2 * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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
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
17 #include "internal/cryptlib.h"
20 #define MONT_WORD /* use the faster word-based algorithm */
23 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
26 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
27 BN_MONT_CTX *mont, BN_CTX *ctx)
31 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
32 int num = mont->N.top;
34 if (num > 1 && a->top == num && b->top == num) {
35 if (bn_wexpand(r, num) == NULL)
37 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
38 r->neg = a->neg ^ b->neg;
47 tmp = BN_CTX_get(ctx);
53 if (!BN_sqr(tmp, a, ctx))
56 if (!BN_mul(tmp, a, b, ctx))
59 /* reduce from aRR to aR */
61 if (!BN_from_montgomery_word(r, tmp, mont))
64 if (!BN_from_montgomery(r, tmp, mont, ctx))
75 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
78 BN_ULONG *ap, *np, *rp, n0, v, carry;
88 max = (2 * nl); /* carry is stored separately */
89 if (bn_wexpand(r, max) == NULL)
96 /* clear the top words of T */
99 memset(&rp[r->top], 0, sizeof(*rp) * i);
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]);
112 if (bn_wexpand(ret, nl) == NULL)
120 # define BRANCH_FREE 1
126 v = bn_sub_words(rp, ap, np, nl) - carry;
128 * if subtraction result is real, then trick unconditional memcpy
129 * below to perform in-place "refresh" instead of actual copy.
133 (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
135 for (i = 0, nl -= 4; i < nl; i += 4) {
136 BN_ULONG t1, t2, t3, t4;
151 for (nl += 4; i < nl; i++)
152 rp[i] = nrp[i], ap[i] = 0;
155 if (bn_sub_words(rp, ap, np, nl) - carry)
156 memcpy(rp, ap, nl * sizeof(BN_ULONG));
164 #endif /* MONT_WORD */
166 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
174 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
175 retn = BN_from_montgomery_word(ret, t, mont);
177 #else /* !MONT_WORD */
181 t1 = BN_CTX_get(ctx);
182 t2 = BN_CTX_get(ctx);
183 if (t1 == NULL || t2 == NULL)
188 BN_mask_bits(t1, mont->ri);
190 if (!BN_mul(t2, t1, &mont->Ni, ctx))
192 BN_mask_bits(t2, mont->ri);
194 if (!BN_mul(t1, t2, &mont->N, ctx))
196 if (!BN_add(t2, a, t1))
198 if (!BN_rshift(ret, t2, mont->ri))
201 if (BN_ucmp(ret, &(mont->N)) >= 0) {
202 if (!BN_usub(ret, ret, &(mont->N)))
209 #endif /* MONT_WORD */
213 BN_MONT_CTX *BN_MONT_CTX_new(void)
217 if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
220 BN_MONT_CTX_init(ret);
221 ret->flags = BN_FLG_MALLOCED;
225 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
231 ctx->n0[0] = ctx->n0[1] = 0;
235 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
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)
247 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
256 if ((Ri = BN_CTX_get(ctx)) == NULL)
258 R = &(mont->RR); /* grab RR as a temp */
259 if (!BN_copy(&(mont->N), mod))
260 goto err; /* Set N */
273 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
275 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
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
284 if (!(BN_set_bit(R, 2 * BN_BITS2)))
288 if ((buf[0] = mod->d[0]))
290 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
293 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
295 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
297 if (!BN_is_zero(Ri)) {
298 if (!BN_sub_word(Ri, 1))
300 } else { /* if N mod word size == 1 */
302 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
304 /* Ri-- (mod double word size) */
310 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
313 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
315 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
316 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
319 if (!(BN_set_bit(R, BN_BITS2)))
322 buf[0] = mod->d[0]; /* tmod = N mod word size */
324 tmod.top = buf[0] != 0 ? 1 : 0;
325 /* Ri = R^-1 mod N */
326 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
328 if (!BN_lshift(Ri, Ri, BN_BITS2))
330 if (!BN_is_zero(Ri)) {
331 if (!BN_sub_word(Ri, 1))
333 } else { /* if N mod word size == 1 */
335 if (!BN_set_word(Ri, BN_MASK2))
336 goto err; /* Ri-- (mod word size) */
338 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
341 * Ni = (R*Ri-1)/N, keep only least significant word:
343 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
347 #else /* !MONT_WORD */
348 { /* bignum version */
349 mont->ri = BN_num_bits(&mont->N);
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)
356 if (!BN_lshift(Ri, Ri, mont->ri))
358 if (!BN_sub_word(Ri, 1))
363 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
368 /* setup RR for conversions */
369 BN_zero(&(mont->RR));
370 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
372 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
381 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
386 if (!BN_copy(&(to->RR), &(from->RR)))
388 if (!BN_copy(&(to->N), &(from->N)))
390 if (!BN_copy(&(to->Ni), &(from->Ni)))
393 to->n0[0] = from->n0[0];
394 to->n0[1] = from->n0[1];
398 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
399 const BIGNUM *mod, BN_CTX *ctx)
403 CRYPTO_THREAD_read_lock(lock);
405 CRYPTO_THREAD_unlock(lock);
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).
417 ret = BN_MONT_CTX_new();
420 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
421 BN_MONT_CTX_free(ret);
425 /* The locked compare-and-set, after the local work is done. */
426 CRYPTO_THREAD_write_lock(lock);
428 BN_MONT_CTX_free(ret);
432 CRYPTO_THREAD_unlock(lock);