crypto/fipsmodule/bn/internal.h - boringssl - Git at Google

 /* 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_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_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_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_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);

 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);


 // 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_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
	/* 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_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_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_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_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[2i]\| and \|rp[2i+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);

	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);


	// 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_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