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boringssl/crypto/bn/gcd.c
Brian Smith ec3cb3adbc Add |BN_mod_inverse_blinded| and use it in RSA blinding. 
Yo dawg I herd you like blinding so I put inversion blinding in your
RSA blinding so you can randomly mask your random mask.

This improves upon the current situation where we pretend that
|BN_mod_inverse_no_branch| is constant-time, and it avoids the need to
exert a lot of effort to make a actually-constant-time modular
inversion function just for RSA blinding.

Note that if the random number generator weren't working correctly then
the blinding of the inversion wouldn't be very effective, but in that
case the RSA blinding itself would probably be completely busted, so
we're not really losing anything by relying on blinding to blind the
blinding.

Change-Id: I771100f0ad8ed3c24e80dd859ec22463ef2a194f
Reviewed-on: https://boringssl-review.googlesource.com/8923
Reviewed-by: Adam Langley <agl@google.com>
Commit-Queue: Adam Langley <agl@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
2016-07-29 18:30:34 +00:00

755 lines
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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 <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 BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, int *out_no_inverse,
const BIGNUM *a, const BIGNUM *n,
BN_CTX *ctx);
static BIGNUM *bn_mod_inverse_ex(BIGNUM *out, int *out_no_inverse,
const BIGNUM *a, const BIGNUM *n,
BN_CTX *ctx) {
BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
BIGNUM *ret = NULL;
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;
}
if (out == NULL) {
R = BN_new();
} else {
R = out;
}
if (R == NULL) {
goto err;
}
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|).
*/
if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS2 <= 32 ? 450 : 2048))) {
/* 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
* sytems, 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;
}
}
}
} else {
/* general inversion algorithm */
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_num_bits(A) == BN_num_bits(B)) {
if (!BN_one(D)) {
goto err;
}
if (!BN_sub(M, A, B)) {
goto err;
}
} else if (BN_num_bits(A) == BN_num_bits(B) + 1) {
/* A/B is 1, 2, or 3 */
if (!BN_lshift1(T, B)) {
goto err;
}
if (BN_ucmp(A, T) < 0) {
/* A < 2*B, so D=1 */
if (!BN_one(D)) {
goto err;
}
if (!BN_sub(M, A, B)) {
goto err;
}
} else {
/* A >= 2*B, so D=2 or D=3 */
if (!BN_sub(M, A, T)) {
goto err;
}
if (!BN_add(D, T, B)) {
goto err; /* use D (:= 3*B) as temp */
}
if (BN_ucmp(A, D) < 0) {
/* A < 3*B, so D=2 */
if (!BN_set_word(D, 2)) {
goto err;
}
/* M (= A - 2*B) already has the correct value */
} else {
/* only D=3 remains */
if (!BN_set_word(D, 3)) {
goto err;
}
/* currently M = A - 2*B, but we need M = A - 3*B */
if (!BN_sub(M, M, B)) {
goto err;
}
}
}
} else {
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. */
/* most of the time D is very small, so we can optimize tmp := D*X+Y */
if (BN_is_one(D)) {
if (!BN_add(tmp, X, Y)) {
goto err;
}
} else {
if (BN_is_word(D, 2)) {
if (!BN_lshift1(tmp, X)) {
goto err;
}
} else if (BN_is_word(D, 4)) {
if (!BN_lshift(tmp, X, 2)) {
goto err;
}
} else if (D->top == 1) {
if (!BN_copy(tmp, X)) {
goto err;
}
if (!BN_mul_word(tmp, D->d[0])) {
goto err;
}
} else {
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 = R;
err:
if (ret == NULL && out == NULL) {
BN_free(R);
}
BN_CTX_end(ctx);
return ret;
}
BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
BN_CTX *ctx) {
int no_inverse;
if ((a->flags & BN_FLG_CONSTTIME) != 0 ||
(n->flags & BN_FLG_CONSTTIME) != 0) {
return BN_mod_inverse_no_branch(out, &no_inverse, a, n, ctx);
}
if (!a->neg && BN_ucmp(a, n) < 0) {
return bn_mod_inverse_ex(out, &no_inverse, a, n, ctx);
}
BIGNUM a_reduced;
BN_init(&a_reduced);
BIGNUM *ret = NULL;
if (!BN_nnmod(&a_reduced, a, n, ctx)) {
goto err;
}
ret = bn_mod_inverse_ex(out, &no_inverse, &a_reduced, n, ctx);
err:
BN_free(&a_reduced);
return ret;
}
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_ex(out, out_no_inverse, out, &mont->N, ctx) == NULL ||
!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_no_branch is a special version of BN_mod_inverse.
* It does not contain branches that may leak sensitive information. */
static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *out, int *out_no_inverse,
const BIGNUM *a, const BIGNUM *n,
BN_CTX *ctx) {
BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
BIGNUM local_A, local_B;
BIGNUM *pA, *pB;
BIGNUM *ret = NULL;
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;
}
if (out == NULL) {
R = BN_new();
} else {
R = out;
}
if (R == NULL) {
goto err;
}
BN_zero(Y);
if (!BN_one(X) || BN_copy(B, a) == NULL || BN_copy(A, n) == NULL) {
goto err;
}
A->neg = 0;
if (B->neg || (BN_ucmp(B, A) >= 0)) {
/* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
* BN_div_no_branch will be called eventually.
*/
pB = &local_B;
BN_with_flags(pB, B, BN_FLG_CONSTTIME);
if (!BN_nnmod(B, pB, A, ctx)) {
goto err;
}
}
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 = R;
err:
if (ret == NULL && out == NULL) {
BN_free(R);
}
BN_CTX_end(ctx);
return ret;
}
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