openssl/crypto/bn/bn_nist.c

/* 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;
}