crypto/bn/bn_mont.c

   1 /*
   2  * Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved.
   3  *
   4  * Licensed under the Apache License 2.0 (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_local.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     int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
  30
  31     bn_correct_top(r);
  32     bn_check_top(r);
  33
  34     return ret;
  35 }
  36
  37 int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
  38                           BN_MONT_CTX *mont, BN_CTX *ctx)
  39 {
  40     BIGNUM *tmp;
  41     int ret = 0;
  42     int num = mont->N.top;
  43
  44 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
  45     if (num > 1 && a->top == num && b->top == num) {
  46         if (bn_wexpand(r, num) == NULL)
  47             return 0;
  48         if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
  49             r->neg = a->neg ^ b->neg;
  50             r->top = num;
  51             r->flags |= BN_FLG_FIXED_TOP;
  52             return 1;
  53         }
  54     }
  55 #endif
  56
  57     if ((a->top + b->top) > 2 * num)
  58         return 0;
  59
  60     BN_CTX_start(ctx);
  61     tmp = BN_CTX_get(ctx);
  62     if (tmp == NULL)
  63         goto err;
  64
  65     bn_check_top(tmp);
  66     if (a == b) {
  67         if (!bn_sqr_fixed_top(tmp, a, ctx))
  68             goto err;
  69     } else {
  70         if (!bn_mul_fixed_top(tmp, a, b, ctx))
  71             goto err;
  72     }
  73     /* reduce from aRR to aR */
  74 #ifdef MONT_WORD
  75     if (!bn_from_montgomery_word(r, tmp, mont))
  76         goto err;
  77 #else
  78     if (!BN_from_montgomery(r, tmp, mont, ctx))
  79         goto err;
  80 #endif
  81     ret = 1;
  82  err:
  83     BN_CTX_end(ctx);
  84     return ret;
  85 }
  86
  87 #ifdef MONT_WORD
  88 static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
  89 {
  90     BIGNUM *n;
  91     BN_ULONG *ap, *np, *rp, n0, v, carry;
  92     int nl, max, i;
  93     unsigned int rtop;
  94
  95     n = &(mont->N);
  96     nl = n->top;
  97     if (nl == 0) {
  98         ret->top = 0;
  99         return 1;
 100     }
 101
 102     max = (2 * nl);             /* carry is stored separately */
 103     if (bn_wexpand(r, max) == NULL)
 104         return 0;
 105
 106     r->neg ^= n->neg;
 107     np = n->d;
 108     rp = r->d;
 109
 110     /* clear the top words of T */
 111     for (rtop = r->top, i = 0; i < max; i++) {
 112         v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));
 113         rp[i] &= v;
 114     }
 115
 116     r->top = max;
 117     r->flags |= BN_FLG_FIXED_TOP;
 118     n0 = mont->n0[0];
 119
 120     /*
 121      * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
 122      * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
 123      * includes |carry| which is stored separately.
 124      */
 125     for (carry = 0, i = 0; i < nl; i++, rp++) {
 126         v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
 127         v = (v + carry + rp[nl]) & BN_MASK2;
 128         carry |= (v != rp[nl]);
 129         carry &= (v <= rp[nl]);
 130         rp[nl] = v;
 131     }
 132
 133     if (bn_wexpand(ret, nl) == NULL)
 134         return 0;
 135     ret->top = nl;
 136     ret->flags |= BN_FLG_FIXED_TOP;
 137     ret->neg = r->neg;
 138
 139     rp = ret->d;
 140
 141     /*
 142      * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
 143      * includes |carry| which is stored separately.
 144      */
 145     ap = &(r->d[nl]);
 146
 147     carry -= bn_sub_words(rp, ap, np, nl);
 148     /*
 149      * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
 150      * |carry| cannot be 1. That would imply the subtraction did not fit in
 151      * |nl| words, and we know at most one subtraction is needed.
 152      */
 153     for (i = 0; i < nl; i++) {
 154         rp[i] = (carry & ap[i]) | (~carry & rp[i]);
 155         ap[i] = 0;
 156     }
 157
 158     return 1;
 159 }
 160 #endif                          /* MONT_WORD */
 161
 162 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 163                        BN_CTX *ctx)
 164 {
 165     int retn;
 166
 167     retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
 168     bn_correct_top(ret);
 169     bn_check_top(ret);
 170
 171     return retn;
 172 }
 173
 174 int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
 175                            BN_CTX *ctx)
 176 {
 177     int retn = 0;
 178 #ifdef MONT_WORD
 179     BIGNUM *t;
 180
 181     BN_CTX_start(ctx);
 182     if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
 183         retn = bn_from_montgomery_word(ret, t, mont);
 184     }
 185     BN_CTX_end(ctx);
 186 #else                           /* !MONT_WORD */
 187     BIGNUM *t1, *t2;
 188
 189     BN_CTX_start(ctx);
 190     t1 = BN_CTX_get(ctx);
 191     t2 = BN_CTX_get(ctx);
 192     if (t2 == NULL)
 193         goto err;
 194
 195     if (!BN_copy(t1, a))
 196         goto err;
 197     BN_mask_bits(t1, mont->ri);
 198
 199     if (!BN_mul(t2, t1, &mont->Ni, ctx))
 200         goto err;
 201     BN_mask_bits(t2, mont->ri);
 202
 203     if (!BN_mul(t1, t2, &mont->N, ctx))
 204         goto err;
 205     if (!BN_add(t2, a, t1))
 206         goto err;
 207     if (!BN_rshift(ret, t2, mont->ri))
 208         goto err;
 209
 210     if (BN_ucmp(ret, &(mont->N)) >= 0) {
 211         if (!BN_usub(ret, ret, &(mont->N)))
 212             goto err;
 213     }
 214     retn = 1;
 215     bn_check_top(ret);
 216  err:
 217     BN_CTX_end(ctx);
 218 #endif                          /* MONT_WORD */
 219     return retn;
 220 }
 221
 222 int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
 223                          BN_CTX *ctx)
 224 {
 225     return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
 226 }
 227
 228 BN_MONT_CTX *BN_MONT_CTX_new(void)
 229 {
 230     BN_MONT_CTX *ret;
 231
 232     if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
 233         ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
 234         return NULL;
 235     }
 236
 237     BN_MONT_CTX_init(ret);
 238     ret->flags = BN_FLG_MALLOCED;
 239     return ret;
 240 }
 241
 242 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
 243 {
 244     ctx->ri = 0;
 245     bn_init(&ctx->RR);
 246     bn_init(&ctx->N);
 247     bn_init(&ctx->Ni);
 248     ctx->n0[0] = ctx->n0[1] = 0;
 249     ctx->flags = 0;
 250 }
 251
 252 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
 253 {
 254     if (mont == NULL)
 255         return;
 256     BN_clear_free(&mont->RR);
 257     BN_clear_free(&mont->N);
 258     BN_clear_free(&mont->Ni);
 259     if (mont->flags & BN_FLG_MALLOCED)
 260         OPENSSL_free(mont);
 261 }
 262
 263 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
 264 {
 265     int i, ret = 0;
 266     BIGNUM *Ri, *R;
 267
 268     if (BN_is_zero(mod))
 269         return 0;
 270
 271     BN_CTX_start(ctx);
 272     if ((Ri = BN_CTX_get(ctx)) == NULL)
 273         goto err;
 274     R = &(mont->RR);            /* grab RR as a temp */
 275     if (!BN_copy(&(mont->N), mod))
 276         goto err;               /* Set N */
 277     if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
 278         BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
 279     mont->N.neg = 0;
 280
 281 #ifdef MONT_WORD
 282     {
 283         BIGNUM tmod;
 284         BN_ULONG buf[2];
 285
 286         bn_init(&tmod);
 287         tmod.d = buf;
 288         tmod.dmax = 2;
 289         tmod.neg = 0;
 290
 291         if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
 292             BN_set_flags(&tmod, BN_FLG_CONSTTIME);
 293
 294         mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
 295
 296 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
 297         /*
 298          * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
 299          * and we could use the #else case (with a shorter R value) for the
 300          * others.  However, currently only the assembler files do know which
 301          * is which.
 302          */
 303
 304         BN_zero(R);
 305         if (!(BN_set_bit(R, 2 * BN_BITS2)))
 306             goto err;
 307
 308         tmod.top = 0;
 309         if ((buf[0] = mod->d[0]))
 310             tmod.top = 1;
 311         if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
 312             tmod.top = 2;
 313
 314         if (BN_is_one(&tmod))
 315             BN_zero(Ri);
 316         else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
 317             goto err;
 318         if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
 319             goto err;           /* R*Ri */
 320         if (!BN_is_zero(Ri)) {
 321             if (!BN_sub_word(Ri, 1))
 322                 goto err;
 323         } else {                /* if N mod word size == 1 */
 324
 325             if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
 326                 goto err;
 327             /* Ri-- (mod double word size) */
 328             Ri->neg = 0;
 329             Ri->d[0] = BN_MASK2;
 330             Ri->d[1] = BN_MASK2;
 331             Ri->top = 2;
 332         }
 333         if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
 334             goto err;
 335         /*
 336          * Ni = (R*Ri-1)/N, keep only couple of least significant words:
 337          */
 338         mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 339         mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
 340 # else
 341         BN_zero(R);
 342         if (!(BN_set_bit(R, BN_BITS2)))
 343             goto err;           /* R */
 344
 345         buf[0] = mod->d[0];     /* tmod = N mod word size */
 346         buf[1] = 0;
 347         tmod.top = buf[0] != 0 ? 1 : 0;
 348         /* Ri = R^-1 mod N */
 349         if (BN_is_one(&tmod))
 350             BN_zero(Ri);
 351         else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
 352             goto err;
 353         if (!BN_lshift(Ri, Ri, BN_BITS2))
 354             goto err;           /* R*Ri */
 355         if (!BN_is_zero(Ri)) {
 356             if (!BN_sub_word(Ri, 1))
 357                 goto err;
 358         } else {                /* if N mod word size == 1 */
 359
 360             if (!BN_set_word(Ri, BN_MASK2))
 361                 goto err;       /* Ri-- (mod word size) */
 362         }
 363         if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
 364             goto err;
 365         /*
 366          * Ni = (R*Ri-1)/N, keep only least significant word:
 367          */
 368         mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
 369         mont->n0[1] = 0;
 370 # endif
 371     }
 372 #else                           /* !MONT_WORD */
 373     {                           /* bignum version */
 374         mont->ri = BN_num_bits(&mont->N);
 375         BN_zero(R);
 376         if (!BN_set_bit(R, mont->ri))
 377             goto err;           /* R = 2^ri */
 378         /* Ri = R^-1 mod N */
 379         if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
 380             goto err;
 381         if (!BN_lshift(Ri, Ri, mont->ri))
 382             goto err;           /* R*Ri */
 383         if (!BN_sub_word(Ri, 1))
 384             goto err;
 385         /*
 386          * Ni = (R*Ri-1) / N
 387          */
 388         if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
 389             goto err;
 390     }
 391 #endif
 392
 393     /* setup RR for conversions */
 394     BN_zero(&(mont->RR));
 395     if (!BN_set_bit(&(mont->RR), mont->ri * 2))
 396         goto err;
 397     if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
 398         goto err;
 399
 400     for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
 401         mont->RR.d[i] = 0;
 402     mont->RR.top = ret;
 403     mont->RR.flags |= BN_FLG_FIXED_TOP;
 404
 405     ret = 1;
 406  err:
 407     BN_CTX_end(ctx);
 408     return ret;
 409 }
 410
 411 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
 412 {
 413     if (to == from)
 414         return to;
 415
 416     if (!BN_copy(&(to->RR), &(from->RR)))
 417         return NULL;
 418     if (!BN_copy(&(to->N), &(from->N)))
 419         return NULL;
 420     if (!BN_copy(&(to->Ni), &(from->Ni)))
 421         return NULL;
 422     to->ri = from->ri;
 423     to->n0[0] = from->n0[0];
 424     to->n0[1] = from->n0[1];
 425     return to;
 426 }
 427
 428 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
 429                                     const BIGNUM *mod, BN_CTX *ctx)
 430 {
 431     BN_MONT_CTX *ret;
 432
 433     CRYPTO_THREAD_read_lock(lock);
 434     ret = *pmont;
 435     CRYPTO_THREAD_unlock(lock);
 436     if (ret)
 437         return ret;
 438
 439     /*
 440      * We don't want to serialize globally while doing our lazy-init math in
 441      * BN_MONT_CTX_set. That punishes threads that are doing independent
 442      * things. Instead, punish the case where more than one thread tries to
 443      * lazy-init the same 'pmont', by having each do the lazy-init math work
 444      * independently and only use the one from the thread that wins the race
 445      * (the losers throw away the work they've done).
 446      */
 447     ret = BN_MONT_CTX_new();
 448     if (ret == NULL)
 449         return NULL;
 450     if (!BN_MONT_CTX_set(ret, mod, ctx)) {
 451         BN_MONT_CTX_free(ret);
 452         return NULL;
 453     }
 454
 455     /* The locked compare-and-set, after the local work is done. */
 456     CRYPTO_THREAD_write_lock(lock);
 457     if (*pmont) {
 458         BN_MONT_CTX_free(ret);
 459         ret = *pmont;
 460     } else
 461         *pmont = ret;
 462     CRYPTO_THREAD_unlock(lock);
 463     return ret;
 464 }