| /* crypto/bn/bn_mont.c */ |
| /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| * All rights reserved. |
| * |
| * This package is an SSL implementation written |
| * by Eric Young (eay@cryptsoft.com). |
| * The implementation was written so as to conform with Netscapes SSL. |
| * |
| * This library is free for commercial and non-commercial use as long as |
| * the following conditions are aheared to. The following conditions |
| * apply to all code found in this distribution, be it the RC4, RSA, |
| * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| * included with this distribution is covered by the same copyright terms |
| * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| * |
| * Copyright remains Eric Young's, and as such any Copyright notices in |
| * the code are not to be removed. |
| * If this package is used in a product, Eric Young should be given attribution |
| * as the author of the parts of the library used. |
| * This can be in the form of a textual message at program startup or |
| * in documentation (online or textual) provided with the package. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * 3. All advertising materials mentioning features or use of this software |
| * must display the following acknowledgement: |
| * "This product includes cryptographic software written by |
| * Eric Young (eay@cryptsoft.com)" |
| * The word 'cryptographic' can be left out if the rouines from the library |
| * being used are not cryptographic related :-). |
| * 4. If you include any Windows specific code (or a derivative thereof) from |
| * the apps directory (application code) you must include an acknowledgement: |
| * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| * |
| * The licence and distribution terms for any publically available version or |
| * derivative of this code cannot be changed. i.e. this code cannot simply be |
| * copied and put under another distribution licence |
| * [including the GNU Public Licence.] |
| */ |
| /* ==================================================================== |
| * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * |
| * 3. All advertising materials mentioning features or use of this |
| * software must display the following acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| * |
| * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| * endorse or promote products derived from this software without |
| * prior written permission. For written permission, please contact |
| * openssl-core@openssl.org. |
| * |
| * 5. Products derived from this software may not be called "OpenSSL" |
| * nor may "OpenSSL" appear in their names without prior written |
| * permission of the OpenSSL Project. |
| * |
| * 6. Redistributions of any form whatsoever must retain the following |
| * acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| * OF THE POSSIBILITY OF SUCH DAMAGE. |
| * ==================================================================== |
| * |
| * This product includes cryptographic software written by Eric Young |
| * (eay@cryptsoft.com). This product includes software written by Tim |
| * Hudson (tjh@cryptsoft.com). |
| * |
| */ |
| |
| /* |
| * Details about Montgomery multiplication algorithms can be found at |
| * http://security.ece.orst.edu/publications.html, e.g. |
| * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and |
| * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf |
| */ |
| |
| #include <openssl/opensslconf.h> |
| #if !defined(OPENSSL_SYS_STARBOARD) |
| #include <stdio.h> |
| #endif // !defined(OPENSSL_SYS_STARBOARD) |
| #include "cryptlib.h" |
| #include "bn_lcl.h" |
| |
| #define MONT_WORD /* use the faster word-based algorithm */ |
| |
| #ifdef MONT_WORD |
| static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont); |
| #endif |
| |
| int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| BN_MONT_CTX *mont, BN_CTX *ctx) |
| { |
| BIGNUM *tmp; |
| int ret = 0; |
| #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD) |
| int num = mont->N.top; |
| |
| if (num > 1 && a->top == num && b->top == num) { |
| if (bn_wexpand(r, num) == NULL) |
| return (0); |
| if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { |
| r->neg = a->neg ^ b->neg; |
| r->top = num; |
| bn_correct_top(r); |
| return (1); |
| } |
| } |
| #endif |
| |
| BN_CTX_start(ctx); |
| tmp = BN_CTX_get(ctx); |
| if (tmp == NULL) |
| goto err; |
| |
| bn_check_top(tmp); |
| if (a == b) { |
| if (!BN_sqr(tmp, a, ctx)) |
| goto err; |
| } else { |
| if (!BN_mul(tmp, a, b, ctx)) |
| goto err; |
| } |
| /* reduce from aRR to aR */ |
| #ifdef MONT_WORD |
| if (!BN_from_montgomery_word(r, tmp, mont)) |
| goto err; |
| #else |
| if (!BN_from_montgomery(r, tmp, mont, ctx)) |
| goto err; |
| #endif |
| bn_check_top(r); |
| ret = 1; |
| err: |
| BN_CTX_end(ctx); |
| return (ret); |
| } |
| |
| #ifdef MONT_WORD |
| static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont) |
| { |
| BIGNUM *n; |
| BN_ULONG *ap, *np, *rp, n0, v, carry; |
| int nl, max, i; |
| |
| n = &(mont->N); |
| nl = n->top; |
| if (nl == 0) { |
| ret->top = 0; |
| return (1); |
| } |
| |
| max = (2 * nl); /* carry is stored separately */ |
| if (bn_wexpand(r, max) == NULL) |
| return (0); |
| |
| r->neg ^= n->neg; |
| np = n->d; |
| rp = r->d; |
| |
| /* clear the top words of T */ |
| # if 1 |
| for (i = r->top; i < max; i++) /* memset? XXX */ |
| rp[i] = 0; |
| # else |
| OPENSSL_port_memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG)); |
| # endif |
| |
| r->top = max; |
| n0 = mont->n0[0]; |
| |
| # ifdef BN_COUNT |
| OPENSSL_port_printferr("word BN_from_montgomery_word %d * %d\n", nl, nl); |
| # endif |
| for (carry = 0, i = 0; i < nl; i++, rp++) { |
| # ifdef __TANDEM |
| { |
| long long t1; |
| long long t2; |
| long long t3; |
| t1 = rp[0] * (n0 & 0177777); |
| t2 = 037777600000l; |
| t2 = n0 & t2; |
| t3 = rp[0] & 0177777; |
| t2 = (t3 * t2) & BN_MASK2; |
| t1 = t1 + t2; |
| v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1); |
| } |
| # else |
| v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); |
| # endif |
| v = (v + carry + rp[nl]) & BN_MASK2; |
| carry |= (v != rp[nl]); |
| carry &= (v <= rp[nl]); |
| rp[nl] = v; |
| } |
| |
| if (bn_wexpand(ret, nl) == NULL) |
| return (0); |
| ret->top = nl; |
| ret->neg = r->neg; |
| |
| rp = ret->d; |
| ap = &(r->d[nl]); |
| |
| # define BRANCH_FREE 1 |
| # if BRANCH_FREE |
| { |
| BN_ULONG *nrp; |
| size_t m; |
| |
| v = bn_sub_words(rp, ap, np, nl) - carry; |
| /* |
| * if subtraction result is real, then trick unconditional memcpy |
| * below to perform in-place "refresh" instead of actual copy. |
| */ |
| m = (0 - (size_t)v); |
| nrp = |
| (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m)); |
| |
| for (i = 0, nl -= 4; i < nl; i += 4) { |
| BN_ULONG t1, t2, t3, t4; |
| |
| t1 = nrp[i + 0]; |
| t2 = nrp[i + 1]; |
| t3 = nrp[i + 2]; |
| ap[i + 0] = 0; |
| t4 = nrp[i + 3]; |
| ap[i + 1] = 0; |
| rp[i + 0] = t1; |
| ap[i + 2] = 0; |
| rp[i + 1] = t2; |
| ap[i + 3] = 0; |
| rp[i + 2] = t3; |
| rp[i + 3] = t4; |
| } |
| for (nl += 4; i < nl; i++) |
| rp[i] = nrp[i], ap[i] = 0; |
| } |
| # else |
| if (bn_sub_words(rp, ap, np, nl) - carry) |
| OPENSSL_port_memcpy(rp, ap, nl * sizeof(BN_ULONG)); |
| # endif |
| bn_correct_top(r); |
| bn_correct_top(ret); |
| bn_check_top(ret); |
| |
| return (1); |
| } |
| #endif /* MONT_WORD */ |
| |
| int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, |
| BN_CTX *ctx) |
| { |
| int retn = 0; |
| #ifdef MONT_WORD |
| BIGNUM *t; |
| |
| BN_CTX_start(ctx); |
| if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) |
| retn = BN_from_montgomery_word(ret, t, mont); |
| BN_CTX_end(ctx); |
| #else /* !MONT_WORD */ |
| BIGNUM *t1, *t2; |
| |
| BN_CTX_start(ctx); |
| t1 = BN_CTX_get(ctx); |
| t2 = BN_CTX_get(ctx); |
| if (t1 == NULL || t2 == NULL) |
| goto err; |
| |
| if (!BN_copy(t1, a)) |
| goto err; |
| BN_mask_bits(t1, mont->ri); |
| |
| if (!BN_mul(t2, t1, &mont->Ni, ctx)) |
| goto err; |
| BN_mask_bits(t2, mont->ri); |
| |
| if (!BN_mul(t1, t2, &mont->N, ctx)) |
| goto err; |
| if (!BN_add(t2, a, t1)) |
| goto err; |
| if (!BN_rshift(ret, t2, mont->ri)) |
| goto err; |
| |
| if (BN_ucmp(ret, &(mont->N)) >= 0) { |
| if (!BN_usub(ret, ret, &(mont->N))) |
| goto err; |
| } |
| retn = 1; |
| bn_check_top(ret); |
| err: |
| BN_CTX_end(ctx); |
| #endif /* MONT_WORD */ |
| return (retn); |
| } |
| |
| BN_MONT_CTX *BN_MONT_CTX_new(void) |
| { |
| BN_MONT_CTX *ret; |
| |
| if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) |
| return (NULL); |
| |
| BN_MONT_CTX_init(ret); |
| ret->flags = BN_FLG_MALLOCED; |
| return (ret); |
| } |
| |
| void BN_MONT_CTX_init(BN_MONT_CTX *ctx) |
| { |
| ctx->ri = 0; |
| BN_init(&(ctx->RR)); |
| BN_init(&(ctx->N)); |
| BN_init(&(ctx->Ni)); |
| ctx->n0[0] = ctx->n0[1] = 0; |
| ctx->flags = 0; |
| } |
| |
| void BN_MONT_CTX_free(BN_MONT_CTX *mont) |
| { |
| if (mont == NULL) |
| return; |
| |
| BN_clear_free(&(mont->RR)); |
| BN_clear_free(&(mont->N)); |
| BN_clear_free(&(mont->Ni)); |
| if (mont->flags & BN_FLG_MALLOCED) |
| OPENSSL_free(mont); |
| } |
| |
| int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) |
| { |
| int ret = 0; |
| BIGNUM *Ri, *R; |
| |
| if (BN_is_zero(mod)) |
| return 0; |
| |
| BN_CTX_start(ctx); |
| if ((Ri = BN_CTX_get(ctx)) == NULL) |
| goto err; |
| R = &(mont->RR); /* grab RR as a temp */ |
| if (!BN_copy(&(mont->N), mod)) |
| goto err; /* Set N */ |
| mont->N.neg = 0; |
| |
| #ifdef MONT_WORD |
| { |
| BIGNUM tmod; |
| BN_ULONG buf[2]; |
| |
| BN_init(&tmod); |
| tmod.d = buf; |
| tmod.dmax = 2; |
| tmod.neg = 0; |
| |
| mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; |
| |
| # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32) |
| /* |
| * Only certain BN_BITS2<=32 platforms actually make use of n0[1], |
| * and we could use the #else case (with a shorter R value) for the |
| * others. However, currently only the assembler files do know which |
| * is which. |
| */ |
| |
| BN_zero(R); |
| if (!(BN_set_bit(R, 2 * BN_BITS2))) |
| goto err; |
| |
| tmod.top = 0; |
| if ((buf[0] = mod->d[0])) |
| tmod.top = 1; |
| if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) |
| tmod.top = 2; |
| |
| if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) |
| goto err; |
| if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) |
| goto err; /* R*Ri */ |
| if (!BN_is_zero(Ri)) { |
| if (!BN_sub_word(Ri, 1)) |
| goto err; |
| } else { /* if N mod word size == 1 */ |
| |
| if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) |
| goto err; |
| /* Ri-- (mod double word size) */ |
| Ri->neg = 0; |
| Ri->d[0] = BN_MASK2; |
| Ri->d[1] = BN_MASK2; |
| Ri->top = 2; |
| } |
| if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) |
| goto err; |
| /* |
| * Ni = (R*Ri-1)/N, keep only couple of least significant words: |
| */ |
| mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; |
| mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; |
| # else |
| BN_zero(R); |
| if (!(BN_set_bit(R, BN_BITS2))) |
| goto err; /* R */ |
| |
| buf[0] = mod->d[0]; /* tmod = N mod word size */ |
| buf[1] = 0; |
| tmod.top = buf[0] != 0 ? 1 : 0; |
| /* Ri = R^-1 mod N */ |
| if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL) |
| goto err; |
| if (!BN_lshift(Ri, Ri, BN_BITS2)) |
| goto err; /* R*Ri */ |
| if (!BN_is_zero(Ri)) { |
| if (!BN_sub_word(Ri, 1)) |
| goto err; |
| } else { /* if N mod word size == 1 */ |
| |
| if (!BN_set_word(Ri, BN_MASK2)) |
| goto err; /* Ri-- (mod word size) */ |
| } |
| if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) |
| goto err; |
| /* |
| * Ni = (R*Ri-1)/N, keep only least significant word: |
| */ |
| mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; |
| mont->n0[1] = 0; |
| # endif |
| } |
| #else /* !MONT_WORD */ |
| { /* bignum version */ |
| mont->ri = BN_num_bits(&mont->N); |
| BN_zero(R); |
| if (!BN_set_bit(R, mont->ri)) |
| goto err; /* R = 2^ri */ |
| /* Ri = R^-1 mod N */ |
| if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL) |
| goto err; |
| if (!BN_lshift(Ri, Ri, mont->ri)) |
| goto err; /* R*Ri */ |
| if (!BN_sub_word(Ri, 1)) |
| goto err; |
| /* |
| * Ni = (R*Ri-1) / N |
| */ |
| if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx)) |
| goto err; |
| } |
| #endif |
| |
| /* setup RR for conversions */ |
| BN_zero(&(mont->RR)); |
| if (!BN_set_bit(&(mont->RR), mont->ri * 2)) |
| goto err; |
| if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) |
| goto err; |
| |
| ret = 1; |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) |
| { |
| if (to == from) |
| return (to); |
| |
| if (!BN_copy(&(to->RR), &(from->RR))) |
| return NULL; |
| if (!BN_copy(&(to->N), &(from->N))) |
| return NULL; |
| if (!BN_copy(&(to->Ni), &(from->Ni))) |
| return NULL; |
| to->ri = from->ri; |
| to->n0[0] = from->n0[0]; |
| to->n0[1] = from->n0[1]; |
| return (to); |
| } |
| |
| BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, |
| const BIGNUM *mod, BN_CTX *ctx) |
| { |
| BN_MONT_CTX *ret; |
| |
| CRYPTO_r_lock(lock); |
| ret = *pmont; |
| CRYPTO_r_unlock(lock); |
| if (ret) |
| return ret; |
| |
| /* |
| * We don't want to serialise globally while doing our lazy-init math in |
| * BN_MONT_CTX_set. That punishes threads that are doing independent |
| * things. Instead, punish the case where more than one thread tries to |
| * lazy-init the same 'pmont', by having each do the lazy-init math work |
| * independently and only use the one from the thread that wins the race |
| * (the losers throw away the work they've done). |
| */ |
| ret = BN_MONT_CTX_new(); |
| if (!ret) |
| return NULL; |
| if (!BN_MONT_CTX_set(ret, mod, ctx)) { |
| BN_MONT_CTX_free(ret); |
| return NULL; |
| } |
| |
| /* The locked compare-and-set, after the local work is done. */ |
| CRYPTO_w_lock(lock); |
| if (*pmont) { |
| BN_MONT_CTX_free(ret); |
| ret = *pmont; |
| } else |
| *pmont = ret; |
| CRYPTO_w_unlock(lock); |
| return ret; |
| } |
