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- /* 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) 1998-2001 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 <openssl/err.h>
-
- #include "internal.h"
-
- static BIGNUM *euclid(BIGNUM *a, BIGNUM *b) {
- BIGNUM *t;
- int shifts = 0;
-
- /* 0 <= b <= a */
- while (!BN_is_zero(b)) {
- /* 0 < b <= a */
-
- if (BN_is_odd(a)) {
- if (BN_is_odd(b)) {
- if (!BN_sub(a, a, b)) {
- goto err;
- }
- if (!BN_rshift1(a, a)) {
- goto err;
- }
- if (BN_cmp(a, b) < 0) {
- t = a;
- a = b;
- b = t;
- }
- } else {
- /* a odd - b even */
- if (!BN_rshift1(b, b)) {
- goto err;
- }
- if (BN_cmp(a, b) < 0) {
- t = a;
- a = b;
- b = t;
- }
- }
- } else {
- /* a is even */
- if (BN_is_odd(b)) {
- if (!BN_rshift1(a, a)) {
- goto err;
- }
- if (BN_cmp(a, b) < 0) {
- t = a;
- a = b;
- b = t;
- }
- } else {
- /* a even - b even */
- if (!BN_rshift1(a, a)) {
- goto err;
- }
- if (!BN_rshift1(b, b)) {
- goto err;
- }
- shifts++;
- }
- }
- /* 0 <= b <= a */
- }
-
- if (shifts) {
- if (!BN_lshift(a, a, shifts)) {
- goto err;
- }
- }
-
- return a;
-
- err:
- return NULL;
- }
-
- int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx) {
- BIGNUM *a, *b, *t;
- int ret = 0;
-
- BN_CTX_start(ctx);
- a = BN_CTX_get(ctx);
- b = BN_CTX_get(ctx);
-
- if (a == NULL || b == NULL) {
- goto err;
- }
- if (BN_copy(a, in_a) == NULL) {
- goto err;
- }
- if (BN_copy(b, in_b) == NULL) {
- goto err;
- }
-
- a->neg = 0;
- b->neg = 0;
-
- if (BN_cmp(a, b) < 0) {
- t = a;
- a = b;
- b = t;
- }
- t = euclid(a, b);
- if (t == NULL) {
- goto err;
- }
-
- if (BN_copy(r, t) == NULL) {
- goto err;
- }
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
- }
-
- /* solves ax == 1 (mod n) */
- static int bn_mod_inverse_general(BIGNUM *out, int *out_no_inverse,
- const BIGNUM *a, const BIGNUM *n,
- BN_CTX *ctx);
-
- int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
- const BIGNUM *n, BN_CTX *ctx) {
- *out_no_inverse = 0;
-
- if (!BN_is_odd(n)) {
- OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
- return 0;
- }
-
- if (BN_is_negative(a) || BN_cmp(a, n) >= 0) {
- OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
- return 0;
- }
-
- BIGNUM *A, *B, *X, *Y;
- int ret = 0;
- int sign;
-
- BN_CTX_start(ctx);
- A = BN_CTX_get(ctx);
- B = BN_CTX_get(ctx);
- X = BN_CTX_get(ctx);
- Y = BN_CTX_get(ctx);
- if (Y == NULL) {
- goto err;
- }
-
- BIGNUM *R = out;
-
- BN_zero(Y);
- if (!BN_one(X) || BN_copy(B, a) == NULL || BN_copy(A, n) == NULL) {
- goto err;
- }
- A->neg = 0;
- sign = -1;
- /* From B = a mod |n|, A = |n| it follows that
- *
- * 0 <= B < A,
- * -sign*X*a == B (mod |n|),
- * sign*Y*a == A (mod |n|).
- */
-
- /* Binary inversion algorithm; requires odd modulus. This is faster than the
- * general algorithm if the modulus is sufficiently small (about 400 .. 500
- * bits on 32-bit systems, but much more on 64-bit systems) */
- int shift;
-
- while (!BN_is_zero(B)) {
- /* 0 < B < |n|,
- * 0 < A <= |n|,
- * (1) -sign*X*a == B (mod |n|),
- * (2) sign*Y*a == A (mod |n|) */
-
- /* Now divide B by the maximum possible power of two in the integers,
- * and divide X by the same value mod |n|.
- * When we're done, (1) still holds. */
- shift = 0;
- while (!BN_is_bit_set(B, shift)) {
- /* note that 0 < B */
- shift++;
-
- if (BN_is_odd(X)) {
- if (!BN_uadd(X, X, n)) {
- goto err;
- }
- }
- /* now X is even, so we can easily divide it by two */
- if (!BN_rshift1(X, X)) {
- goto err;
- }
- }
- if (shift > 0) {
- if (!BN_rshift(B, B, shift)) {
- goto err;
- }
- }
-
- /* Same for A and Y. Afterwards, (2) still holds. */
- shift = 0;
- while (!BN_is_bit_set(A, shift)) {
- /* note that 0 < A */
- shift++;
-
- if (BN_is_odd(Y)) {
- if (!BN_uadd(Y, Y, n)) {
- goto err;
- }
- }
- /* now Y is even */
- if (!BN_rshift1(Y, Y)) {
- goto err;
- }
- }
- if (shift > 0) {
- if (!BN_rshift(A, A, shift)) {
- goto err;
- }
- }
-
- /* We still have (1) and (2).
- * Both A and B are odd.
- * The following computations ensure that
- *
- * 0 <= B < |n|,
- * 0 < A < |n|,
- * (1) -sign*X*a == B (mod |n|),
- * (2) sign*Y*a == A (mod |n|),
- *
- * and that either A or B is even in the next iteration. */
- if (BN_ucmp(B, A) >= 0) {
- /* -sign*(X + Y)*a == B - A (mod |n|) */
- if (!BN_uadd(X, X, Y)) {
- goto err;
- }
- /* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
- * actually makes the algorithm slower */
- if (!BN_usub(B, B, A)) {
- goto err;
- }
- } else {
- /* sign*(X + Y)*a == A - B (mod |n|) */
- if (!BN_uadd(Y, Y, X)) {
- goto err;
- }
- /* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
- if (!BN_usub(A, A, B)) {
- goto err;
- }
- }
- }
-
- if (!BN_is_one(A)) {
- *out_no_inverse = 1;
- OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
- goto err;
- }
-
- /* The while loop (Euclid's algorithm) ends when
- * A == gcd(a,n);
- * we have
- * sign*Y*a == A (mod |n|),
- * where Y is non-negative. */
-
- if (sign < 0) {
- if (!BN_sub(Y, n, Y)) {
- goto err;
- }
- }
- /* Now Y*a == A (mod |n|). */
-
- /* Y*a == 1 (mod |n|) */
- if (!Y->neg && BN_ucmp(Y, n) < 0) {
- if (!BN_copy(R, Y)) {
- goto err;
- }
- } else {
- if (!BN_nnmod(R, Y, n, ctx)) {
- goto err;
- }
- }
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
- }
-
- BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
- BN_CTX *ctx) {
- int no_inverse;
-
- BIGNUM *a_reduced = NULL;
-
- BIGNUM *new_out = NULL;
- if (out == NULL) {
- new_out = BN_new();
- if (new_out == NULL) {
- OPENSSL_PUT_ERROR(BN, ERR_R_MALLOC_FAILURE);
- return NULL;
- }
- out = new_out;
- }
-
- int ok = 0;
-
- int no_branch =
- (a->flags & BN_FLG_CONSTTIME) != 0 || (n->flags & BN_FLG_CONSTTIME) != 0;
-
- if (a->neg || BN_ucmp(a, n) >= 0) {
- a_reduced = BN_dup(a);
- if (a_reduced == NULL) {
- goto err;
- }
- if (no_branch) {
- BN_set_flags(a_reduced, BN_FLG_CONSTTIME);
- }
- if (!BN_nnmod(a_reduced, a_reduced, n, ctx)) {
- goto err;
- }
- a = a_reduced;
- }
-
- if (no_branch || !BN_is_odd(n)) {
- if (!bn_mod_inverse_general(out, &no_inverse, a, n, ctx)) {
- goto err;
- }
- } else if (!BN_mod_inverse_odd(out, &no_inverse, a, n, ctx)) {
- goto err;
- }
-
- ok = 1;
-
- err:
- if (!ok) {
- BN_free(new_out);
- out = NULL;
- }
- BN_free(a_reduced);
- return out;
- }
-
- int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
- const BN_MONT_CTX *mont, BN_CTX *ctx) {
- *out_no_inverse = 0;
-
- if (BN_is_negative(a) || BN_cmp(a, &mont->N) >= 0) {
- OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
- return 0;
- }
-
- int ret = 0;
- BIGNUM blinding_factor;
- BN_init(&blinding_factor);
-
- if (!BN_rand_range_ex(&blinding_factor, 1, &mont->N) ||
- !BN_mod_mul_montgomery(out, &blinding_factor, a, mont, ctx) ||
- !BN_mod_inverse_odd(out, out_no_inverse, out, &mont->N, ctx) ||
- !BN_mod_mul_montgomery(out, &blinding_factor, out, mont, ctx)) {
- OPENSSL_PUT_ERROR(BN, ERR_R_BN_LIB);
- goto err;
- }
-
- ret = 1;
-
- err:
- BN_free(&blinding_factor);
- return ret;
- }
-
- /* bn_mod_inverse_general is the general inversion algorithm that works for
- * both even and odd |n|. It was specifically designed to contain fewer
- * branches that may leak sensitive information. See "New Branch Prediction
- * Vulnerabilities in OpenSSL and Necessary Software Countermeasures" by
- * Onur Acıçmez, Shay Gueron, and Jean-Pierre Seifert. */
- static int bn_mod_inverse_general(BIGNUM *out, int *out_no_inverse,
- const BIGNUM *a, const BIGNUM *n,
- BN_CTX *ctx) {
- BIGNUM *A, *B, *X, *Y, *M, *D, *T;
- BIGNUM local_A;
- BIGNUM *pA;
- int ret = 0;
- int sign;
-
- *out_no_inverse = 0;
-
- BN_CTX_start(ctx);
- A = BN_CTX_get(ctx);
- B = BN_CTX_get(ctx);
- X = BN_CTX_get(ctx);
- D = BN_CTX_get(ctx);
- M = BN_CTX_get(ctx);
- Y = BN_CTX_get(ctx);
- T = BN_CTX_get(ctx);
- if (T == NULL) {
- goto err;
- }
-
- BIGNUM *R = out;
-
- BN_zero(Y);
- if (!BN_one(X) || BN_copy(B, a) == NULL || BN_copy(A, n) == NULL) {
- goto err;
- }
- A->neg = 0;
-
- sign = -1;
- /* From B = a mod |n|, A = |n| it follows that
- *
- * 0 <= B < A,
- * -sign*X*a == B (mod |n|),
- * sign*Y*a == A (mod |n|).
- */
-
- while (!BN_is_zero(B)) {
- BIGNUM *tmp;
-
- /*
- * 0 < B < A,
- * (*) -sign*X*a == B (mod |n|),
- * sign*Y*a == A (mod |n|)
- */
-
- /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
- * BN_div_no_branch will be called eventually.
- */
- pA = &local_A;
- BN_with_flags(pA, A, BN_FLG_CONSTTIME);
-
- /* (D, M) := (A/B, A%B) ... */
- if (!BN_div(D, M, pA, B, ctx)) {
- goto err;
- }
-
- /* Now
- * A = D*B + M;
- * thus we have
- * (**) sign*Y*a == D*B + M (mod |n|).
- */
-
- tmp = A; /* keep the BIGNUM object, the value does not matter */
-
- /* (A, B) := (B, A mod B) ... */
- A = B;
- B = M;
- /* ... so we have 0 <= B < A again */
-
- /* Since the former M is now B and the former B is now A,
- * (**) translates into
- * sign*Y*a == D*A + B (mod |n|),
- * i.e.
- * sign*Y*a - D*A == B (mod |n|).
- * Similarly, (*) translates into
- * -sign*X*a == A (mod |n|).
- *
- * Thus,
- * sign*Y*a + D*sign*X*a == B (mod |n|),
- * i.e.
- * sign*(Y + D*X)*a == B (mod |n|).
- *
- * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
- * -sign*X*a == B (mod |n|),
- * sign*Y*a == A (mod |n|).
- * Note that X and Y stay non-negative all the time.
- */
-
- if (!BN_mul(tmp, D, X, ctx)) {
- goto err;
- }
- if (!BN_add(tmp, tmp, Y)) {
- goto err;
- }
-
- M = Y; /* keep the BIGNUM object, the value does not matter */
- Y = X;
- X = tmp;
- sign = -sign;
- }
-
- if (!BN_is_one(A)) {
- *out_no_inverse = 1;
- OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
- goto err;
- }
-
- /*
- * The while loop (Euclid's algorithm) ends when
- * A == gcd(a,n);
- * we have
- * sign*Y*a == A (mod |n|),
- * where Y is non-negative.
- */
-
- if (sign < 0) {
- if (!BN_sub(Y, n, Y)) {
- goto err;
- }
- }
- /* Now Y*a == A (mod |n|). */
-
- /* Y*a == 1 (mod |n|) */
- if (!Y->neg && BN_ucmp(Y, n) < 0) {
- if (!BN_copy(R, Y)) {
- goto err;
- }
- } else {
- if (!BN_nnmod(R, Y, n, ctx)) {
- goto err;
- }
- }
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
- }
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