| /* 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). */ |
| |
| #include <openssl/bn.h> |
| |
| #include <openssl/mem.h> |
| #include <openssl/thread.h> |
| |
| #include "internal.h" |
| |
| |
| #if !defined(OPENSSL_NO_ASM) && \ |
| (defined(OPENSSL_X86) || defined(OPENSSL_X86_64)) |
| #define OPENSSL_BN_ASM_MONT |
| #endif |
| |
| BN_MONT_CTX *BN_MONT_CTX_new(void) { |
| BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX)); |
| |
| if (ret == NULL) { |
| return NULL; |
| } |
| |
| BN_MONT_CTX_init(ret); |
| ret->flags = BN_FLG_MALLOCED; |
| return ret; |
| } |
| |
| void BN_MONT_CTX_init(BN_MONT_CTX *mont) { |
| memset(mont, 0, sizeof(BN_MONT_CTX)); |
| BN_init(&mont->RR); |
| BN_init(&mont->N); |
| BN_init(&mont->Ni); |
| } |
| |
| void BN_MONT_CTX_free(BN_MONT_CTX *mont) { |
| if (mont == NULL) { |
| return; |
| } |
| |
| BN_free(&mont->RR); |
| BN_free(&mont->N); |
| BN_free(&mont->Ni); |
| if (mont->flags & BN_FLG_MALLOCED) { |
| OPENSSL_free(mont); |
| } |
| } |
| |
| 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) || |
| !BN_copy(&to->N, &from->N) || |
| !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; |
| } |
| |
| int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { |
| int ret = 0; |
| BIGNUM *Ri, *R; |
| BIGNUM tmod; |
| BN_ULONG buf[2]; |
| |
| BN_CTX_start(ctx); |
| Ri = BN_CTX_get(ctx); |
| if (Ri == 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; |
| |
| 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 |
| |
| /* 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_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; |
| } |
| |
| int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, |
| BN_CTX *ctx) { |
| return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx); |
| } |
| |
| #if 0 |
| static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, |
| const BN_MONT_CTX *mont) { |
| const 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 (max > r->top) { |
| memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG)); |
| } |
| |
| r->top = max; |
| n0 = mont->n0[0]; |
| |
| for (carry = 0, i = 0; i < nl; i++, rp++) { |
| v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2); |
| 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]); |
| |
| { |
| 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 *)(((intptr_t)rp & ~m) | ((intptr_t)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; |
| } |
| } |
| |
| bn_correct_top(r); |
| bn_correct_top(ret); |
| |
| return 1; |
| } |
| #endif |
| |
| #define PTR_SIZE_INT size_t |
| |
| static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, const BN_MONT_CTX *mont) |
| { |
| BIGNUM *n; |
| BN_ULONG *ap,*np,*rp,n0,v,carry; |
| int nl,max,i; |
| |
| n= (BIGNUM*) &(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 |
| memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); |
| #endif |
| |
| r->top=max; |
| n0=mont->n0[0]; |
| |
| for (carry=0, i=0; i<nl; i++, rp++) |
| { |
| v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); |
| 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]); |
| |
| { |
| 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; |
| } |
| bn_correct_top(r); |
| bn_correct_top(ret); |
| |
| return(1); |
| } |
| |
| int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont, |
| BN_CTX *ctx) { |
| int retn = 0; |
| BIGNUM *t; |
| |
| BN_CTX_start(ctx); |
| t = BN_CTX_get(ctx); |
| if (t == NULL) { |
| return 0; |
| } |
| |
| if (BN_copy(t, a)) |
| retn = BN_from_montgomery_word(ret, t, mont); |
| BN_CTX_end(ctx); |
| |
| return retn; |
| } |
| |
| int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| const BN_MONT_CTX *mont, BN_CTX *ctx) { |
| BIGNUM *tmp; |
| int ret = 0; |
| |
| #if defined(OPENSSL_BN_ASM_MONT) |
| 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; |
| } |
| |
| 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 */ |
| if (!BN_from_montgomery_word(r, tmp, mont)) { |
| goto err; |
| } |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |