/* 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(BORINGSSL_HAS_UINT128)
// MSVC doesn't support two-word integers on 64-bit.
#define BN_ULLONG uint128_t
#if defined(BORINGSSL_CAN_DIVIDE_UINT128)
#define BN_CAN_DIVIDE_ULLONG
#endif
#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_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_CAN_DIVIDE_ULLONG
#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_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))
#define Hw(t) ((BN_ULONG)((t) >> BN_BITS2))
#endif
// bn_minimal_width returns the minimal value of |bn->top| which fits the
// value of |bn|.
int bn_minimal_width(const BIGNUM *bn);
// bn_correct_top decrements |bn->top| to |bn_minimal_width|. 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_resize_words adjusts |bn->top| to be |words|. It returns one on success
// and zero on allocation error or if |bn|'s value is too large.
//
// Do not call this function outside of unit tests. Most functions currently
// require |BIGNUM|s be minimal. This function breaks that invariant. It is
// introduced early so the invariant may be relaxed incrementally.
int bn_resize_words(BIGNUM *bn, size_t words);
// 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_fits_in_words returns one if |bn| may be represented in |num| words, plus
// a sign bit, and zero otherwise.
int bn_fits_in_words(const BIGNUM *bn, size_t num);
// bn_copy_words copies the value of |bn| to |out| and returns one if the value
// is representable in |num| words. Otherwise, it returns zero.
int bn_copy_words(BN_ULONG *out, size_t num, const BIGNUM *bn);
// bn_mul_add_words multiples |ap| by |w|, adds the result to |rp|, and places
// the result in |rp|. |ap| and |rp| must both be |num| words long. It returns
// the carry word of the operation. |ap| and |rp| may be equal but otherwise may
// not alias.
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
BN_ULONG w);
// bn_mul_words multiples |ap| by |w| and places the result in |rp|. |ap| and
// |rp| must both be |num| words long. It returns the carry word of the
// operation. |ap| and |rp| may be equal but otherwise may not alias.
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w);
// bn_sqr_words sets |rp[2*i]| and |rp[2*i+1]| to |ap[i]|'s square, for all |i|
// up to |num|. |ap| is an array of |num| words and |rp| an array of |2*num|
// words. |ap| and |rp| may not alias.
//
// This gives the contribution of the |ap[i]*ap[i]| terms when squaring |ap|.
void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num);
// bn_add_words adds |ap| to |bp| and places the result in |rp|, each of which
// are |num| words long. It returns the carry bit, which is one if the operation
// overflowed and zero otherwise. Any pair of |ap|, |bp|, and |rp| may be equal
// to each other but otherwise may not alias.
BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
size_t num);
// bn_sub_words subtracts |bp| from |ap| and places the result in |rp|. It
// returns the borrow bit, which is one if the computation underflowed and zero
// otherwise. Any pair of |ap|, |bp|, and |rp| may be equal to each other but
// otherwise may not alias.
BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
size_t num);
// bn_mul_comba4 sets |r| to the product of |a| and |b|.
void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]);
// bn_mul_comba8 sets |r| to the product of |a| and |b|.
void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]);
// bn_sqr_comba8 sets |r| to |a|^2.
void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[4]);
// bn_sqr_comba4 sets |r| to |a|^2.
void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]);
// 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);
// bn_less_than_words returns one if |a| < |b| and zero otherwise, where |a|
// and |b| both are |len| words long. It runs in constant time.
int bn_less_than_words(const BN_ULONG *a, const BN_ULONG *b, size_t len);
// bn_in_range_words returns one if |min_inclusive| <= |a| < |max_exclusive|,
// where |a| and |max_exclusive| both are |len| words long. This function leaks
// which of [0, min_inclusive), [min_inclusive, max_exclusive), and
// [max_exclusive, 2^(BN_BITS2*len)) contains |a|, but otherwise the value of
// |a| is secret.
int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive,
const BN_ULONG *max_exclusive, size_t len);
// bn_rand_range_words sets |out| to a uniformly distributed random number from
// |min_inclusive| to |max_exclusive|. Both |out| and |max_exclusive| are |len|
// words long.
//
// This function runs in time independent of the result, but |min_inclusive| and
// |max_exclusive| are public data. (Information about the range is unavoidably
// leaked by how many iterations it took to select a number.)
int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive,
const BN_ULONG *max_exclusive, size_t len,
const uint8_t additional_data[32]);
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);
// bn_is_bit_set_words returns one if bit |bit| is set in |a| and zero
// otherwise.
int bn_is_bit_set_words(const BN_ULONG *a, size_t num, unsigned bit);
// bn_one_to_montgomery sets |r| to one in Montgomery form. It returns one on
// success and zero on error. This function treats the bit width of the modulus
// as public.
int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx);
// bn_less_than_montgomery_R returns one if |bn| is less than the Montgomery R
// value for |mont| and zero otherwise.
int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont);
// Low-level operations for small numbers.
//
// The following functions implement algorithms suitable for use with scalars
// and field elements in elliptic curves. They rely on the number being small
// both to stack-allocate various temporaries and because they do not implement
// optimizations useful for the larger values used in RSA.
// BN_SMALL_MAX_WORDS is the largest size input these functions handle. This
// limit allows temporaries to be more easily stack-allocated. This limit is set
// to accommodate P-521.
#if defined(OPENSSL_32_BIT)
#define BN_SMALL_MAX_WORDS 17
#else
#define BN_SMALL_MAX_WORDS 9
#endif
// bn_mul_small sets |r| to |a|*|b|. |num_r| must be |num_a| + |num_b|. |r| may
// not alias with |a| or |b|. This function returns one on success and zero if
// lengths are inconsistent.
int bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
const BN_ULONG *b, size_t num_b);
// bn_sqr_small sets |r| to |a|^2. |num_a| must be at most |BN_SMALL_MAX_WORDS|.
// |num_r| must be |num_a|*2. |r| and |a| may not alias. This function returns
// one on success and zero on programmer error.
int bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a);
// In the following functions, the modulus must be at most |BN_SMALL_MAX_WORDS|
// words long.
// bn_to_montgomery_small sets |r| to |a| translated to the Montgomery domain.
// |num_a| and |num_r| must be the length of the modulus, which is
// |mont->N.top|. |a| must be fully reduced. This function returns one on
// success and zero if lengths are inconsistent. |r| and |a| may alias.
int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
size_t num_a, const BN_MONT_CTX *mont);
// bn_from_montgomery_small sets |r| to |a| translated out of the Montgomery
// domain. |num_r| must be the length of the modulus, which is |mont->N.top|.
// |a| must be at most |mont->N.top| * R and |num_a| must be at most 2 *
// |mont->N.top|. This function returns one on success and zero if lengths are
// inconsistent. |r| and |a| may alias.
int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
size_t num_a, const BN_MONT_CTX *mont);
// bn_one_to_montgomery_small sets |r| to one in Montgomery form. It returns one
// on success and zero on error. |num_r| must be the length of the modulus,
// which is |mont->N.top|. This function treats the bit width of the modulus as
// public.
int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r,
const BN_MONT_CTX *mont);
// bn_mod_mul_montgomery_small sets |r| to |a| * |b| mod |mont->N|. Both inputs
// and outputs are in the Montgomery domain. |num_r| must be the length of the
// modulus, which is |mont->N.top|. This function returns one on success and
// zero on internal error or inconsistent lengths. Any two of |r|, |a|, and |b|
// may alias.
//
// This function requires |a| * |b| < N * R, where N is the modulus and R is the
// Montgomery divisor, 2^(N.top * BN_BITS2). This should generally be satisfied
// by ensuring |a| and |b| are fully reduced, however ECDSA has one computation
// which requires the more general bound.
int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
size_t num_a, const BN_ULONG *b, size_t num_b,
const BN_MONT_CTX *mont);
// bn_mod_exp_mont_small sets |r| to |a|^|p| mod |mont->N|. It returns one on
// success and zero on programmer or internal error. Both inputs and outputs are
// in the Montgomery domain. |num_r| and |num_a| must be |mont->N.top|, which
// must be at most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This
// function runs in time independent of |a|, but |p| and |mont->N| are public
// values.
//
// Note this function differs from |BN_mod_exp_mont| which uses Montgomery
// reduction but takes input and output outside the Montgomery domain. Combine
// this function with |bn_from_montgomery_small| and |bn_to_montgomery_small|
// if necessary.
int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
size_t num_a, const BN_ULONG *p, size_t num_p,
const BN_MONT_CTX *mont);
// bn_mod_inverse_prime_mont_small sets |r| to |a|^-1 mod |mont->N|. |mont->N|
// must be a prime. |num_r| and |num_a| must be |mont->N.top|, which must be at
// most |BN_SMALL_MAX_WORDS|. |a| must be fully-reduced. This function runs in
// time independent of |a|, but |mont->N| is a public value.
int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r,
const BN_ULONG *a, size_t num_a,
const BN_MONT_CTX *mont);
#if defined(__cplusplus)
} // extern C
#endif
#endif // OPENSSL_HEADER_BN_INTERNAL_H