boringssl / boringssl / 6dfb479755a4a22960dc68efb65e9d061ce1f65f / . / crypto / fipsmodule / bn / gcd.c

/* 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" | |

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_consttime(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; | |

} | |

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; | |

} |