bn_nist.c

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/* crypto/bn/bn_nist.c */
/*
 * Written by Nils Larsch for the OpenSSL project
 */
/* ====================================================================
 * Copyright (c) 1998-2005 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
 *    [e-mail].
 *
 * 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
 * ([e-mail]).  This product includes software written by Tim
 * Hudson ([e-mail]).
 *
 */

#include "bn_lcl.h"
#include "cryptlib.h"

#define BN_NIST_192_TOP	(192+BN_BITS2-1)/BN_BITS2
#define BN_NIST_224_TOP	(224+BN_BITS2-1)/BN_BITS2
#define BN_NIST_256_TOP	(256+BN_BITS2-1)/BN_BITS2
#define BN_NIST_384_TOP	(384+BN_BITS2-1)/BN_BITS2
#define BN_NIST_521_TOP	(521+BN_BITS2-1)/BN_BITS2

#if BN_BITS2 == 64
static const BN_ULONG _nist_p_192[] =
	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,
	0xFFFFFFFFFFFFFFFFULL};
static const BN_ULONG _nist_p_224[] =
	{0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
	0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL};
static const BN_ULONG _nist_p_256[] =
	{0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
	0x0000000000000000ULL,0xFFFFFFFF00000001ULL};
static const BN_ULONG _nist_p_384[] =
	{0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,
	0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL};
static const BN_ULONG _nist_p_521[] =
	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0x00000000000001FFULL};
#elif BN_BITS2 == 32
static const BN_ULONG _nist_p_192[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
static const BN_ULONG _nist_p_224[] = {0x00000001,0x00000000,0x00000000,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
static const BN_ULONG _nist_p_256[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0x00000000,0x00000000,0x00000000,0x00000001,0xFFFFFFFF};
static const BN_ULONG _nist_p_384[] = {0xFFFFFFFF,0x00000000,0x00000000,
	0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0xFFFFFFFF,0x000001FF};
#elif BN_BITS2 == 16
static const BN_ULONG _nist_p_192[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFE,
	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
static const BN_ULONG _nist_p_224[] = {0x0001,0x0000,0x0000,0x0000,0x0000,
	0x0000,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
static const BN_ULONG _nist_p_256[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
	0xFFFF,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0001,0x0000,0xFFFF,
	0xFFFF};
static const BN_ULONG _nist_p_384[] = {0xFFFF,0xFFFF,0x0000,0x0000,0x0000,
	0x0000,0xFFFF,0xFFFF,0xFFFE,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
static const BN_ULONG _nist_p_521[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0x01FF};
#elif BN_BITS2 == 8
static const BN_ULONG _nist_p_192[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFE,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF};
static const BN_ULONG _nist_p_224[] = {0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
	0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF};
static const BN_ULONG _nist_p_256[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
	0x00,0x00,0x01,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF};
static const BN_ULONG _nist_p_384[] = {0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
	0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF};
static const BN_ULONG _nist_p_521[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
	0xFF,0x01};
#endif

const BIGNUM *BN_get0_nist_prime_192(void)
	{
	static BIGNUM const_nist_192 = { (BN_ULONG *)_nist_p_192,
		BN_NIST_192_TOP, BN_NIST_192_TOP, 0, BN_FLG_STATIC_DATA };
	return &const_nist_192;
	}

const BIGNUM *BN_get0_nist_prime_224(void)
	{
	static BIGNUM const_nist_224 = { (BN_ULONG *)_nist_p_224,
		BN_NIST_224_TOP, BN_NIST_224_TOP, 0, BN_FLG_STATIC_DATA };
	return &const_nist_224;
	}

const BIGNUM *BN_get0_nist_prime_256(void)
	{
	static BIGNUM const_nist_256 = { (BN_ULONG *)_nist_p_256,
		BN_NIST_256_TOP, BN_NIST_256_TOP, 0, BN_FLG_STATIC_DATA };
	return &const_nist_256;
	}

const BIGNUM *BN_get0_nist_prime_384(void)
	{
	static BIGNUM const_nist_384 = { (BN_ULONG *)_nist_p_384,
		BN_NIST_384_TOP, BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA };
	return &const_nist_384;
	}

const BIGNUM *BN_get0_nist_prime_521(void)
	{
	static BIGNUM const_nist_521 = { (BN_ULONG *)_nist_p_521,
		BN_NIST_521_TOP, BN_NIST_521_TOP, 0, BN_FLG_STATIC_DATA };
	return &const_nist_521;
	}

/* some misc internal functions */
#if BN_BITS2 != 64
static BN_ULONG _256_data[BN_NIST_256_TOP*6];
static int _is_set_256_data = 0;
static void _init_256_data(void);

static BN_ULONG _384_data[BN_NIST_384_TOP*8];
static int _is_set_384_data = 0;
static void _init_384_data(void);
#endif

#define BN_NIST_ADD_ONE(a)	while (!(++(*(a)))) ++(a);

static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
        {
	int i;
        BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
        for (i = (top); i != 0; i--)
                *_tmp1++ = *_tmp2++;
        for (i = (max) - (top); i != 0; i--)
                *_tmp1++ = (BN_ULONG) 0;
        }

static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
        { 
	int i;
        BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
        for (i = (top); i != 0; i--)
                *_tmp1++ = *_tmp2++;
        }

#if BN_BITS2 == 64
#define bn_cp_64(to, n, from, m)	(to)[n] = (from)[m];
#define bn_64_set_0(to, n)		(to)[n] = (BN_ULONG)0;
/* TBD */
#define bn_cp_32(to, n, from, m)	(to)[n] = (from)[m];
#define bn_32_set_0(to, n)		(to)[n] = (BN_ULONG)0;
#else
#define bn_cp_64(to, n, from, m) \
	{ \
	bn_cp_32(to, (n)*2, from, (m)*2); \
	bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
	}
#define bn_64_set_0(to, n) \
	{ \
	bn_32_set_0(to, (n)*2); \
	bn_32_set_0(to, (n)*2+1); \
	}
#if BN_BITS2 == 32
#define bn_cp_32(to, n, from, m)	(to)[n] = (from)[m];
#define bn_32_set_0(to, n)		(to)[n] = (BN_ULONG)0;
#elif BN_BITS2 == 16
#define bn_cp_32(to, n, from, m) \
	{ \
	(to)[(n)*2]   = (from)[(m)*2];  \
	(to)[(n)*2+1] = (from)[(m)*2+1];\
	}
#define bn_32_set_0(to, n) { (to)[(n)*2] = 0; (to)[(n)*2+1] = 0; }
#elif BN_BITS2 == 8
#define bn_cp_32(to, n, from, m) \
	{ \
	(to)[(n)*4]   = (from)[(m)*4];  \
	(to)[(n)*4+1] = (from)[(m)*4+1];\
	(to)[(n)*4+2] = (from)[(m)*4+2];\
	(to)[(n)*4+3] = (from)[(m)*4+3];\
	}
#define bn_32_set_0(to, n) \
	{ (to)[(n)*4]   = (BN_ULONG)0; (to)[(n)*4+1] = (BN_ULONG)0; \
	  (to)[(n)*4+2] = (BN_ULONG)0; (to)[(n)*4+3] = (BN_ULONG)0; }
#endif
#endif /* BN_BITS2 != 64 */


#define nist_set_192(to, from, a1, a2, a3) \
	{ \
	if (a3 != 0) bn_cp_64(to, 0, from, (a3) - 3) else bn_64_set_0(to, 0)\
	bn_cp_64(to, 1, from, (a2) - 3) \
	if (a1 != 0) bn_cp_64(to, 2, from, (a1) - 3) else bn_64_set_0(to, 2)\
	}

int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
	int      top = a->top, i;
	BN_ULONG carry = 0;
	register BN_ULONG *r_d, *a_d = a->d;
	BN_ULONG t_d[BN_NIST_192_TOP],
	         buf[BN_NIST_192_TOP];

	i = BN_ucmp(field, a);
	if (i == 0)
		{
		BN_zero(r);
		return 1;
		}
	else if (i > 0)
		return (r == a) ? 1 : (BN_copy(r ,a) != NULL);

	if (top == BN_NIST_192_TOP)
		return BN_usub(r, a, field);

	if (r != a)
		{
		if (!bn_wexpand(r, BN_NIST_192_TOP))
			return 0;
		r_d = r->d;
		nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
		}
	else
		r_d = a_d;

	nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);

#if defined(OPENSSL_SYS_VMS) && defined(__DECC)
# pragma message save
# pragma message disable BADSUBSCRIPT
#endif

	nist_set_192(t_d, buf, 0, 3, 3);
	if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
		++carry;

	nist_set_192(t_d, buf, 4, 4, 0);
	if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
		++carry;

#if defined(OPENSSL_SYS_VMS) && defined(__DECC)
# pragma message restore
#endif

	nist_set_192(t_d, buf, 5, 5, 5)
	if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
		++carry;

	while (carry)
		{
		if (bn_sub_words(r_d, r_d, _nist_p_192, BN_NIST_192_TOP))
			--carry; 
		}
	r->top = BN_NIST_192_TOP;
	bn_correct_top(r);
	if (BN_ucmp(r, field) >= 0)
		{
		bn_sub_words(r_d, r_d, _nist_p_192, BN_NIST_192_TOP);
		bn_correct_top(r);
		}

	bn_check_top(r);
	return 1;
	}

#define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
	{ \
	if (a7 != 0) bn_cp_32(to, 0, from, (a7) - 7) else bn_32_set_0(to, 0)\
	if (a6 != 0) bn_cp_32(to, 1, from, (a6) - 7) else bn_32_set_0(to, 1)\
	if (a5 != 0) bn_cp_32(to, 2, from, (a5) - 7) else bn_32_set_0(to, 2)\
	if (a4 != 0) bn_cp_32(to, 3, from, (a4) - 7) else bn_32_set_0(to, 3)\
	if (a3 != 0) bn_cp_32(to, 4, from, (a3) - 7) else bn_32_set_0(to, 4)\
	if (a2 != 0) bn_cp_32(to, 5, from, (a2) - 7) else bn_32_set_0(to, 5)\
	if (a1 != 0) bn_cp_32(to, 6, from, (a1) - 7) else bn_32_set_0(to, 6)\
	}

int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
#if BN_BITS2 != 64
	int	top = a->top, i;
	int	carry = 0;
	BN_ULONG *r_d, *a_d = a->d;
	BN_ULONG t_d[BN_NIST_224_TOP],
	         buf[BN_NIST_224_TOP];

	i = BN_ucmp(field, a);
	if (i == 0)
		{
		BN_zero(r);
		return 1;
		}
	else if (i > 0)
		return (r == a)? 1 : (BN_copy(r ,a) != NULL);

	if (top == BN_NIST_224_TOP)
		return BN_usub(r, a, field);

	if (r != a)
		{
		if (!bn_wexpand(r, BN_NIST_224_TOP))
			return 0;
		r_d = r->d;
		nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
		}
	else
		r_d = a_d;

	nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);

	nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
	if (bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP))
		++carry;
	nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
	if (bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP))
		++carry;
	nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
		--carry;
	nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
		--carry;

	if (carry > 0)
		while (carry)
			{
			if (bn_sub_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP))
				--carry;
			}