2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
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
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)
29 int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
37 int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
38 BN_MONT_CTX *mont, BN_CTX *ctx)
42 int num = mont->N.top;
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)
48 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
49 r->neg = a->neg ^ b->neg;
51 r->flags |= BN_FLG_FIXED_TOP;
57 if ((a->top + b->top) > 2 * num)
61 tmp = BN_CTX_get(ctx);
67 if (!bn_sqr_fixed_top(tmp, a, ctx))
70 if (!bn_mul_fixed_top(tmp, a, b, ctx))
73 /* reduce from aRR to aR */
75 if (!bn_from_montgomery_word(r, tmp, mont))
78 if (!BN_from_montgomery(r, tmp, mont, ctx))
88 static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
91 BN_ULONG *ap, *np, *rp, n0, v, carry;
102 max = (2 * nl); /* carry is stored separately */
103 if (bn_wexpand(r, max) == NULL)
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));
117 r->flags |= BN_FLG_FIXED_TOP;
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.
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]);
133 if (bn_wexpand(ret, nl) == NULL)
136 ret->flags |= BN_FLG_FIXED_TOP;
142 * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
143 * includes |carry| which is stored separately.
147 carry -= bn_sub_words(rp, ap, np, nl);
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.
153 for (i = 0; i < nl; i++) {
154 rp[i] = (carry & ap[i]) | (~carry & rp[i]);
160 #endif /* MONT_WORD */
162 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
167 retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
174 int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
182 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
183 retn = bn_from_montgomery_word(ret, t, mont);
186 #else /* !MONT_WORD */
190 t1 = BN_CTX_get(ctx);
191 t2 = BN_CTX_get(ctx);
197 BN_mask_bits(t1, mont->ri);
199 if (!BN_mul(t2, t1, &mont->Ni, ctx))
201 BN_mask_bits(t2, mont->ri);
203 if (!BN_mul(t1, t2, &mont->N, ctx))
205 if (!BN_add(t2, a, t1))
207 if (!BN_rshift(ret, t2, mont->ri))
210 if (BN_ucmp(ret, &(mont->N)) >= 0) {
211 if (!BN_usub(ret, ret, &(mont->N)))
218 #endif /* MONT_WORD */
222 int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
225 return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
228 BN_MONT_CTX *BN_MONT_CTX_new(void)
232 if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
233 BNerr(BN_F_BN_MONT_CTX_NEW, ERR_R_MALLOC_FAILURE);
237 BN_MONT_CTX_init(ret);
238 ret->flags = BN_FLG_MALLOCED;
242 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
248 ctx->n0[0] = ctx->n0[1] = 0;
252 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
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)
263 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
272 if ((Ri = BN_CTX_get(ctx)) == NULL)
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);
291 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
292 BN_set_flags(&tmod, BN_FLG_CONSTTIME);
294 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
296 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
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
305 if (!(BN_set_bit(R, 2 * BN_BITS2)))
309 if ((buf[0] = mod->d[0]))
311 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
314 if (BN_is_one(&tmod))
316 else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
318 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
320 if (!BN_is_zero(Ri)) {
321 if (!BN_sub_word(Ri, 1))
323 } else { /* if N mod word size == 1 */
325 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
327 /* Ri-- (mod double word size) */
333 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
336 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
338 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
339 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
342 if (!(BN_set_bit(R, BN_BITS2)))
345 buf[0] = mod->d[0]; /* tmod = N mod word size */
347 tmod.top = buf[0] != 0 ? 1 : 0;
348 /* Ri = R^-1 mod N */
349 if (BN_is_one(&tmod))
351 else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
353 if (!BN_lshift(Ri, Ri, BN_BITS2))
355 if (!BN_is_zero(Ri)) {
356 if (!BN_sub_word(Ri, 1))
358 } else { /* if N mod word size == 1 */
360 if (!BN_set_word(Ri, BN_MASK2))
361 goto err; /* Ri-- (mod word size) */
363 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
366 * Ni = (R*Ri-1)/N, keep only least significant word:
368 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
372 #else /* !MONT_WORD */
373 { /* bignum version */
374 mont->ri = BN_num_bits(&mont->N);
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)
381 if (!BN_lshift(Ri, Ri, mont->ri))
383 if (!BN_sub_word(Ri, 1))
388 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
393 /* setup RR for conversions */
394 BN_zero(&(mont->RR));
395 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
397 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
400 for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
403 mont->RR.flags |= BN_FLG_FIXED_TOP;
411 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
416 if (!BN_copy(&(to->RR), &(from->RR)))
418 if (!BN_copy(&(to->N), &(from->N)))
420 if (!BN_copy(&(to->Ni), &(from->Ni)))
423 to->n0[0] = from->n0[0];
424 to->n0[1] = from->n0[1];
428 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
429 const BIGNUM *mod, BN_CTX *ctx)
433 CRYPTO_THREAD_read_lock(lock);
435 CRYPTO_THREAD_unlock(lock);
440 * We don't want to serialise 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).
447 ret = BN_MONT_CTX_new();
450 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
451 BN_MONT_CTX_free(ret);
455 /* The locked compare-and-set, after the local work is done. */
456 CRYPTO_THREAD_write_lock(lock);
458 BN_MONT_CTX_free(ret);
462 CRYPTO_THREAD_unlock(lock);