bn_nist.c   [plain text]

/* 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
 *    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 "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

/* pre-computed tables are "carry-less" values of modulus*(i+1) */
#if BN_BITS2 == 64
static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
	{0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
	{0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
	};
static const BN_ULONG _nist_p_192_sqr[] = {
	0x0000000000000001ULL,0x0000000000000002ULL,0x0000000000000001ULL,
	0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL
	};
static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
	{0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
	 0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
	{0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
	 0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
	};
static const BN_ULONG _nist_p_224_sqr[] = {
	0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
	0xFFFFFFFFFFFFFFFFULL,0x0000000200000000ULL,
	0x0000000000000000ULL,0xFFFFFFFFFFFFFFFEULL,
	0xFFFFFFFFFFFFFFFFULL
	};
static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
	{0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
	 0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
	{0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
	 0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
	{0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
	 0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
	{0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
	 0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
	{0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
	 0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
	};
static const BN_ULONG _nist_p_256_sqr[] = {
	0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
	0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFEULL,
	0x00000001FFFFFFFEULL,0x00000001FFFFFFFEULL,
	0xFFFFFFFE00000001ULL,0xFFFFFFFE00000002ULL
	};
static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
	{0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
	{0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
	{0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
	{0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
	{0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
	};
static const BN_ULONG _nist_p_384_sqr[] = {
	0xFFFFFFFE00000001ULL,0x0000000200000000ULL,0xFFFFFFFE00000000ULL,
	0x0000000200000000ULL,0x0000000000000001ULL,0x0000000000000000ULL,
	0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL
	};
static const BN_ULONG _nist_p_521[] =
	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0x00000000000001FFULL};
static const BN_ULONG _nist_p_521_sqr[] = {
	0x0000000000000001ULL,0x0000000000000000ULL,0x0000000000000000ULL,
	0x0000000000000000ULL,0x0000000000000000ULL,0x0000000000000000ULL,
	0x0000000000000000ULL,0x0000000000000000ULL,0xFFFFFFFFFFFFFC00ULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
	0xFFFFFFFFFFFFFFFFULL,0x000000000003FFFFULL
	};
#elif BN_BITS2 == 32
static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
	{0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
	};
static const BN_ULONG _nist_p_192_sqr[] = {
	0x00000001,0x00000000,0x00000002,0x00000000,0x00000001,0x00000000,
	0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
	};
static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
	{0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
	};
static const BN_ULONG _nist_p_224_sqr[] = {
	0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
	0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000002,
	0x00000000,0x00000000,0xFFFFFFFE,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF
	};
static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
	{0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
	 0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
	{0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
	 0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
	{0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
	 0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
	{0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
	 0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
	{0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
	 0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
	};
static const BN_ULONG _nist_p_256_sqr[] = {
	0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0x00000001,
	0xFFFFFFFE,0x00000001,0xFFFFFFFE,0x00000001,
	0x00000001,0xFFFFFFFE,0x00000002,0xFFFFFFFE
	};
static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
	{0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	{0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
	};
static const BN_ULONG _nist_p_384_sqr[] = {
	0x00000001,0xFFFFFFFE,0x00000000,0x00000002,0x00000000,0xFFFFFFFE,
	0x00000000,0x00000002,0x00000001,0x00000000,0x00000000,0x00000000,
	0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,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};
static const BN_ULONG _nist_p_521_sqr[] = {
	0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
	0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
	0x00000000,0x00000000,0x00000000,0x00000000,0xFFFFFC00,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
	0xFFFFFFFF,0xFFFFFFFF,0x0003FFFF
	};
#else
#error "unsupported BN_BITS2"
#endif


static const BIGNUM _bignum_nist_p_192 =
	{
	(BN_ULONG *)_nist_p_192[0],
	BN_NIST_192_TOP,
	BN_NIST_192_TOP,
	0,
	BN_FLG_STATIC_DATA
	};

static const BIGNUM _bignum_nist_p_224 =
	{
	(BN_ULONG *)_nist_p_224[0],
	BN_NIST_224_TOP,
	BN_NIST_224_TOP,
	0,
	BN_FLG_STATIC_DATA
	};

static const BIGNUM _bignum_nist_p_256 =
	{
	(BN_ULONG *)_nist_p_256[0],
	BN_NIST_256_TOP,
	BN_NIST_256_TOP,
	0,
	BN_FLG_STATIC_DATA
	};

static const BIGNUM _bignum_nist_p_384 =
	{
	(BN_ULONG *)_nist_p_384[0],
	BN_NIST_384_TOP,
	BN_NIST_384_TOP,
	0,
	BN_FLG_STATIC_DATA
	};

static const BIGNUM _bignum_nist_p_521 =
	{
	(BN_ULONG *)_nist_p_521,
	BN_NIST_521_TOP,
	BN_NIST_521_TOP,
	0,
	BN_FLG_STATIC_DATA
	};


const BIGNUM *BN_get0_nist_prime_192(void)
	{
	return &_bignum_nist_p_192;
	}

const BIGNUM *BN_get0_nist_prime_224(void)
	{
	return &_bignum_nist_p_224;
	}

const BIGNUM *BN_get0_nist_prime_256(void)
	{
	return &_bignum_nist_p_256;
	}

const BIGNUM *BN_get0_nist_prime_384(void)
	{
	return &_bignum_nist_p_384;
	}

const BIGNUM *BN_get0_nist_prime_521(void)
	{
	return &_bignum_nist_p_521;
	}


static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
	{
	int i;
	BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);

#ifdef BN_DEBUG
	OPENSSL_assert(top <= max);
#endif
	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] = (m>=0)?((from)[m]):0;
#define bn_64_set_0(to, n)		(to)[n] = (BN_ULONG)0;
/*
 * two following macros are implemented under assumption that they
 * are called in a sequence with *ascending* n, i.e. as they are...
 */
#define bn_cp_32_naked(to, n, from, m)	(((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\
						:(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
#define bn_32_set_0(to, n)		(((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
#define bn_cp_32(to,n,from,m)		((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
#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] = (m>=0)?((from)[m]):0;
#define bn_32_set_0(to, n)		(to)[n] = (BN_ULONG)0;
#endif
#endif /* BN_BITS2 != 64 */


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

int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
	int      top = a->top, i;
	int      carry;
	register BN_ULONG *r_d, *a_d = a->d;
	BN_ULONG t_d[BN_NIST_192_TOP],
	         buf[BN_NIST_192_TOP],
		 c_d[BN_NIST_192_TOP],
		*res;
	size_t   mask;
	static const BIGNUM _bignum_nist_p_192_sqr = {
		(BN_ULONG *)_nist_p_192_sqr,
		sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
		sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
		0,BN_FLG_STATIC_DATA };

	field = &_bignum_nist_p_192; /* just to make sure */

 	if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
		return BN_nnmod(r, a, field, ctx);

	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 (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);

	nist_set_192(t_d, buf, 0, 3, 3);
	carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
	nist_set_192(t_d, buf, 4, 4, 0);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
	nist_set_192(t_d, buf, 5, 5, 5)
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);

	if (carry > 0)
		carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
	else
		carry = 1;

	/*
	 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
	 * as comparison implies subtraction, we can write
	 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
	 * this is what happens below, but without explicit if:-) a.
	 */
	mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
	mask &= 0-(size_t)carry;
	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
	nist_cp_bn(r_d, res, BN_NIST_192_TOP);
	r->top = BN_NIST_192_TOP;
	bn_correct_top(r);

	return 1;
	}

typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);

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

int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
	int	top = a->top, i;
	int	carry;
	BN_ULONG *r_d, *a_d = a->d;
	BN_ULONG t_d[BN_NIST_224_TOP],
	         buf[BN_NIST_224_TOP],
		 c_d[BN_NIST_224_TOP],
		*res;
	size_t   mask;
	union { bn_addsub_f f; size_t p; } u;
	static const BIGNUM _bignum_nist_p_224_sqr = {
		(BN_ULONG *)_nist_p_224_sqr,
		sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
		sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
		0,BN_FLG_STATIC_DATA };


	field = &_bignum_nist_p_224; /* just to make sure */

 	if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
		return BN_nnmod(r, a, field, ctx);

	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 (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;

#if BN_BITS2==64
	/* copy upper 256 bits of 448 bit number ... */
	nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
	/* ... and right shift by 32 to obtain upper 224 bits */
	nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
	/* truncate lower part to 224 bits too */
	r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
#else
	nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
#endif
	nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
	carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
	nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
	nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
	nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);

#if BN_BITS2==64
	carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
#endif
	u.f = bn_sub_words;
	if (carry > 0)
		{
		carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
#if BN_BITS2==64
		carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
#endif
		}
	else if (carry < 0)
		{
		/* it's a bit more comlicated logic in this case.
		 * if bn_add_words yields no carry, then result
		 * has to be adjusted by unconditionally *adding*
		 * the modulus. but if it does, then result has
		 * to be compared to the modulus and conditionally
		 * adjusted by *subtracting* the latter. */
		carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
		mask = 0-(size_t)carry;
		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
		}
	else
		carry = 1;

	/* otherwise it's effectively same as in BN_nist_mod_192... */
	mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
	mask &= 0-(size_t)carry;
	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
	nist_cp_bn(r_d, res, BN_NIST_224_TOP);
	r->top = BN_NIST_224_TOP;
	bn_correct_top(r);

	return 1;
	}

#define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
	{ \
	bn_cp_32(to, 0, from, (a8) - 8) \
	bn_cp_32(to, 1, from, (a7) - 8) \
	bn_cp_32(to, 2, from, (a6) - 8) \
	bn_cp_32(to, 3, from, (a5) - 8) \
	bn_cp_32(to, 4, from, (a4) - 8) \
	bn_cp_32(to, 5, from, (a3) - 8) \
	bn_cp_32(to, 6, from, (a2) - 8) \
	bn_cp_32(to, 7, from, (a1) - 8) \
	}

int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
	int	i, top = a->top;
	int	carry = 0;
	register BN_ULONG *a_d = a->d, *r_d;
	BN_ULONG t_d[BN_NIST_256_TOP],
	         buf[BN_NIST_256_TOP],
		 c_d[BN_NIST_256_TOP],
		*res;
	size_t   mask;
	union { bn_addsub_f f; size_t p; } u;
	static const BIGNUM _bignum_nist_p_256_sqr = {
		(BN_ULONG *)_nist_p_256_sqr,
		sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
		sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
		0,BN_FLG_STATIC_DATA };

	field = &_bignum_nist_p_256; /* just to make sure */

 	if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
		return BN_nnmod(r, a, field, ctx);

	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 (r != a)
		{
		if (!bn_wexpand(r, BN_NIST_256_TOP))
			return 0;
		r_d = r->d;
		nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
		}
	else
		r_d = a_d;

	nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);

	/*S1*/
	nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
	/*S2*/
	nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
	carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
	/* left shift */
		{
		register BN_ULONG *ap,t,c;
		ap = t_d;
		c=0;
		for (i = BN_NIST_256_TOP; i != 0; --i)
			{
			t= *ap;
			*(ap++)=((t<<1)|c)&BN_MASK2;
			c=(t & BN_TBIT)?1:0;
			}
		carry <<= 1;
		carry  |= c;
		}
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
	/*S3*/
	nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
	/*S4*/
	nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
	/*D1*/
	nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
	/*D2*/
	nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
	/*D3*/
	nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
	/*D4*/
	nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);

	/* see BN_nist_mod_224 for explanation */
	u.f = bn_sub_words;
	if (carry > 0)
		carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
	else if (carry < 0)
		{
		carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
		mask = 0-(size_t)carry;
		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
		}
	else
		carry = 1;

	mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
	mask &= 0-(size_t)carry;
	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
	nist_cp_bn(r_d, res, BN_NIST_256_TOP);
	r->top = BN_NIST_256_TOP;
	bn_correct_top(r);

	return 1;
	}

#define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
	{ \
	bn_cp_32(to, 0, from,  (a12) - 12) \
	bn_cp_32(to, 1, from,  (a11) - 12) \
	bn_cp_32(to, 2, from,  (a10) - 12) \
	bn_cp_32(to, 3, from,  (a9) - 12)  \
	bn_cp_32(to, 4, from,  (a8) - 12)  \
	bn_cp_32(to, 5, from,  (a7) - 12)  \
	bn_cp_32(to, 6, from,  (a6) - 12)  \
	bn_cp_32(to, 7, from,  (a5) - 12)  \
	bn_cp_32(to, 8, from,  (a4) - 12)  \
	bn_cp_32(to, 9, from,  (a3) - 12)  \
	bn_cp_32(to, 10, from, (a2) - 12)  \
	bn_cp_32(to, 11, from, (a1) - 12)  \
	}

int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
	int	i, top = a->top;
	int	carry = 0;
	register BN_ULONG *r_d, *a_d = a->d;
	BN_ULONG t_d[BN_NIST_384_TOP],
	         buf[BN_NIST_384_TOP],
		 c_d[BN_NIST_384_TOP],
		*res;
	size_t	 mask;
	union { bn_addsub_f f; size_t p; } u;
	static const BIGNUM _bignum_nist_p_384_sqr = {
		(BN_ULONG *)_nist_p_384_sqr,
		sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
		sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
		0,BN_FLG_STATIC_DATA };


	field = &_bignum_nist_p_384; /* just to make sure */

 	if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
		return BN_nnmod(r, a, field, ctx);

	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 (r != a)
		{
		if (!bn_wexpand(r, BN_NIST_384_TOP))
			return 0;
		r_d = r->d;
		nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
		}
	else
		r_d = a_d;

	nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);

	/*S1*/
	nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
		/* left shift */
		{
		register BN_ULONG *ap,t,c;
		ap = t_d;
		c=0;
		for (i = 3; i != 0; --i)
			{
			t= *ap;
			*(ap++)=((t<<1)|c)&BN_MASK2;
			c=(t & BN_TBIT)?1:0;
			}
		*ap=c;
		}
	carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2), 
		t_d, BN_NIST_256_TOP);
	/*S2 */
	carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
	/*S3*/
	nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
	/*S4*/
	nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
	/*S5*/
	nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
	/*S6*/
	nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
	carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
	/*D1*/
	nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
	/*D2*/
	nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
	/*D3*/
	nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
	carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);

	/* see BN_nist_mod_224 for explanation */
	u.f = bn_sub_words;
	if (carry > 0)
		carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
	else if (carry < 0)
		{
		carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
		mask = 0-(size_t)carry;
		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
		}
	else
		carry = 1;

	mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
	mask &= 0-(size_t)carry;
	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
	nist_cp_bn(r_d, res, BN_NIST_384_TOP);
	r->top = BN_NIST_384_TOP;
	bn_correct_top(r);

	return 1;
	}

#define BN_NIST_521_RSHIFT	(521%BN_BITS2)
#define BN_NIST_521_LSHIFT	(BN_BITS2-BN_NIST_521_RSHIFT)
#define BN_NIST_521_TOP_MASK	((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)

int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
	BN_CTX *ctx)
	{
	int	top = a->top, i;
	BN_ULONG *r_d, *a_d = a->d,
		 t_d[BN_NIST_521_TOP],
		 val,tmp,*res;
	size_t	mask;
	static const BIGNUM _bignum_nist_p_521_sqr = {
		(BN_ULONG *)_nist_p_521_sqr,
		sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
		sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
		0,BN_FLG_STATIC_DATA };

	field = &_bignum_nist_p_521; /* just to make sure */

 	if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
		return BN_nnmod(r, a, field, ctx);

	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 (r != a)
		{
		if (!bn_wexpand(r,BN_NIST_521_TOP))
			return 0;
		r_d = r->d;
		nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
		}
	else
		r_d = a_d;

	/* upper 521 bits, copy ... */
	nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
	/* ... and right shift */
	for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
		{
		tmp = val>>BN_NIST_521_RSHIFT;
		val = t_d[i+1];
		t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
		}
	t_d[i] = val>>BN_NIST_521_RSHIFT;
	/* lower 521 bits */
	r_d[i] &= BN_NIST_521_TOP_MASK;

	bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
	mask = 0-(size_t)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
	res  = (BN_ULONG *)(((size_t)t_d&~mask) | ((size_t)r_d&mask));
	nist_cp_bn(r_d,res,BN_NIST_521_TOP);
	r->top = BN_NIST_521_TOP;
	bn_correct_top(r);

	return 1;
	}