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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;
      PTR_SIZE_INT 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-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
      mask &= 0-(PTR_SIZE_INT)carry;
      res   = (BN_ULONG *)
       (((PTR_SIZE_INT)c_d&~mask) | ((PTR_SIZE_INT)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;
      PTR_SIZE_INT mask;
      union { bn_addsub_f f; PTR_SIZE_INT 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-(PTR_SIZE_INT)carry;
            u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
             ((PTR_SIZE_INT)bn_add_words&~mask);
            }
      else
            carry = 1;

      /* otherwise it's effectively same as in BN_nist_mod_192... */
      mask  = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
      mask &= 0-(PTR_SIZE_INT)carry;
      res   = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
       ((PTR_SIZE_INT)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;
      PTR_SIZE_INT mask;
      union { bn_addsub_f f; PTR_SIZE_INT 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-(PTR_SIZE_INT)carry;
            u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
             ((PTR_SIZE_INT)bn_add_words&~mask);
            }
      else
            carry = 1;

      mask  = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
      mask &= 0-(PTR_SIZE_INT)carry;
      res   = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
       ((PTR_SIZE_INT)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;
      PTR_SIZE_INT mask;
      union { bn_addsub_f f; PTR_SIZE_INT 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-(PTR_SIZE_INT)carry;
            u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
             ((PTR_SIZE_INT)bn_add_words&~mask);
            }
      else
            carry = 1;

      mask  = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
      mask &= 0-(PTR_SIZE_INT)carry;
      res   = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
       ((PTR_SIZE_INT)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;
      PTR_SIZE_INT 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-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
      res  = (BN_ULONG *)(((PTR_SIZE_INT)t_d&~mask) |
       ((PTR_SIZE_INT)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;
      }

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