[331] | 1 | /*
|
---|
| 2 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
|
---|
| 3 | *
|
---|
| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
|
---|
| 5 | * this file except in compliance with the License. You can obtain a copy
|
---|
| 6 | * in the file LICENSE in the source distribution or at
|
---|
| 7 | * https://www.openssl.org/source/license.html
|
---|
| 8 | */
|
---|
| 9 |
|
---|
| 10 | /*
|
---|
| 11 | * Details about Montgomery multiplication algorithms can be found at
|
---|
| 12 | * http://security.ece.orst.edu/publications.html, e.g.
|
---|
| 13 | * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
|
---|
| 14 | * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
|
---|
| 15 | */
|
---|
| 16 |
|
---|
| 17 | #include "internal/cryptlib.h"
|
---|
| 18 | #include "bn_lcl.h"
|
---|
| 19 |
|
---|
| 20 | #define MONT_WORD /* use the faster word-based algorithm */
|
---|
| 21 |
|
---|
| 22 | #ifdef MONT_WORD
|
---|
| 23 | static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
|
---|
| 24 | #endif
|
---|
| 25 |
|
---|
| 26 | int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
| 27 | BN_MONT_CTX *mont, BN_CTX *ctx)
|
---|
| 28 | {
|
---|
| 29 | BIGNUM *tmp;
|
---|
| 30 | int ret = 0;
|
---|
| 31 | #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
|
---|
| 32 | int num = mont->N.top;
|
---|
| 33 |
|
---|
| 34 | if (num > 1 && a->top == num && b->top == num) {
|
---|
| 35 | if (bn_wexpand(r, num) == NULL)
|
---|
| 36 | return (0);
|
---|
| 37 | if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
|
---|
| 38 | r->neg = a->neg ^ b->neg;
|
---|
| 39 | r->top = num;
|
---|
| 40 | bn_correct_top(r);
|
---|
| 41 | return (1);
|
---|
| 42 | }
|
---|
| 43 | }
|
---|
| 44 | #endif
|
---|
| 45 |
|
---|
| 46 | BN_CTX_start(ctx);
|
---|
| 47 | tmp = BN_CTX_get(ctx);
|
---|
| 48 | if (tmp == NULL)
|
---|
| 49 | goto err;
|
---|
| 50 |
|
---|
| 51 | bn_check_top(tmp);
|
---|
| 52 | if (a == b) {
|
---|
| 53 | if (!BN_sqr(tmp, a, ctx))
|
---|
| 54 | goto err;
|
---|
| 55 | } else {
|
---|
| 56 | if (!BN_mul(tmp, a, b, ctx))
|
---|
| 57 | goto err;
|
---|
| 58 | }
|
---|
| 59 | /* reduce from aRR to aR */
|
---|
| 60 | #ifdef MONT_WORD
|
---|
| 61 | if (!BN_from_montgomery_word(r, tmp, mont))
|
---|
| 62 | goto err;
|
---|
| 63 | #else
|
---|
| 64 | if (!BN_from_montgomery(r, tmp, mont, ctx))
|
---|
| 65 | goto err;
|
---|
| 66 | #endif
|
---|
| 67 | bn_check_top(r);
|
---|
| 68 | ret = 1;
|
---|
| 69 | err:
|
---|
| 70 | BN_CTX_end(ctx);
|
---|
| 71 | return (ret);
|
---|
| 72 | }
|
---|
| 73 |
|
---|
| 74 | #ifdef MONT_WORD
|
---|
| 75 | static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
|
---|
| 76 | {
|
---|
| 77 | BIGNUM *n;
|
---|
| 78 | BN_ULONG *ap, *np, *rp, n0, v, carry;
|
---|
| 79 | int nl, max, i;
|
---|
| 80 |
|
---|
| 81 | n = &(mont->N);
|
---|
| 82 | nl = n->top;
|
---|
| 83 | if (nl == 0) {
|
---|
| 84 | ret->top = 0;
|
---|
| 85 | return (1);
|
---|
| 86 | }
|
---|
| 87 |
|
---|
| 88 | max = (2 * nl); /* carry is stored separately */
|
---|
| 89 | if (bn_wexpand(r, max) == NULL)
|
---|
| 90 | return (0);
|
---|
| 91 |
|
---|
| 92 | r->neg ^= n->neg;
|
---|
| 93 | np = n->d;
|
---|
| 94 | rp = r->d;
|
---|
| 95 |
|
---|
| 96 | /* clear the top words of T */
|
---|
| 97 | i = max - r->top;
|
---|
| 98 | if (i)
|
---|
| 99 | memset(&rp[r->top], 0, sizeof(*rp) * i);
|
---|
| 100 |
|
---|
| 101 | r->top = max;
|
---|
| 102 | n0 = mont->n0[0];
|
---|
| 103 |
|
---|
| 104 | for (carry = 0, i = 0; i < nl; i++, rp++) {
|
---|
| 105 | v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
|
---|
| 106 | v = (v + carry + rp[nl]) & BN_MASK2;
|
---|
| 107 | carry |= (v != rp[nl]);
|
---|
| 108 | carry &= (v <= rp[nl]);
|
---|
| 109 | rp[nl] = v;
|
---|
| 110 | }
|
---|
| 111 |
|
---|
| 112 | if (bn_wexpand(ret, nl) == NULL)
|
---|
| 113 | return (0);
|
---|
| 114 | ret->top = nl;
|
---|
| 115 | ret->neg = r->neg;
|
---|
| 116 |
|
---|
| 117 | rp = ret->d;
|
---|
| 118 | ap = &(r->d[nl]);
|
---|
| 119 |
|
---|
| 120 | # define BRANCH_FREE 1
|
---|
| 121 | # if BRANCH_FREE
|
---|
| 122 | {
|
---|
| 123 | BN_ULONG *nrp;
|
---|
| 124 | size_t m;
|
---|
| 125 |
|
---|
| 126 | v = bn_sub_words(rp, ap, np, nl) - carry;
|
---|
| 127 | /*
|
---|
| 128 | * if subtraction result is real, then trick unconditional memcpy
|
---|
| 129 | * below to perform in-place "refresh" instead of actual copy.
|
---|
| 130 | */
|
---|
| 131 | m = (0 - (size_t)v);
|
---|
| 132 | nrp =
|
---|
| 133 | (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
|
---|
| 134 |
|
---|
| 135 | for (i = 0, nl -= 4; i < nl; i += 4) {
|
---|
| 136 | BN_ULONG t1, t2, t3, t4;
|
---|
| 137 |
|
---|
| 138 | t1 = nrp[i + 0];
|
---|
| 139 | t2 = nrp[i + 1];
|
---|
| 140 | t3 = nrp[i + 2];
|
---|
| 141 | ap[i + 0] = 0;
|
---|
| 142 | t4 = nrp[i + 3];
|
---|
| 143 | ap[i + 1] = 0;
|
---|
| 144 | rp[i + 0] = t1;
|
---|
| 145 | ap[i + 2] = 0;
|
---|
| 146 | rp[i + 1] = t2;
|
---|
| 147 | ap[i + 3] = 0;
|
---|
| 148 | rp[i + 2] = t3;
|
---|
| 149 | rp[i + 3] = t4;
|
---|
| 150 | }
|
---|
| 151 | for (nl += 4; i < nl; i++)
|
---|
| 152 | rp[i] = nrp[i], ap[i] = 0;
|
---|
| 153 | }
|
---|
| 154 | # else
|
---|
| 155 | if (bn_sub_words(rp, ap, np, nl) - carry)
|
---|
| 156 | memcpy(rp, ap, nl * sizeof(BN_ULONG));
|
---|
| 157 | # endif
|
---|
| 158 | bn_correct_top(r);
|
---|
| 159 | bn_correct_top(ret);
|
---|
| 160 | bn_check_top(ret);
|
---|
| 161 |
|
---|
| 162 | return (1);
|
---|
| 163 | }
|
---|
| 164 | #endif /* MONT_WORD */
|
---|
| 165 |
|
---|
| 166 | int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
|
---|
| 167 | BN_CTX *ctx)
|
---|
| 168 | {
|
---|
| 169 | int retn = 0;
|
---|
| 170 | #ifdef MONT_WORD
|
---|
| 171 | BIGNUM *t;
|
---|
| 172 |
|
---|
| 173 | BN_CTX_start(ctx);
|
---|
| 174 | if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
|
---|
| 175 | retn = BN_from_montgomery_word(ret, t, mont);
|
---|
| 176 | BN_CTX_end(ctx);
|
---|
| 177 | #else /* !MONT_WORD */
|
---|
| 178 | BIGNUM *t1, *t2;
|
---|
| 179 |
|
---|
| 180 | BN_CTX_start(ctx);
|
---|
| 181 | t1 = BN_CTX_get(ctx);
|
---|
| 182 | t2 = BN_CTX_get(ctx);
|
---|
| 183 | if (t1 == NULL || t2 == NULL)
|
---|
| 184 | goto err;
|
---|
| 185 |
|
---|
| 186 | if (!BN_copy(t1, a))
|
---|
| 187 | goto err;
|
---|
| 188 | BN_mask_bits(t1, mont->ri);
|
---|
| 189 |
|
---|
| 190 | if (!BN_mul(t2, t1, &mont->Ni, ctx))
|
---|
| 191 | goto err;
|
---|
| 192 | BN_mask_bits(t2, mont->ri);
|
---|
| 193 |
|
---|
| 194 | if (!BN_mul(t1, t2, &mont->N, ctx))
|
---|
| 195 | goto err;
|
---|
| 196 | if (!BN_add(t2, a, t1))
|
---|
| 197 | goto err;
|
---|
| 198 | if (!BN_rshift(ret, t2, mont->ri))
|
---|
| 199 | goto err;
|
---|
| 200 |
|
---|
| 201 | if (BN_ucmp(ret, &(mont->N)) >= 0) {
|
---|
| 202 | if (!BN_usub(ret, ret, &(mont->N)))
|
---|
| 203 | goto err;
|
---|
| 204 | }
|
---|
| 205 | retn = 1;
|
---|
| 206 | bn_check_top(ret);
|
---|
| 207 | err:
|
---|
| 208 | BN_CTX_end(ctx);
|
---|
| 209 | #endif /* MONT_WORD */
|
---|
| 210 | return (retn);
|
---|
| 211 | }
|
---|
| 212 |
|
---|
| 213 | BN_MONT_CTX *BN_MONT_CTX_new(void)
|
---|
| 214 | {
|
---|
| 215 | BN_MONT_CTX *ret;
|
---|
| 216 |
|
---|
| 217 | if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
|
---|
| 218 | return (NULL);
|
---|
| 219 |
|
---|
| 220 | BN_MONT_CTX_init(ret);
|
---|
| 221 | ret->flags = BN_FLG_MALLOCED;
|
---|
| 222 | return (ret);
|
---|
| 223 | }
|
---|
| 224 |
|
---|
| 225 | void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
|
---|
| 226 | {
|
---|
| 227 | ctx->ri = 0;
|
---|
| 228 | bn_init(&(ctx->RR));
|
---|
| 229 | bn_init(&(ctx->N));
|
---|
| 230 | bn_init(&(ctx->Ni));
|
---|
| 231 | ctx->n0[0] = ctx->n0[1] = 0;
|
---|
| 232 | ctx->flags = 0;
|
---|
| 233 | }
|
---|
| 234 |
|
---|
| 235 | void BN_MONT_CTX_free(BN_MONT_CTX *mont)
|
---|
| 236 | {
|
---|
| 237 | if (mont == NULL)
|
---|
| 238 | return;
|
---|
| 239 |
|
---|
| 240 | BN_clear_free(&(mont->RR));
|
---|
| 241 | BN_clear_free(&(mont->N));
|
---|
| 242 | BN_clear_free(&(mont->Ni));
|
---|
| 243 | if (mont->flags & BN_FLG_MALLOCED)
|
---|
| 244 | OPENSSL_free(mont);
|
---|
| 245 | }
|
---|
| 246 |
|
---|
| 247 | int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
|
---|
| 248 | {
|
---|
| 249 | int ret = 0;
|
---|
| 250 | BIGNUM *Ri, *R;
|
---|
| 251 |
|
---|
| 252 | if (BN_is_zero(mod))
|
---|
| 253 | return 0;
|
---|
| 254 |
|
---|
| 255 | BN_CTX_start(ctx);
|
---|
| 256 | if ((Ri = BN_CTX_get(ctx)) == NULL)
|
---|
| 257 | goto err;
|
---|
| 258 | R = &(mont->RR); /* grab RR as a temp */
|
---|
| 259 | if (!BN_copy(&(mont->N), mod))
|
---|
| 260 | goto err; /* Set N */
|
---|
| 261 | mont->N.neg = 0;
|
---|
| 262 |
|
---|
| 263 | #ifdef MONT_WORD
|
---|
| 264 | {
|
---|
| 265 | BIGNUM tmod;
|
---|
| 266 | BN_ULONG buf[2];
|
---|
| 267 |
|
---|
| 268 | bn_init(&tmod);
|
---|
| 269 | tmod.d = buf;
|
---|
| 270 | tmod.dmax = 2;
|
---|
| 271 | tmod.neg = 0;
|
---|
| 272 |
|
---|
| 273 | mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
|
---|
| 274 |
|
---|
| 275 | # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
|
---|
| 276 | /*
|
---|
| 277 | * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
|
---|
| 278 | * and we could use the #else case (with a shorter R value) for the
|
---|
| 279 | * others. However, currently only the assembler files do know which
|
---|
| 280 | * is which.
|
---|
| 281 | */
|
---|
| 282 |
|
---|
| 283 | BN_zero(R);
|
---|
| 284 | if (!(BN_set_bit(R, 2 * BN_BITS2)))
|
---|
| 285 | goto err;
|
---|
| 286 |
|
---|
| 287 | tmod.top = 0;
|
---|
| 288 | if ((buf[0] = mod->d[0]))
|
---|
| 289 | tmod.top = 1;
|
---|
| 290 | if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
|
---|
| 291 | tmod.top = 2;
|
---|
| 292 |
|
---|
| 293 | if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
|
---|
| 294 | goto err;
|
---|
| 295 | if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
|
---|
| 296 | goto err; /* R*Ri */
|
---|
| 297 | if (!BN_is_zero(Ri)) {
|
---|
| 298 | if (!BN_sub_word(Ri, 1))
|
---|
| 299 | goto err;
|
---|
| 300 | } else { /* if N mod word size == 1 */
|
---|
| 301 |
|
---|
| 302 | if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
|
---|
| 303 | goto err;
|
---|
| 304 | /* Ri-- (mod double word size) */
|
---|
| 305 | Ri->neg = 0;
|
---|
| 306 | Ri->d[0] = BN_MASK2;
|
---|
| 307 | Ri->d[1] = BN_MASK2;
|
---|
| 308 | Ri->top = 2;
|
---|
| 309 | }
|
---|
| 310 | if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
|
---|
| 311 | goto err;
|
---|
| 312 | /*
|
---|
| 313 | * Ni = (R*Ri-1)/N, keep only couple of least significant words:
|
---|
| 314 | */
|
---|
| 315 | mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
|
---|
| 316 | mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
|
---|
| 317 | # else
|
---|
| 318 | BN_zero(R);
|
---|
| 319 | if (!(BN_set_bit(R, BN_BITS2)))
|
---|
| 320 | goto err; /* R */
|
---|
| 321 |
|
---|
| 322 | buf[0] = mod->d[0]; /* tmod = N mod word size */
|
---|
| 323 | buf[1] = 0;
|
---|
| 324 | tmod.top = buf[0] != 0 ? 1 : 0;
|
---|
| 325 | /* Ri = R^-1 mod N */
|
---|
| 326 | if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
|
---|
| 327 | goto err;
|
---|
| 328 | if (!BN_lshift(Ri, Ri, BN_BITS2))
|
---|
| 329 | goto err; /* R*Ri */
|
---|
| 330 | if (!BN_is_zero(Ri)) {
|
---|
| 331 | if (!BN_sub_word(Ri, 1))
|
---|
| 332 | goto err;
|
---|
| 333 | } else { /* if N mod word size == 1 */
|
---|
| 334 |
|
---|
| 335 | if (!BN_set_word(Ri, BN_MASK2))
|
---|
| 336 | goto err; /* Ri-- (mod word size) */
|
---|
| 337 | }
|
---|
| 338 | if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
|
---|
| 339 | goto err;
|
---|
| 340 | /*
|
---|
| 341 | * Ni = (R*Ri-1)/N, keep only least significant word:
|
---|
| 342 | */
|
---|
| 343 | mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
|
---|
| 344 | mont->n0[1] = 0;
|
---|
| 345 | # endif
|
---|
| 346 | }
|
---|
| 347 | #else /* !MONT_WORD */
|
---|
| 348 | { /* bignum version */
|
---|
| 349 | mont->ri = BN_num_bits(&mont->N);
|
---|
| 350 | BN_zero(R);
|
---|
| 351 | if (!BN_set_bit(R, mont->ri))
|
---|
| 352 | goto err; /* R = 2^ri */
|
---|
| 353 | /* Ri = R^-1 mod N */
|
---|
| 354 | if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
|
---|
| 355 | goto err;
|
---|
| 356 | if (!BN_lshift(Ri, Ri, mont->ri))
|
---|
| 357 | goto err; /* R*Ri */
|
---|
| 358 | if (!BN_sub_word(Ri, 1))
|
---|
| 359 | goto err;
|
---|
| 360 | /*
|
---|
| 361 | * Ni = (R*Ri-1) / N
|
---|
| 362 | */
|
---|
| 363 | if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
|
---|
| 364 | goto err;
|
---|
| 365 | }
|
---|
| 366 | #endif
|
---|
| 367 |
|
---|
| 368 | /* setup RR for conversions */
|
---|
| 369 | BN_zero(&(mont->RR));
|
---|
| 370 | if (!BN_set_bit(&(mont->RR), mont->ri * 2))
|
---|
| 371 | goto err;
|
---|
| 372 | if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
|
---|
| 373 | goto err;
|
---|
| 374 |
|
---|
| 375 | ret = 1;
|
---|
| 376 | err:
|
---|
| 377 | BN_CTX_end(ctx);
|
---|
| 378 | return ret;
|
---|
| 379 | }
|
---|
| 380 |
|
---|
| 381 | BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
|
---|
| 382 | {
|
---|
| 383 | if (to == from)
|
---|
| 384 | return (to);
|
---|
| 385 |
|
---|
| 386 | if (!BN_copy(&(to->RR), &(from->RR)))
|
---|
| 387 | return NULL;
|
---|
| 388 | if (!BN_copy(&(to->N), &(from->N)))
|
---|
| 389 | return NULL;
|
---|
| 390 | if (!BN_copy(&(to->Ni), &(from->Ni)))
|
---|
| 391 | return NULL;
|
---|
| 392 | to->ri = from->ri;
|
---|
| 393 | to->n0[0] = from->n0[0];
|
---|
| 394 | to->n0[1] = from->n0[1];
|
---|
| 395 | return (to);
|
---|
| 396 | }
|
---|
| 397 |
|
---|
| 398 | BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
|
---|
| 399 | const BIGNUM *mod, BN_CTX *ctx)
|
---|
| 400 | {
|
---|
| 401 | BN_MONT_CTX *ret;
|
---|
| 402 |
|
---|
| 403 | CRYPTO_THREAD_read_lock(lock);
|
---|
| 404 | ret = *pmont;
|
---|
| 405 | CRYPTO_THREAD_unlock(lock);
|
---|
| 406 | if (ret)
|
---|
| 407 | return ret;
|
---|
| 408 |
|
---|
| 409 | /*
|
---|
| 410 | * We don't want to serialise globally while doing our lazy-init math in
|
---|
| 411 | * BN_MONT_CTX_set. That punishes threads that are doing independent
|
---|
| 412 | * things. Instead, punish the case where more than one thread tries to
|
---|
| 413 | * lazy-init the same 'pmont', by having each do the lazy-init math work
|
---|
| 414 | * independently and only use the one from the thread that wins the race
|
---|
| 415 | * (the losers throw away the work they've done).
|
---|
| 416 | */
|
---|
| 417 | ret = BN_MONT_CTX_new();
|
---|
| 418 | if (ret == NULL)
|
---|
| 419 | return NULL;
|
---|
| 420 | if (!BN_MONT_CTX_set(ret, mod, ctx)) {
|
---|
| 421 | BN_MONT_CTX_free(ret);
|
---|
| 422 | return NULL;
|
---|
| 423 | }
|
---|
| 424 |
|
---|
| 425 | /* The locked compare-and-set, after the local work is done. */
|
---|
| 426 | CRYPTO_THREAD_write_lock(lock);
|
---|
| 427 | if (*pmont) {
|
---|
| 428 | BN_MONT_CTX_free(ret);
|
---|
| 429 | ret = *pmont;
|
---|
| 430 | } else
|
---|
| 431 | *pmont = ret;
|
---|
| 432 | CRYPTO_THREAD_unlock(lock);
|
---|
| 433 | return ret;
|
---|
| 434 | }
|
---|