/* 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) {
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;
BIGNUM *a_reduced = NULL;
if (a->neg || BN_ucmp(a, n) >= 0) {
a_reduced = BN_dup(a);
if (a_reduced == NULL) {
goto err;
}
if (!BN_nnmod(a_reduced, a_reduced, n, ctx)) {
goto err;
}
a = a_reduced;
}
int no_inverse;
if (!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;
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|)
*/
/* (D, M) := (A/B, A%B) ... */
if (!BN_div(D, M, A, 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;
}
int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
BN_CTX *ctx, const BN_MONT_CTX *mont_p) {
BN_CTX_start(ctx);
BIGNUM *p_minus_2 = BN_CTX_get(ctx);
int ok = p_minus_2 != NULL &&
BN_copy(p_minus_2, p) &&
BN_sub_word(p_minus_2, 2) &&
BN_mod_exp_mont(out, a, p_minus_2, p, ctx, mont_p);
BN_CTX_end(ctx);
return ok;
}
int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
BN_CTX *ctx, const BN_MONT_CTX *mont_p) {
BN_CTX_start(ctx);
BIGNUM *p_minus_2 = BN_CTX_get(ctx);
int ok = p_minus_2 != NULL &&
BN_copy(p_minus_2, p) &&
BN_sub_word(p_minus_2, 2) &&
BN_mod_exp_mont_consttime(out, a, p_minus_2, p, ctx, mont_p);
BN_CTX_end(ctx);
return ok;
}