/* 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 <assert.h> | |

#include <string.h> | |

#include <openssl/err.h> | |

#include <openssl/mem.h> | |

#include <openssl/thread.h> | |

#include "internal.h" | |

#include "../internal.h" | |

#if !defined(OPENSSL_NO_ASM) && \ | |

(defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \ | |

defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64)) | |

#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; | |

} | |

OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX)); | |

BN_init(&ret->RR); | |

BN_init(&ret->N); | |

return ret; | |

} | |

void BN_MONT_CTX_free(BN_MONT_CTX *mont) { | |

if (mont == NULL) { | |

return; | |

} | |

BN_free(&mont->RR); | |

BN_free(&mont->N); | |

OPENSSL_free(mont); | |

} | |

BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) { | |

if (to == from) { | |

return to; | |

} | |

if (!BN_copy(&to->RR, &from->RR) || | |

!BN_copy(&to->N, &from->N)) { | |

return NULL; | |

} | |

to->n0[0] = from->n0[0]; | |

to->n0[1] = from->n0[1]; | |

return to; | |

} | |

OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2, | |

BN_MONT_CTX_N0_LIMBS_VALUE_INVALID); | |

OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS == | |

sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch); | |

int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { | |

if (BN_is_zero(mod)) { | |

OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); | |

return 0; | |

} | |

if (!BN_is_odd(mod)) { | |

OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS); | |

return 0; | |

} | |

if (BN_is_negative(mod)) { | |

OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); | |

return 0; | |

} | |

/* Save the modulus. */ | |

if (!BN_copy(&mont->N, mod)) { | |

OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); | |

return 0; | |

} | |

/* Find n0 such that n0 * N == -1 (mod r). | |

* | |

* Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the | |

* others, we could use a shorter R value and use faster |BN_ULONG|-based | |

* math instead of |uint64_t|-based math, which would be double-precision. | |

* However, currently only the assembler files know which is which. */ | |

uint64_t n0 = bn_mont_n0(mod); | |

mont->n0[0] = (BN_ULONG)n0; | |

#if BN_MONT_CTX_N0_LIMBS == 2 | |

mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2); | |

#else | |

mont->n0[1] = 0; | |

#endif | |

/* Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS such that R | |

* > mod. Even though the assembly on some 32-bit platforms works with 64-bit | |

* values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS * | |

* BN_BITS2|, is correct because R**2 will still be a multiple of the latter | |

* as |BN_MONT_CTX_N0_LIMBS| is either one or two. | |

* | |

* XXX: This is not constant time with respect to |mont->N|, but it should | |

* be. */ | |

unsigned lgBigR = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2; | |

if (!bn_mod_exp_base_2_vartime(&mont->RR, lgBigR * 2, &mont->N)) { | |

return 0; | |

} | |

return 1; | |

} | |

int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock, | |

const BIGNUM *mod, BN_CTX *bn_ctx) { | |

CRYPTO_MUTEX_lock_read(lock); | |

BN_MONT_CTX *ctx = *pmont; | |

CRYPTO_MUTEX_unlock_read(lock); | |

if (ctx) { | |

return 1; | |

} | |

CRYPTO_MUTEX_lock_write(lock); | |

ctx = *pmont; | |

if (ctx) { | |

goto out; | |

} | |

ctx = BN_MONT_CTX_new(); | |

if (ctx == NULL) { | |

goto out; | |

} | |

if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) { | |

BN_MONT_CTX_free(ctx); | |

ctx = NULL; | |

goto out; | |

} | |

*pmont = ctx; | |

out: | |

CRYPTO_MUTEX_unlock_write(lock); | |

return ctx != NULL; | |

} | |

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); | |

} | |

static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, | |

const BN_MONT_CTX *mont) { | |

BN_ULONG *ap, *np, *rp, n0, v, carry; | |

int nl, max, i; | |

const BIGNUM *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) { | |

OPENSSL_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; | |

uintptr_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 = (0u - (uintptr_t)v); | |

nrp = (BN_ULONG *)(((uintptr_t)rp & ~m) | ((uintptr_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; | |

} | |

int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont, | |

BN_CTX *ctx) { | |

int ret = 0; | |

BIGNUM *t; | |

BN_CTX_start(ctx); | |

t = BN_CTX_get(ctx); | |

if (t == NULL || | |

!BN_copy(t, a)) { | |

goto err; | |

} | |

ret = BN_from_montgomery_word(r, t, mont); | |

err: | |

BN_CTX_end(ctx); | |

return ret; | |

} | |

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; | |

} |