a684152a2f
We only ever compute it for odd (actually, prime) modulus as part of BN_mod_sqrt. If we cared, we could probably drop this from most binaries. This is used to when modular square root needs Tonelli-Shanks. Modular square root is only used for compressed coordinates. Of our supported curves (I'm handwaiving away EC_GROUP_new_curve_GFp here[*]), only P-224 needs the full Tonelli-Shanks algorithm (p is 1 mod 8). That computes the Legendre symbol a bunch to find a non-square mod p. But p is known at compile-time, so we can just hard-code a sample non-square. Sadly, BN_mod_sqrt has some callers outside of crypto/ec, so there's also that. Anyway, it's also not that large of a function. [*] Glancing through SEC 2 and Brainpool, secp224r1 is the only curve listed in either document whose prime is not either 3 mod 4 or 5 mod 8. Even 5 mod 8 is rare: only secp224k1. It's unlikely anyone would notice if we broke annoying primes. Though OpenSSL does support "WTLS" curves which has an additional 1 mod 8 case. Change-Id: If36aa78c0d41253ec024f2d90692949515356cd1 Reviewed-on: https://boringssl-review.googlesource.com/15425 Reviewed-by: Adam Langley <agl@google.com>
272 lines
12 KiB
C
272 lines
12 KiB
C
/* Copyright (C) 1995-1997 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).
|
|
*
|
|
*/
|
|
/* ====================================================================
|
|
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
|
|
*
|
|
* Portions of the attached software ("Contribution") are developed by
|
|
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
|
|
*
|
|
* The Contribution is licensed pursuant to the Eric Young open source
|
|
* license provided above.
|
|
*
|
|
* The binary polynomial arithmetic software is originally written by
|
|
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
|
|
* Laboratories. */
|
|
|
|
#ifndef OPENSSL_HEADER_BN_INTERNAL_H
|
|
#define OPENSSL_HEADER_BN_INTERNAL_H
|
|
|
|
#include <openssl/base.h>
|
|
|
|
#if defined(OPENSSL_X86_64) && defined(_MSC_VER)
|
|
OPENSSL_MSVC_PRAGMA(warning(push, 3))
|
|
#include <intrin.h>
|
|
OPENSSL_MSVC_PRAGMA(warning(pop))
|
|
#pragma intrinsic(__umulh, _umul128)
|
|
#endif
|
|
|
|
#include "../internal.h"
|
|
|
|
#if defined(__cplusplus)
|
|
extern "C" {
|
|
#endif
|
|
|
|
#if defined(OPENSSL_64_BIT)
|
|
|
|
#if !defined(_MSC_VER)
|
|
/* MSVC doesn't support two-word integers on 64-bit. */
|
|
#define BN_ULLONG uint128_t
|
|
#endif
|
|
|
|
#define BN_BITS2 64
|
|
#define BN_BYTES 8
|
|
#define BN_BITS4 32
|
|
#define BN_MASK2 (0xffffffffffffffffUL)
|
|
#define BN_MASK2l (0xffffffffUL)
|
|
#define BN_MASK2h (0xffffffff00000000UL)
|
|
#define BN_MASK2h1 (0xffffffff80000000UL)
|
|
#define BN_MONT_CTX_N0_LIMBS 1
|
|
#define BN_TBIT (0x8000000000000000UL)
|
|
#define BN_DEC_CONV (10000000000000000000UL)
|
|
#define BN_DEC_NUM 19
|
|
#define TOBN(hi, lo) ((BN_ULONG)(hi) << 32 | (lo))
|
|
|
|
#elif defined(OPENSSL_32_BIT)
|
|
|
|
#define BN_ULLONG uint64_t
|
|
#define BN_BITS2 32
|
|
#define BN_BYTES 4
|
|
#define BN_BITS4 16
|
|
#define BN_MASK2 (0xffffffffUL)
|
|
#define BN_MASK2l (0xffffUL)
|
|
#define BN_MASK2h1 (0xffff8000UL)
|
|
#define BN_MASK2h (0xffff0000UL)
|
|
/* On some 32-bit platforms, Montgomery multiplication is done using 64-bit
|
|
* arithmetic with SIMD instructions. On such platforms, |BN_MONT_CTX::n0|
|
|
* needs to be two words long. Only certain 32-bit platforms actually make use
|
|
* of n0[1] and shorter R value would suffice for the others. However,
|
|
* currently only the assembly files know which is which. */
|
|
#define BN_MONT_CTX_N0_LIMBS 2
|
|
#define BN_TBIT (0x80000000UL)
|
|
#define BN_DEC_CONV (1000000000UL)
|
|
#define BN_DEC_NUM 9
|
|
#define TOBN(hi, lo) (lo), (hi)
|
|
|
|
#else
|
|
#error "Must define either OPENSSL_32_BIT or OPENSSL_64_BIT"
|
|
#endif
|
|
|
|
|
|
#define STATIC_BIGNUM(x) \
|
|
{ \
|
|
(BN_ULONG *)(x), sizeof(x) / sizeof(BN_ULONG), \
|
|
sizeof(x) / sizeof(BN_ULONG), 0, BN_FLG_STATIC_DATA \
|
|
}
|
|
|
|
#if defined(BN_ULLONG)
|
|
#define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
|
|
#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
|
|
#endif
|
|
|
|
/* bn_correct_top decrements |bn->top| until |bn->d[top-1]| is non-zero or
|
|
* until |top| is zero. If |bn| is zero, |bn->neg| is set to zero. */
|
|
void bn_correct_top(BIGNUM *bn);
|
|
|
|
/* bn_wexpand ensures that |bn| has at least |words| works of space without
|
|
* altering its value. It returns one on success or zero on allocation
|
|
* failure. */
|
|
int bn_wexpand(BIGNUM *bn, size_t words);
|
|
|
|
/* bn_expand acts the same as |bn_wexpand|, but takes a number of bits rather
|
|
* than a number of words. */
|
|
int bn_expand(BIGNUM *bn, size_t bits);
|
|
|
|
/* bn_set_words sets |bn| to the value encoded in the |num| words in |words|,
|
|
* least significant word first. */
|
|
int bn_set_words(BIGNUM *bn, const BN_ULONG *words, size_t num);
|
|
|
|
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
|
|
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
|
|
void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
|
|
BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
|
|
BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
|
|
|
|
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
|
|
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
|
|
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
|
|
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
|
|
|
|
/* bn_cmp_words returns a value less than, equal to or greater than zero if
|
|
* the, length |n|, array |a| is less than, equal to or greater than |b|. */
|
|
int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
|
|
|
|
/* bn_cmp_words returns a value less than, equal to or greater than zero if the
|
|
* array |a| is less than, equal to or greater than |b|. The arrays can be of
|
|
* different lengths: |cl| gives the minimum of the two lengths and |dl| gives
|
|
* the length of |a| minus the length of |b|. */
|
|
int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
|
|
|
|
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
|
|
const BN_ULONG *np, const BN_ULONG *n0, int num);
|
|
|
|
uint64_t bn_mont_n0(const BIGNUM *n);
|
|
int bn_mod_exp_base_2_vartime(BIGNUM *r, unsigned p, const BIGNUM *n);
|
|
|
|
#if defined(OPENSSL_X86_64) && defined(_MSC_VER)
|
|
#define BN_UMULT_LOHI(low, high, a, b) ((low) = _umul128((a), (b), &(high)))
|
|
#endif
|
|
|
|
#if !defined(BN_ULLONG) && !defined(BN_UMULT_LOHI)
|
|
#error "Either BN_ULLONG or BN_UMULT_LOHI must be defined on every platform."
|
|
#endif
|
|
|
|
/* bn_mod_inverse_prime sets |out| to the modular inverse of |a| modulo |p|,
|
|
* computed with Fermat's Little Theorem. It returns one on success and zero on
|
|
* error. If |mont_p| is NULL, one will be computed temporarily. */
|
|
int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
|
|
BN_CTX *ctx, const BN_MONT_CTX *mont_p);
|
|
|
|
/* bn_mod_inverse_secret_prime behaves like |bn_mod_inverse_prime| but uses
|
|
* |BN_mod_exp_mont_consttime| instead of |BN_mod_exp_mont| in hopes of
|
|
* protecting the exponent. */
|
|
int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
|
|
BN_CTX *ctx, const BN_MONT_CTX *mont_p);
|
|
|
|
/* bn_jacobi returns the Jacobi symbol of |a| and |b| (which is -1, 0 or 1), or
|
|
* -2 on error. */
|
|
int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
|
|
|
|
|
|
#if defined(__cplusplus)
|
|
} /* extern C */
|
|
#endif
|
|
|
|
#endif /* OPENSSL_HEADER_BN_INTERNAL_H */
|