/* 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_grpc/bn.h> #include <assert.h> #include <stdio.h> #include <stdlib.h> #include <string.h> #include <openssl_grpc/err.h> #include <openssl_grpc/mem.h> #include <openssl_grpc/thread.h> #include <openssl_grpc/type_check.h> #include "internal.h" #include "../../internal.h" 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; } static int bn_mont_ctx_set_N_and_n0(BN_MONT_CTX *mont, const BIGNUM *mod) { 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; } // |mont->N| is always stored minimally. Computing RR efficiently leaks the // size of the modulus. While the modulus may be private in RSA (one of the // primes), their sizes are public, so this is fine. bn_set_minimal_width(&mont->N); // 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. OPENSSL_STATIC_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2, "BN_MONT_CTX_N0_LIMBS value is invalid"); OPENSSL_STATIC_ASSERT( sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS == sizeof(uint64_t), "uint64_t is insufficient precision for n0"); uint64_t n0 = bn_mont_n0(&mont->N); 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 return 1; } int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) { if (!bn_mont_ctx_set_N_and_n0(mont, mod)) { return 0; } BN_CTX *new_ctx = NULL; if (ctx == NULL) { new_ctx = BN_CTX_new(); if (new_ctx == NULL) { return 0; } ctx = new_ctx; } // Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 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. unsigned lgBigR = mont->N.width * BN_BITS2; BN_zero(&mont->RR); int ok = BN_set_bit(&mont->RR, lgBigR * 2) && BN_mod(&mont->RR, &mont->RR, &mont->N, ctx) && bn_resize_words(&mont->RR, mont->N.width); BN_CTX_free(new_ctx); return ok; } BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx) { BN_MONT_CTX *mont = BN_MONT_CTX_new(); if (mont == NULL || !BN_MONT_CTX_set(mont, mod, ctx)) { BN_MONT_CTX_free(mont); return NULL; } return mont; } BN_MONT_CTX *BN_MONT_CTX_new_consttime(const BIGNUM *mod, BN_CTX *ctx) { BN_MONT_CTX *mont = BN_MONT_CTX_new(); if (mont == NULL || !bn_mont_ctx_set_N_and_n0(mont, mod)) { goto err; } unsigned lgBigR = mont->N.width * BN_BITS2; if (!bn_mod_exp_base_2_consttime(&mont->RR, lgBigR * 2, &mont->N, ctx) || !bn_resize_words(&mont->RR, mont->N.width)) { goto err; } return mont; err: BN_MONT_CTX_free(mont); return NULL; } 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); if (*pmont == NULL) { *pmont = BN_MONT_CTX_new_for_modulus(mod, bn_ctx); } const int ok = *pmont != NULL; CRYPTO_MUTEX_unlock_write(lock); return ok; } 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_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a, size_t num_a, const BN_MONT_CTX *mont) { const BN_ULONG *n = mont->N.d; size_t num_n = mont->N.width; if (num_r != num_n || num_a != 2 * num_n) { OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } // Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On // input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r| // includes |carry| which is stored separately. BN_ULONG n0 = mont->n0[0]; BN_ULONG carry = 0; for (size_t i = 0; i < num_n; i++) { BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0); v += carry + a[i + num_n]; carry |= (v != a[i + num_n]); carry &= (v <= a[i + num_n]); a[i + num_n] = v; } // Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a| // includes |carry| which is stored separately. a += num_n; // |a| thus requires at most one additional subtraction |n| to be reduced. bn_reduce_once(r, a, carry, n, num_n); return 1; } static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, const BN_MONT_CTX *mont) { if (r->neg) { OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); return 0; } const BIGNUM *n = &mont->N; if (n->width == 0) { ret->width = 0; return 1; } int max = 2 * n->width; // carry is stored separately if (!bn_resize_words(r, max) || !bn_wexpand(ret, n->width)) { return 0; } ret->width = n->width; ret->neg = 0; return bn_from_montgomery_in_place(ret->d, ret->width, r->d, r->width, mont); } 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_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx) { // If the high bit of |n| is set, R = 2^(width*BN_BITS2) < 2 * |n|, so we // compute R - |n| rather than perform Montgomery reduction. const BIGNUM *n = &mont->N; if (n->width > 0 && (n->d[n->width - 1] >> (BN_BITS2 - 1)) != 0) { if (!bn_wexpand(r, n->width)) { return 0; } r->d[0] = 0 - n->d[0]; for (int i = 1; i < n->width; i++) { r->d[i] = ~n->d[i]; } r->width = n->width; r->neg = 0; return 1; } return BN_from_montgomery(r, &mont->RR, mont, ctx); } static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BN_MONT_CTX *mont, BN_CTX *ctx) { int ret = 0; BN_CTX_start(ctx); BIGNUM *tmp = BN_CTX_get(ctx); if (tmp == NULL) { goto err; } if (a == b) { if (!bn_sqr_consttime(tmp, a, ctx)) { goto err; } } else { if (!bn_mul_consttime(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; } int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BN_MONT_CTX *mont, BN_CTX *ctx) { if (a->neg || b->neg) { OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); return 0; } #if defined(OPENSSL_BN_ASM_MONT) // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. int num = mont->N.width; if (num >= (128 / BN_BITS2) && a->width == num && b->width == num) { if (!bn_wexpand(r, num)) { return 0; } if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) { // The check above ensures this won't happen. assert(0); OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR); return 0; } r->neg = 0; r->width = num; return 1; } #endif return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx); } int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont) { return !BN_is_negative(bn) && bn_fits_in_words(bn, mont->N.width); } void bn_to_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num, const BN_MONT_CTX *mont) { bn_mod_mul_montgomery_small(r, a, mont->RR.d, num, mont); } void bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a, const BN_MONT_CTX *mont) { if (num_r != (size_t)mont->N.width || num_r > BN_SMALL_MAX_WORDS || num_a > 2 * num_r) { abort(); } BN_ULONG tmp[BN_SMALL_MAX_WORDS * 2] = {0}; OPENSSL_memcpy(tmp, a, num_a * sizeof(BN_ULONG)); if (!bn_from_montgomery_in_place(r, num_r, tmp, 2 * num_r, mont)) { abort(); } OPENSSL_cleanse(tmp, 2 * num_r * sizeof(BN_ULONG)); } void bn_mod_mul_montgomery_small(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, size_t num, const BN_MONT_CTX *mont) { if (num != (size_t)mont->N.width || num > BN_SMALL_MAX_WORDS) { abort(); } #if defined(OPENSSL_BN_ASM_MONT) // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. if (num >= (128 / BN_BITS2)) { if (!bn_mul_mont(r, a, b, mont->N.d, mont->n0, num)) { abort(); // The check above ensures this won't happen. } return; } #endif // Compute the product. BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS]; if (a == b) { bn_sqr_small(tmp, 2 * num, a, num); } else { bn_mul_small(tmp, 2 * num, a, num, b, num); } // Reduce. if (!bn_from_montgomery_in_place(r, num, tmp, 2 * num, mont)) { abort(); } OPENSSL_cleanse(tmp, 2 * num * sizeof(BN_ULONG)); }