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464 lines
12 KiB
C
464 lines
12 KiB
C
/*
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* Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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/*
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* Details about Montgomery multiplication algorithms can be found at
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* http://security.ece.orst.edu/publications.html, e.g.
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* http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
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* sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
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*/
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#include "internal/cryptlib.h"
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#include "bn_lcl.h"
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#define MONT_WORD /* use the faster word-based algorithm */
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#ifdef MONT_WORD
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static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
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#endif
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int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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BN_MONT_CTX *mont, BN_CTX *ctx)
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{
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int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
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bn_correct_top(r);
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bn_check_top(r);
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return ret;
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}
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int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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BN_MONT_CTX *mont, BN_CTX *ctx)
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{
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BIGNUM *tmp;
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int ret = 0;
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int num = mont->N.top;
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#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
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if (num > 1 && a->top == num && b->top == num) {
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if (bn_wexpand(r, num) == NULL)
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return 0;
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if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
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r->neg = a->neg ^ b->neg;
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r->top = num;
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r->flags |= BN_FLG_FIXED_TOP;
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return 1;
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}
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}
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#endif
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if ((a->top + b->top) > 2 * num)
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return 0;
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BN_CTX_start(ctx);
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tmp = BN_CTX_get(ctx);
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if (tmp == NULL)
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goto err;
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bn_check_top(tmp);
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if (a == b) {
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if (!bn_sqr_fixed_top(tmp, a, ctx))
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goto err;
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} else {
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if (!bn_mul_fixed_top(tmp, a, b, ctx))
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goto err;
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}
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/* reduce from aRR to aR */
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#ifdef MONT_WORD
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if (!bn_from_montgomery_word(r, tmp, mont))
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goto err;
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#else
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if (!BN_from_montgomery(r, tmp, mont, ctx))
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goto err;
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#endif
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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#ifdef MONT_WORD
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static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
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{
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BIGNUM *n;
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BN_ULONG *ap, *np, *rp, n0, v, carry;
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int nl, max, i;
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unsigned int rtop;
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n = &(mont->N);
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nl = n->top;
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if (nl == 0) {
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ret->top = 0;
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return 1;
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}
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max = (2 * nl); /* carry is stored separately */
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if (bn_wexpand(r, max) == NULL)
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return 0;
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r->neg ^= n->neg;
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np = n->d;
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rp = r->d;
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/* clear the top words of T */
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for (rtop = r->top, i = 0; i < max; i++) {
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v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));
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rp[i] &= v;
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}
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r->top = max;
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r->flags |= BN_FLG_FIXED_TOP;
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n0 = mont->n0[0];
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/*
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* Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
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* input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
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* includes |carry| which is stored separately.
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*/
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for (carry = 0, i = 0; i < nl; i++, rp++) {
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v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
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v = (v + carry + rp[nl]) & BN_MASK2;
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carry |= (v != rp[nl]);
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carry &= (v <= rp[nl]);
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rp[nl] = v;
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}
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if (bn_wexpand(ret, nl) == NULL)
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return 0;
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ret->top = nl;
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ret->flags |= BN_FLG_FIXED_TOP;
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ret->neg = r->neg;
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rp = ret->d;
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/*
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* Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
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* includes |carry| which is stored separately.
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*/
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ap = &(r->d[nl]);
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carry -= bn_sub_words(rp, ap, np, nl);
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/*
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* |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
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* |carry| cannot be 1. That would imply the subtraction did not fit in
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* |nl| words, and we know at most one subtraction is needed.
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*/
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for (i = 0; i < nl; i++) {
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rp[i] = (carry & ap[i]) | (~carry & rp[i]);
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ap[i] = 0;
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}
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return 1;
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}
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#endif /* MONT_WORD */
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int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
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BN_CTX *ctx)
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{
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int retn;
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retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
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bn_correct_top(ret);
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bn_check_top(ret);
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return retn;
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}
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int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
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BN_CTX *ctx)
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{
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int retn = 0;
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#ifdef MONT_WORD
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BIGNUM *t;
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BN_CTX_start(ctx);
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if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
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retn = bn_from_montgomery_word(ret, t, mont);
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}
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BN_CTX_end(ctx);
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#else /* !MONT_WORD */
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BIGNUM *t1, *t2;
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BN_CTX_start(ctx);
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t1 = BN_CTX_get(ctx);
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t2 = BN_CTX_get(ctx);
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if (t2 == NULL)
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goto err;
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if (!BN_copy(t1, a))
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goto err;
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BN_mask_bits(t1, mont->ri);
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if (!BN_mul(t2, t1, &mont->Ni, ctx))
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goto err;
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BN_mask_bits(t2, mont->ri);
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if (!BN_mul(t1, t2, &mont->N, ctx))
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goto err;
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if (!BN_add(t2, a, t1))
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goto err;
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if (!BN_rshift(ret, t2, mont->ri))
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goto err;
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if (BN_ucmp(ret, &(mont->N)) >= 0) {
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if (!BN_usub(ret, ret, &(mont->N)))
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goto err;
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}
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retn = 1;
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bn_check_top(ret);
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err:
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BN_CTX_end(ctx);
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#endif /* MONT_WORD */
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return retn;
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}
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int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
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BN_CTX *ctx)
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{
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return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
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}
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BN_MONT_CTX *BN_MONT_CTX_new(void)
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{
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BN_MONT_CTX *ret;
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if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
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BNerr(BN_F_BN_MONT_CTX_NEW, ERR_R_MALLOC_FAILURE);
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return NULL;
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}
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BN_MONT_CTX_init(ret);
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ret->flags = BN_FLG_MALLOCED;
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return ret;
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}
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void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
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{
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ctx->ri = 0;
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bn_init(&ctx->RR);
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bn_init(&ctx->N);
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bn_init(&ctx->Ni);
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ctx->n0[0] = ctx->n0[1] = 0;
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ctx->flags = 0;
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}
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void BN_MONT_CTX_free(BN_MONT_CTX *mont)
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{
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if (mont == NULL)
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return;
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BN_clear_free(&mont->RR);
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BN_clear_free(&mont->N);
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BN_clear_free(&mont->Ni);
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if (mont->flags & BN_FLG_MALLOCED)
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OPENSSL_free(mont);
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}
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int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
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{
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int i, ret = 0;
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BIGNUM *Ri, *R;
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if (BN_is_zero(mod))
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return 0;
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BN_CTX_start(ctx);
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if ((Ri = BN_CTX_get(ctx)) == NULL)
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goto err;
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R = &(mont->RR); /* grab RR as a temp */
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if (!BN_copy(&(mont->N), mod))
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goto err; /* Set N */
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if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
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BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
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mont->N.neg = 0;
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#ifdef MONT_WORD
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{
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BIGNUM tmod;
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BN_ULONG buf[2];
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bn_init(&tmod);
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tmod.d = buf;
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tmod.dmax = 2;
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tmod.neg = 0;
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if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
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BN_set_flags(&tmod, BN_FLG_CONSTTIME);
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mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
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# if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
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/*
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* Only certain BN_BITS2<=32 platforms actually make use of n0[1],
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* and we could use the #else case (with a shorter R value) for the
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* others. However, currently only the assembler files do know which
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* is which.
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*/
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BN_zero(R);
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if (!(BN_set_bit(R, 2 * BN_BITS2)))
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goto err;
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tmod.top = 0;
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if ((buf[0] = mod->d[0]))
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tmod.top = 1;
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if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
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tmod.top = 2;
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if (BN_is_one(&tmod))
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BN_zero(Ri);
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else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
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goto err;
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if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
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goto err; /* R*Ri */
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if (!BN_is_zero(Ri)) {
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if (!BN_sub_word(Ri, 1))
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goto err;
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} else { /* if N mod word size == 1 */
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if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
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goto err;
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/* Ri-- (mod double word size) */
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Ri->neg = 0;
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Ri->d[0] = BN_MASK2;
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Ri->d[1] = BN_MASK2;
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Ri->top = 2;
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}
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if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
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goto err;
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/*
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* Ni = (R*Ri-1)/N, keep only couple of least significant words:
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*/
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mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
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mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
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# else
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BN_zero(R);
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if (!(BN_set_bit(R, BN_BITS2)))
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goto err; /* R */
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buf[0] = mod->d[0]; /* tmod = N mod word size */
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buf[1] = 0;
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tmod.top = buf[0] != 0 ? 1 : 0;
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/* Ri = R^-1 mod N */
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if (BN_is_one(&tmod))
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BN_zero(Ri);
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else if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
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goto err;
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if (!BN_lshift(Ri, Ri, BN_BITS2))
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goto err; /* R*Ri */
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if (!BN_is_zero(Ri)) {
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if (!BN_sub_word(Ri, 1))
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goto err;
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} else { /* if N mod word size == 1 */
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if (!BN_set_word(Ri, BN_MASK2))
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goto err; /* Ri-- (mod word size) */
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}
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if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
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goto err;
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/*
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* Ni = (R*Ri-1)/N, keep only least significant word:
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*/
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mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
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mont->n0[1] = 0;
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# endif
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}
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#else /* !MONT_WORD */
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{ /* bignum version */
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mont->ri = BN_num_bits(&mont->N);
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BN_zero(R);
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if (!BN_set_bit(R, mont->ri))
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goto err; /* R = 2^ri */
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/* Ri = R^-1 mod N */
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if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
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goto err;
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if (!BN_lshift(Ri, Ri, mont->ri))
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goto err; /* R*Ri */
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if (!BN_sub_word(Ri, 1))
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goto err;
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/*
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* Ni = (R*Ri-1) / N
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*/
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if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
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goto err;
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}
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#endif
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/* setup RR for conversions */
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BN_zero(&(mont->RR));
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if (!BN_set_bit(&(mont->RR), mont->ri * 2))
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goto err;
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if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
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goto err;
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for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
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mont->RR.d[i] = 0;
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mont->RR.top = ret;
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mont->RR.flags |= BN_FLG_FIXED_TOP;
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
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{
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if (to == from)
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return to;
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if (!BN_copy(&(to->RR), &(from->RR)))
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return NULL;
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if (!BN_copy(&(to->N), &(from->N)))
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return NULL;
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if (!BN_copy(&(to->Ni), &(from->Ni)))
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return NULL;
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to->ri = from->ri;
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to->n0[0] = from->n0[0];
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to->n0[1] = from->n0[1];
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return to;
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}
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BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
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const BIGNUM *mod, BN_CTX *ctx)
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{
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BN_MONT_CTX *ret;
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CRYPTO_THREAD_read_lock(lock);
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ret = *pmont;
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CRYPTO_THREAD_unlock(lock);
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if (ret)
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return ret;
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/*
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* We don't want to serialise globally while doing our lazy-init math in
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* BN_MONT_CTX_set. That punishes threads that are doing independent
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* things. Instead, punish the case where more than one thread tries to
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* lazy-init the same 'pmont', by having each do the lazy-init math work
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* independently and only use the one from the thread that wins the race
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* (the losers throw away the work they've done).
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*/
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ret = BN_MONT_CTX_new();
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if (ret == NULL)
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return NULL;
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if (!BN_MONT_CTX_set(ret, mod, ctx)) {
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BN_MONT_CTX_free(ret);
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return NULL;
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}
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/* The locked compare-and-set, after the local work is done. */
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CRYPTO_THREAD_write_lock(lock);
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if (*pmont) {
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BN_MONT_CTX_free(ret);
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ret = *pmont;
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} else
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*pmont = ret;
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CRYPTO_THREAD_unlock(lock);
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return ret;
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}
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