 | |
| 529 if (in == NULL) | |
| 530 R=BN_new(); | |
| 531 else | |
| 532 R=in; | |
| 533 if (R == NULL) goto err; | |
| 534 | |
| 535 BN_one(X); | |
| 536 BN_zero(Y); | |
| 537 if (BN_copy(B,a) == NULL) goto err; | |
| 538 if (BN_copy(A,n) == NULL) goto err; | |
| 539 A->neg = 0; | |
| 540 | |
| 541 if (B->neg || (BN_ucmp(B, A) >= 0)) | |
| 542 { | |
| 543 /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked
, | |
| 544 * BN_div_no_branch will be called eventually. | |
| 545 */ | |
| 546 pB = &local_B; | |
| 547 BN_with_flags(pB, B, BN_FLG_CONSTTIME); | |
| 548 if (!BN_nnmod(B, pB, A, ctx)) goto err; | |
| 549 } | |
| 550 sign = -1; | |
| 551 /* From B = a mod |n|, A = |n| it follows that | |
| 552 * | |
| 553 * 0 <= B < A, | |
| 554 * -sign*X*a == B (mod |n|), | |
| 555 * sign*Y*a == A (mod |n|). | |
| 556 */ | |
| 557 | |
| 558 while (!BN_is_zero(B)) | |
| 559 { | |
| 560 BIGNUM *tmp; | |
| 561 | |
| 562 /* | |
| 563 * 0 < B < A, | |
| 564 * (*) -sign*X*a == B (mod |n|), | |
| 565 * sign*Y*a == A (mod |n|) | |
| 566 */ | |
| 567 | |
| 568 /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked
, | |
| 569 * BN_div_no_branch will be called eventually. | |
| 570 */ | |
| 571 pA = &local_A; | |
| 572 BN_with_flags(pA, A, BN_FLG_CONSTTIME); | |
| 573 | |
| 574 /* (D, M) := (A/B, A%B) ... */ | |
| 575 if (!BN_div(D,M,pA,B,ctx)) goto err; | |
| 576 | |
| 577 /* Now | |
| 578 * A = D*B + M; | |
| 579 * thus we have | |
| 580 * (**) sign*Y*a == D*B + M (mod |n|). | |
| 581 */ | |
| 582 | |
| 583 tmp=A; /* keep the BIGNUM object, the value does not matter */ | |
| 584 | |
| 585 /* (A, B) := (B, A mod B) ... */ | |
| 586 A=B; | |
| 587 B=M; | |
| 588 /* ... so we have 0 <= B < A again */ | |
| 589 | |
| 590 /* Since the former M is now B and the former B is now A, | |
| 591 * (**) translates into | |
| 592 * sign*Y*a == D*A + B (mod |n|), | |
| 593 * i.e. | |
| 594 * sign*Y*a - D*A == B (mod |n|). | |
| 595 * Similarly, (*) translates into | |
| 596 * -sign*X*a == A (mod |n|). | |
| 597 * | |
| 598 * Thus, | |
| 599 * sign*Y*a + D*sign*X*a == B (mod |n|), | |
| 600 * i.e. | |
| 601 * sign*(Y + D*X)*a == B (mod |n|). | |
| 602 * | |
| 603 * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive
back at | |
| 604 * -sign*X*a == B (mod |n|), | |
| 605 * sign*Y*a == A (mod |n|). | |
| 606 * Note that X and Y stay non-negative all the time. | |
| 607 */ | |
| 608 | |
| 609 if (!BN_mul(tmp,D,X,ctx)) goto err; | |
| 610 if (!BN_add(tmp,tmp,Y)) goto err; | |
| 611 | |
| 612 M=Y; /* keep the BIGNUM object, the value does not matter */ | |
| 613 Y=X; | |
| 614 X=tmp; | |
| 615 sign = -sign; | |
| 616 } | |
| 617 | |
| 618 /* | |
| 619 * The while loop (Euclid's algorithm) ends when | |
| 620 * A == gcd(a,n); | |
| 621 * we have | |
| 622 * sign*Y*a == A (mod |n|), | |
| 623 * where Y is non-negative. | |
| 624 */ | |
| 625 | |
| 626 if (sign < 0) | |
| 627 { | |
| 628 if (!BN_sub(Y,n,Y)) goto err; | |
| 629 } | |
| 630 /* Now Y*a == A (mod |n|). */ | |
| 631 | |
| 632 if (BN_is_one(A)) | |
| 633 { | |
| 634 /* Y*a == 1 (mod |n|) */ | |
| 635 if (!Y->neg && BN_ucmp(Y,n) < 0) | |
| 636 { | |
| 637 if (!BN_copy(R,Y)) goto err; | |
| 638 } | |
| 639 else | |
| 640 { | |
| 641 if (!BN_nnmod(R,Y,n,ctx)) goto err; | |
| 642 } | |
| 643 } | |
| 644 else | |
| 645 { | |
| 646 BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE); | |
| 647 goto err; | |
| 648 } | |
| 649 ret=R; | |
| 650 err: | |
| 651 if ((ret == NULL) && (in == NULL)) BN_free(R); | |
| 652 BN_CTX_end(ctx); | |
| 653 bn_check_top(ret); | |
| 654 return(ret); | |
| 655 } | |
| OLD | NEW |
|---|
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