crypto/bn/bn_mont.c

   1 /*
   2  * Copyright 1995-2018 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     int num = mont->N.top;
  32
  33 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
  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     if ((a->top + b->top) > 2 * num)
  47         return 0;
  48
  49     BN_CTX_start(ctx);
  50     tmp = BN_CTX_get(ctx);
  51     if (tmp == NULL)
  52         goto err;
  53
  54     bn_check_top(tmp);
  55     if (a == b) {
  56         if (!BN_sqr(tmp, a, ctx))
  57             goto err;
  58     } else {
  59         if (!BN_mul(tmp, a, b, ctx))
  60             goto err;
  61     }
  62     /* reduce from aRR to aR */
  63 #ifdef MONT_WORD
  64     if (!BN_from_montgomery_word(r, tmp, mont))
  65         goto err;
  66 #else
  67     if (!BN_from_montgomery(r, tmp, mont, ctx))
  68         goto err;
  69 #endif
  70     bn_check_top(r);
  71     ret = 1;
  72  err:
  73     BN_CTX_end(ctx);
  74     return ret;
  75 }
  76
  77 #ifdef MONT_WORD
  78 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
  79 {
  80     BIGNUM *n;
  81     BN_ULONG *ap, *np, *rp, n0, v, carry;
  82     int nl, max, i;
  83
  84     n = &(mont->N);
  85     nl = n->top;
  86     if (nl == 0) {
  87         ret->top = 0;
  88         return 1;
  89     }
  90
  91     max = (2 * nl);             /* carry is stored separately */
  92     if (bn_wexpand(r, max) == NULL)
  93         return 0;
  94
  95     r->neg ^= n->neg;
  96     np = n->d;
  97     rp = r->d;
  98
  99     /* clear the top words of T */
 100     i = max - r->top;
 101     if (i)
 102         memset(&rp[r->top], 0, sizeof(*rp) * i);
 103
 104     r->top = max;
 105     n0 = mont->n0[0];
 106
 107     /*
 108      * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
 109      * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
 110      * includes |carry| which is stored separately.
 111      */
 112     for (carry = 0, i = 0; i < nl; i++, rp++) {
 113         v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
 114         v = (v + carry + rp[nl]) & BN_MASK2;
 115         carry |= (v != rp[nl]);
 116         carry &= (v <= rp[nl]);
 117         rp[nl] = v;
 118     }
 119
 120     if (bn_wexpand(ret, nl) == NULL)
 121         return 0;
 122     ret->top = nl;
 123     ret->neg = r->neg;
 124
 125     rp = ret->d;
 126
 127     /*
 128      * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
 129      * includes |carry| which is stored separately.
 130      */
 131     ap = &(r->d[nl]);
 132
 133     /*
 134      * |v| is one if |ap| - |np| underflowed or zero if it did not. Note |v|
 135      * cannot be -1. That would imply the subtraction did not fit in |nl| words,
 136      * and we know at most one subtraction is needed.
 137      */
 138     v = bn_sub_words(rp, ap, np, nl) - carry;
 139     v = 0 - v;
 140     for (i = 0; i < nl; i++) {
 141         rp[i] = (v & ap[i]) | (~v & rp[i]);
 142         ap[i] = 0;
 143     }
 144     bn_correct_top(r);
 145     bn_correct_top(ret);
 146     bn_check_top(ret);
 147
 148     return 1;
 149 }
 150 #endif                          /* MONT_WORD */
 151
 152 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 153                        BN_CTX *ctx)
 154 {
 155     int retn = 0;
 156 #ifdef MONT_WORD
 157     BIGNUM *t;
 158
 159     BN_CTX_start(ctx);
 160     if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
 161         retn = BN_from_montgomery_word(ret, t, mont);
 162     BN_CTX_end(ctx);
 163 #else                           /* !MONT_WORD */
 164     BIGNUM *t1, *t2;
 165
 166     BN_CTX_start(ctx);
 167     t1 = BN_CTX_get(ctx);
 168     t2 = BN_CTX_get(ctx);
 169     if (t2 == NULL)
 170         goto err;
 171
 172     if (!BN_copy(t1, a))
 173         goto err;
 174     BN_mask_bits(t1, mont->ri);
 175
 176     if (!BN_mul(t2, t1, &mont->Ni, ctx))
 177         goto err;
 178     BN_mask_bits(t2, mont->ri);
 179
 180     if (!BN_mul(t1, t2, &mont->N, ctx))
 181         goto err;
 182     if (!BN_add(t2, a, t1))
 183         goto err;
 184     if (!BN_rshift(ret, t2, mont->ri))
 185         goto err;
 186
 187     if (BN_ucmp(ret, &(mont->N)) >= 0) {
 188         if (!BN_usub(ret, ret, &(mont->N)))
 189             goto err;
 190     }
 191     retn = 1;
 192     bn_check_top(ret);
 193  err:
 194     BN_CTX_end(ctx);
 195 #endif                          /* MONT_WORD */
 196     return retn;
 197 }
 198
 199 BN_MONT_CTX *BN_MONT_CTX_new(void)
 200 {
 201     BN_MONT_CTX *ret;
 202
 203     if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
 204         BNerr(BN_F_BN_MONT_CTX_NEW, ERR_R_MALLOC_FAILURE);
 205         return NULL;
 206     }
 207
 208     BN_MONT_CTX_init(ret);
 209     ret->flags = BN_FLG_MALLOCED;
 210     return ret;
 211 }
 212
 213 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 214 {
 215     ctx->ri = 0;
 216     bn_init(&ctx->RR);
 217     bn_init(&ctx->N);
 218     bn_init(&ctx->Ni);
 219     ctx->n0[0] = ctx->n0[1] = 0;
 220     ctx->flags = 0;
 221 }
 222
 223 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 224 {
 225     if (mont == NULL)
 226         return;
 227     BN_clear_free(&mont->RR);
 228     BN_clear_free(&mont->N);
 229     BN_clear_free(&mont->Ni);
 230     if (mont->flags & BN_FLG_MALLOCED)
 231         OPENSSL_free(mont);
 232 }
 233
 234 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 235 {
 236     int ret = 0;
 237     BIGNUM *Ri, *R;
 238
 239     if (BN_is_zero(mod))
 240         return 0;
 241
 242     BN_CTX_start(ctx);
 243     if ((Ri = BN_CTX_get(ctx)) == NULL)
 244         goto err;
 245     R = &(mont->RR);            /* grab RR as a temp */
 246     if (!BN_copy(&(mont->N), mod))
 247         goto err;               /* Set N */
 248     if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
 249         BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
 250     mont->N.neg = 0;
 251
 252 #ifdef MONT_WORD
 253     {
 254         BIGNUM tmod;
 255         BN_ULONG buf[2];
 256
 257         bn_init(&tmod);
 258         tmod.d = buf;
 259         tmod.dmax = 2;
 260         tmod.neg = 0;
 261
 262         if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
 263             BN_set_flags(&tmod, BN_FLG_CONSTTIME);
 264
 265         mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
 266
 267 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
 268         /*
 269          * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
 270          * and we could use the #else case (with a shorter R value) for the
 271          * others.  However, currently only the assembler files do know which
 272          * is which.
 273          */
 274
 275         BN_zero(R);
 276         if (!(BN_set_bit(R, 2 * BN_BITS2)))
 277             goto err;
 278
 279         tmod.top = 0;
 280         if ((buf[0] = mod->d[0]))
 281             tmod.top = 1;
 282         if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
 283             tmod.top = 2;
 284
 285         if (BN_is_one(&tmod))
 286             BN_zero(Ri);
 287         else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
 288             goto err;
 289         if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
 290             goto err;           /* R*Ri */
 291         if (!BN_is_zero(Ri)) {
 292             if (!BN_sub_word(Ri, 1))
 293                 goto err;
 294         } else {                /* if N mod word size == 1 */
 295
 296             if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
 297                 goto err;
 298             /* Ri-- (mod double word size) */
 299             Ri->neg = 0;
 300             Ri->d[0] = BN_MASK2;
 301             Ri->d[1] = BN_MASK2;
 302             Ri->top = 2;
 303         }
 304         if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
 305             goto err;
 306         /*
 307          * Ni = (R*Ri-1)/N, keep only couple of least significant words:
 308          */
 309         mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 310         mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
 311 # else
 312         BN_zero(R);
 313         if (!(BN_set_bit(R, BN_BITS2)))
 314             goto err;           /* R */
 315
 316         buf[0] = mod->d[0];     /* tmod = N mod word size */
 317         buf[1] = 0;
 318         tmod.top = buf[0] != 0 ? 1 : 0;
 319         /* Ri = R^-1 mod N */
 320         if (BN_is_one(&tmod))
 321             BN_zero(Ri);
 322         else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
 323             goto err;
 324         if (!BN_lshift(Ri, Ri, BN_BITS2))
 325             goto err;           /* R*Ri */
 326         if (!BN_is_zero(Ri)) {
 327             if (!BN_sub_word(Ri, 1))
 328                 goto err;
 329         } else {                /* if N mod word size == 1 */
 330
 331             if (!BN_set_word(Ri, BN_MASK2))
 332                 goto err;       /* Ri-- (mod word size) */
 333         }
 334         if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
 335             goto err;
 336         /*
 337          * Ni = (R*Ri-1)/N, keep only least significant word:
 338          */
 339         mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 340         mont->n0[1] = 0;
 341 # endif
 342     }
 343 #else                           /* !MONT_WORD */
 344     {                           /* bignum version */
 345         mont->ri = BN_num_bits(&mont->N);
 346         BN_zero(R);
 347         if (!BN_set_bit(R, mont->ri))
 348             goto err;           /* R = 2^ri */
 349         /* Ri = R^-1 mod N */
 350         if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
 351             goto err;
 352         if (!BN_lshift(Ri, Ri, mont->ri))
 353             goto err;           /* R*Ri */
 354         if (!BN_sub_word(Ri, 1))
 355             goto err;
 356         /*
 357          * Ni = (R*Ri-1) / N
 358          */
 359         if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
 360             goto err;
 361     }
 362 #endif
 363
 364     /* setup RR for conversions */
 365     BN_zero(&(mont->RR));
 366     if (!BN_set_bit(&(mont->RR), mont->ri * 2))
 367         goto err;
 368     if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
 369         goto err;
 370
 371     ret = 1;
 372  err:
 373     BN_CTX_end(ctx);
 374     return ret;
 375 }
 376
 377 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 378 {
 379     if (to == from)
 380         return to;
 381
 382     if (!BN_copy(&(to->RR), &(from->RR)))
 383         return NULL;
 384     if (!BN_copy(&(to->N), &(from->N)))
 385         return NULL;
 386     if (!BN_copy(&(to->Ni), &(from->Ni)))
 387         return NULL;
 388     to->ri = from->ri;
 389     to->n0[0] = from->n0[0];
 390     to->n0[1] = from->n0[1];
 391     return to;
 392 }
 393
 394 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
 395                                     const BIGNUM *mod, BN_CTX *ctx)
 396 {
 397     BN_MONT_CTX *ret;
 398
 399     CRYPTO_THREAD_read_lock(lock);
 400     ret = *pmont;
 401     CRYPTO_THREAD_unlock(lock);
 402     if (ret)
 403         return ret;
 404
 405     /*
 406      * We don't want to serialise globally while doing our lazy-init math in
 407      * BN_MONT_CTX_set. That punishes threads that are doing independent
 408      * things. Instead, punish the case where more than one thread tries to
 409      * lazy-init the same 'pmont', by having each do the lazy-init math work
 410      * independently and only use the one from the thread that wins the race
 411      * (the losers throw away the work they've done).
 412      */
 413     ret = BN_MONT_CTX_new();
 414     if (ret == NULL)
 415         return NULL;
 416     if (!BN_MONT_CTX_set(ret, mod, ctx)) {
 417         BN_MONT_CTX_free(ret);
 418         return NULL;
 419     }
 420
 421     /* The locked compare-and-set, after the local work is done. */
 422     CRYPTO_THREAD_write_lock(lock);
 423     if (*pmont) {
 424         BN_MONT_CTX_free(ret);
 425         ret = *pmont;
 426     } else
 427         *pmont = ret;
 428     CRYPTO_THREAD_unlock(lock);
 429     return ret;
 430 }