crypto/bn/bn_nist.c

   1 /* crypto/bn/bn_nist.c */
   2 /*
   3  * Written by Nils Larsch for the OpenSSL project
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    openssl-core@openssl.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58
  59 #include "bn_lcl.h"
  60 #include "cryptlib.h"
  61
  62 #define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
  63 #define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
  64 #define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
  65 #define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
  66 #define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
  67
  68 /* pre-computed tables are "carry-less" values of modulus*(i+1) */
  69 #if BN_BITS2 == 64
  70 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
  71         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
  72         {0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
  73         {0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
  74         };
  75 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
  76         {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
  77          0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
  78         {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
  79          0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL}
  80         };
  81 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
  82         {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
  83          0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
  84         {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
  85          0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
  86         {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
  87          0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
  88         {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
  89          0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
  90         {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
  91          0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
  92         };
  93 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
  94         {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
  95          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
  96         {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
  97          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
  98         {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
  99          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 100         {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
 101          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 102         {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
 103          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 104         };
 105 static const BN_ULONG _nist_p_521[] =
 106         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 107         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 108         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 109         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 110         0x00000000000001FFULL};
 111 #elif BN_BITS2 == 32
 112 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
 113         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 114         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 115         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 116         };
 117 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
 118         {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
 119          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 120         {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
 121          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 122         };
 123 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
 124         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
 125          0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
 126         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
 127          0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
 128         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
 129          0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
 130         {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
 131          0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
 132         {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
 133          0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
 134         };
 135 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
 136         {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
 137          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 138         {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
 139          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 140         {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
 141          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 142         {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
 143          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 144         {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
 145          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 146         };
 147 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 148         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 149         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 150         0xFFFFFFFF,0x000001FF};
 151 #endif
 152
 153 const BIGNUM *BN_get0_nist_prime_192(void)
 154         {
 155         static BIGNUM const_nist_192 = { (BN_ULONG *)_nist_p_192[0],
 156                 BN_NIST_192_TOP, BN_NIST_192_TOP, 0, BN_FLG_STATIC_DATA };
 157         return &const_nist_192;
 158         }
 159
 160 const BIGNUM *BN_get0_nist_prime_224(void)
 161         {
 162         static BIGNUM const_nist_224 = { (BN_ULONG *)_nist_p_224[0],
 163                 BN_NIST_224_TOP, BN_NIST_224_TOP, 0, BN_FLG_STATIC_DATA };
 164         return &const_nist_224;
 165         }
 166
 167 const BIGNUM *BN_get0_nist_prime_256(void)
 168         {
 169         static BIGNUM const_nist_256 = { (BN_ULONG *)_nist_p_256[0],
 170                 BN_NIST_256_TOP, BN_NIST_256_TOP, 0, BN_FLG_STATIC_DATA };
 171         return &const_nist_256;
 172         }
 173
 174 const BIGNUM *BN_get0_nist_prime_384(void)
 175         {
 176         static BIGNUM const_nist_384 = { (BN_ULONG *)_nist_p_384[0],
 177                 BN_NIST_384_TOP, BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA };
 178         return &const_nist_384;
 179         }
 180
 181 const BIGNUM *BN_get0_nist_prime_521(void)
 182         {
 183         static BIGNUM const_nist_521 = { (BN_ULONG *)_nist_p_521,
 184                 BN_NIST_521_TOP, BN_NIST_521_TOP, 0, BN_FLG_STATIC_DATA };
 185         return &const_nist_521;
 186         }
 187
 188 #define BN_NIST_ADD_ONE(a)      while (!(*(a)=(*(a)+1)&BN_MASK2)) ++(a);
 189
 190 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
 191         {
 192         int i;
 193         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 194         for (i = (top); i != 0; i--)
 195                 *_tmp1++ = *_tmp2++;
 196         for (i = (max) - (top); i != 0; i--)
 197                 *_tmp1++ = (BN_ULONG) 0;
 198         }
 199
 200 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 201         {
 202         int i;
 203         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 204         for (i = (top); i != 0; i--)
 205                 *_tmp1++ = *_tmp2++;
 206         }
 207
 208 #if BN_BITS2 == 64
 209 #define bn_cp_64(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 210 #define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 211 /*
 212  * two following macros are implemented under assumption that they
 213  * are called in a sequence with *ascending* n, i.e. as they are...
 214  */
 215 #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))\
 216                                                 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
 217 #define bn_32_set_0(to, n)              (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
 218 #define bn_cp_32(to,n,from,m)           ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
 219 #else
 220 #define bn_cp_64(to, n, from, m) \
 221         { \
 222         bn_cp_32(to, (n)*2, from, (m)*2); \
 223         bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
 224         }
 225 #define bn_64_set_0(to, n) \
 226         { \
 227         bn_32_set_0(to, (n)*2); \
 228         bn_32_set_0(to, (n)*2+1); \
 229         }
 230 #if BN_BITS2 == 32
 231 #define bn_cp_32(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 232 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 233 #endif
 234 #endif /* BN_BITS2 != 64 */
 235
 236
 237 #define nist_set_192(to, from, a1, a2, a3) \
 238         { \
 239         bn_cp_64(to, 0, from, (a3) - 3) \
 240         bn_cp_64(to, 1, from, (a2) - 3) \
 241         bn_cp_64(to, 2, from, (a1) - 3) \
 242         }
 243
 244 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 245         BN_CTX *ctx)
 246         {
 247         int      top = a->top, i;
 248         int      carry;
 249         register BN_ULONG *r_d, *a_d = a->d;
 250         BN_ULONG t_d[BN_NIST_192_TOP],
 251                  buf[BN_NIST_192_TOP],
 252                  c_d[BN_NIST_192_TOP],
 253                 *res;
 254         size_t   mask;
 255
 256         i = BN_ucmp(field, a);
 257         if (i == 0)
 258                 {
 259                 BN_zero(r);
 260                 return 1;
 261                 }
 262         else if (i > 0)
 263                 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
 264
 265         if (top == BN_NIST_192_TOP)
 266                 return BN_usub(r, a, field);
 267
 268         if (r != a)
 269                 {
 270                 if (!bn_wexpand(r, BN_NIST_192_TOP))
 271                         return 0;
 272                 r_d = r->d;
 273                 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
 274                 }
 275         else
 276                 r_d = a_d;
 277
 278         nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
 279
 280         nist_set_192(t_d, buf, 0, 3, 3);
 281         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 282         nist_set_192(t_d, buf, 4, 4, 0);
 283         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 284         nist_set_192(t_d, buf, 5, 5, 5)
 285         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 286
 287         if (carry > 0)
 288                 carry = bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
 289         else
 290                 carry = 1;
 291
 292         /*
 293          * we need 'if (carry==0 || result>=modulus) result-=modulus;'
 294          * as comparison implies subtraction, we can write
 295          * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
 296          * this is what happens below, but without explicit if:-) a.
 297          */
 298         mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
 299         mask &= 0-(size_t)carry;
 300         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 301         nist_cp_bn(r_d, res, BN_NIST_192_TOP);
 302         r->top = BN_NIST_192_TOP;
 303         bn_correct_top(r);
 304
 305         return 1;
 306         }
 307
 308 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
 309
 310 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 311         { \
 312         bn_cp_32(to, 0, from, (a7) - 7) \
 313         bn_cp_32(to, 1, from, (a6) - 7) \
 314         bn_cp_32(to, 2, from, (a5) - 7) \
 315         bn_cp_32(to, 3, from, (a4) - 7) \
 316         bn_cp_32(to, 4, from, (a3) - 7) \
 317         bn_cp_32(to, 5, from, (a2) - 7) \
 318         bn_cp_32(to, 6, from, (a1) - 7) \
 319         }
 320
 321 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 322         BN_CTX *ctx)
 323         {
 324 #if BN_BITS2 == 32
 325         int     top = a->top, i;
 326         int     carry;
 327         BN_ULONG *r_d, *a_d = a->d;
 328         BN_ULONG t_d[BN_NIST_224_TOP],
 329                  buf[BN_NIST_224_TOP],
 330                  c_d[BN_NIST_224_TOP],
 331                 *res;
 332         size_t   mask;
 333         union { bn_addsub_f f; size_t p; } u;
 334
 335         i = BN_ucmp(field, a);
 336         if (i == 0)
 337                 {
 338                 BN_zero(r);
 339                 return 1;
 340                 }
 341         else if (i > 0)
 342                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 343
 344         if (top == BN_NIST_224_TOP)
 345                 return BN_usub(r, a, field);
 346
 347         if (r != a)
 348                 {
 349                 if (!bn_wexpand(r, BN_NIST_224_TOP))
 350                         return 0;
 351                 r_d = r->d;
 352                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
 353                 }
 354         else
 355                 r_d = a_d;
 356
 357         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
 358
 359         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 360         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 361         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
 362         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 363         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
 364         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 365         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
 366         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 367
 368         u.f = bn_sub_words;
 369         if (carry > 0)
 370                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
 371         else if (carry < 0)
 372                 {
 373                 /* it's a bit more comlicated logic in this case.
 374                  * if bn_add_words yields no carry, then result
 375                  * has to be adjusted by unconditionally *adding*
 376                  * the modulus. but if it does, then result has
 377                  * to be compared to the modulus and conditionally
 378                  * adjusted by *subtracting* the latter. */
 379                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
 380                 mask = 0-(size_t)carry;
 381                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 382                 }
 383         else
 384                 carry = 1;
 385
 386         /* otherwise it's effectively same as in BN_nist_mod_192... */
 387         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
 388         mask &= 0-(size_t)carry;
 389         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 390         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
 391         r->top = BN_NIST_224_TOP;
 392         bn_correct_top(r);
 393
 394         return 1;
 395 #else   /* BN_BITS!=32 */
 396         return 0;
 397 #endif
 398         }
 399
 400 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 401         { \
 402         bn_cp_32(to, 0, from, (a8) - 8) \
 403         bn_cp_32(to, 1, from, (a7) - 8) \
 404         bn_cp_32(to, 2, from, (a6) - 8) \
 405         bn_cp_32(to, 3, from, (a5) - 8) \
 406         bn_cp_32(to, 4, from, (a4) - 8) \
 407         bn_cp_32(to, 5, from, (a3) - 8) \
 408         bn_cp_32(to, 6, from, (a2) - 8) \
 409         bn_cp_32(to, 7, from, (a1) - 8) \
 410         }
 411
 412 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 413         BN_CTX *ctx)
 414         {
 415         int     i, top = a->top;
 416         int     carry = 0;
 417         register BN_ULONG *a_d = a->d, *r_d;
 418         BN_ULONG t_d[BN_NIST_256_TOP],
 419                  buf[BN_NIST_256_TOP],
 420                  c_d[BN_NIST_256_TOP],
 421                 *res;
 422         size_t   mask;
 423         union { bn_addsub_f f; size_t p; } u;
 424
 425         i = BN_ucmp(field, a);
 426         if (i == 0)
 427                 {
 428                 BN_zero(r);
 429                 return 1;
 430                 }
 431         else if (i > 0)
 432                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 433
 434         if (top == BN_NIST_256_TOP)
 435                 return BN_usub(r, a, field);
 436
 437         if (r != a)
 438                 {
 439                 if (!bn_wexpand(r, BN_NIST_256_TOP))
 440                         return 0;
 441                 r_d = r->d;
 442                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
 443                 }
 444         else
 445                 r_d = a_d;
 446
 447         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
 448
 449         /*S1*/
 450         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 451         /*S2*/
 452         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
 453         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
 454         /* left shift */
 455                 {
 456                 register BN_ULONG *ap,t,c;
 457                 ap = t_d;
 458                 c=0;
 459                 for (i = BN_NIST_256_TOP; i != 0; --i)
 460                         {
 461                         t= *ap;
 462                         *(ap++)=((t<<1)|c)&BN_MASK2;
 463                         c=(t & BN_TBIT)?1:0;
 464                         }
 465                 carry <<= 1;
 466                 carry  |= c;
 467                 }
 468         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 469         /*S3*/
 470         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
 471         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 472         /*S4*/
 473         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
 474         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 475         /*D1*/
 476         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
 477         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 478         /*D2*/
 479         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
 480         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 481         /*D3*/
 482         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
 483         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 484         /*D4*/
 485         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
 486         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 487
 488         /* see BN_nist_mod_224 for explanation */
 489         u.f = bn_sub_words;
 490         if (carry > 0)
 491                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
 492         else if (carry < 0)
 493                 {
 494                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
 495                 mask = 0-(size_t)carry;
 496                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 497                 }
 498         else
 499                 carry = 1;
 500
 501         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
 502         mask &= 0-(size_t)carry;
 503         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 504         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
 505         r->top = BN_NIST_256_TOP;
 506         bn_correct_top(r);
 507
 508         return 1;
 509         }
 510
 511 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 512         { \
 513         bn_cp_32(to, 0, from,  (a12) - 12) \
 514         bn_cp_32(to, 1, from,  (a11) - 12) \
 515         bn_cp_32(to, 2, from,  (a10) - 12) \
 516         bn_cp_32(to, 3, from,  (a9) - 12)  \
 517         bn_cp_32(to, 4, from,  (a8) - 12)  \
 518         bn_cp_32(to, 5, from,  (a7) - 12)  \
 519         bn_cp_32(to, 6, from,  (a6) - 12)  \
 520         bn_cp_32(to, 7, from,  (a5) - 12)  \
 521         bn_cp_32(to, 8, from,  (a4) - 12)  \
 522         bn_cp_32(to, 9, from,  (a3) - 12)  \
 523         bn_cp_32(to, 10, from, (a2) - 12)  \
 524         bn_cp_32(to, 11, from, (a1) - 12)  \
 525         }
 526
 527 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 528         BN_CTX *ctx)
 529         {
 530         int     i, top = a->top;
 531         int     carry = 0;
 532         register BN_ULONG *r_d, *a_d = a->d;
 533         BN_ULONG t_d[BN_NIST_384_TOP],
 534                  buf[BN_NIST_384_TOP],
 535                  c_d[BN_NIST_384_TOP],
 536                 *res;
 537         size_t   mask;
 538         union { bn_addsub_f f; size_t p; } u;
 539
 540         i = BN_ucmp(field, a);
 541         if (i == 0)
 542                 {
 543                 BN_zero(r);
 544                 return 1;
 545                 }
 546         else if (i > 0)
 547                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 548
 549         if (top == BN_NIST_384_TOP)
 550                 return BN_usub(r, a, field);
 551
 552         if (r != a)
 553                 {
 554                 if (!bn_wexpand(r, BN_NIST_384_TOP))
 555                         return 0;
 556                 r_d = r->d;
 557                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
 558                 }
 559         else
 560                 r_d = a_d;
 561
 562         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
 563
 564         /*S1*/
 565         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
 566                 /* left shift */
 567                 {
 568                 register BN_ULONG *ap,t,c;
 569                 ap = t_d;
 570                 c=0;
 571                 for (i = 3; i != 0; --i)
 572                         {
 573                         t= *ap;
 574                         *(ap++)=((t<<1)|c)&BN_MASK2;
 575                         c=(t & BN_TBIT)?1:0;
 576                         }
 577                 *ap=c;
 578                 }
 579         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 580                 t_d, BN_NIST_256_TOP);
 581         /*S2 */
 582         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
 583         /*S3*/
 584         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
 585         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 586         /*S4*/
 587         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
 588         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 589         /*S5*/
 590         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
 591         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 592         /*S6*/
 593         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
 594         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 595         /*D1*/
 596         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
 597         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 598         /*D2*/
 599         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
 600         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 601         /*D3*/
 602         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
 603         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 604
 605         /* see BN_nist_mod_224 for explanation */
 606         u.f = bn_sub_words;
 607         if (carry > 0)
 608                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
 609         else if (carry < 0)
 610                 {
 611                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
 612                 mask = 0-(size_t)carry;
 613                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 614                 }
 615         else
 616                 carry = 1;
 617
 618         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
 619         mask &= 0-(size_t)carry;
 620         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 621         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
 622         r->top = BN_NIST_384_TOP;
 623         bn_correct_top(r);
 624
 625         return 1;
 626         }
 627
 628 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 629         BN_CTX *ctx)
 630         {
 631 #if BN_BITS2 == 64
 632 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 633 #elif BN_BITS2 == 32
 634 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 635 #endif
 636         int     top, ret = 0;
 637         BN_ULONG *r_d;
 638         BIGNUM  *tmp;
 639
 640         /* check whether a reduction is necessary */
 641         top = a->top;
 642         if (top < BN_NIST_521_TOP  || ( top == BN_NIST_521_TOP &&
 643            (!(a->d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))))
 644                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 645
 646         BN_CTX_start(ctx);
 647         tmp = BN_CTX_get(ctx);
 648         if (!tmp)
 649                 goto err;
 650
 651         if (!bn_wexpand(tmp, BN_NIST_521_TOP))
 652                 goto err;
 653         nist_cp_bn(tmp->d, a->d, BN_NIST_521_TOP);
 654
 655         tmp->top = BN_NIST_521_TOP;
 656         tmp->d[BN_NIST_521_TOP-1]  &= BN_NIST_521_TOP_MASK;
 657         bn_correct_top(tmp);
 658
 659         if (!BN_rshift(r, a, 521))
 660                 goto err;
 661
 662         if (!BN_uadd(r, tmp, r))
 663                 goto err;
 664         top = r->top;
 665         r_d = r->d;
 666         if (top == BN_NIST_521_TOP  &&
 667            (r_d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))
 668                 {
 669                 BN_NIST_ADD_ONE(r_d)
 670                 r->d[BN_NIST_521_TOP-1] &= BN_NIST_521_TOP_MASK;
 671                 }
 672         bn_correct_top(r);
 673
 674         ret = 1;
 675 err:
 676         BN_CTX_end(ctx);
 677
 678         bn_check_top(r);
 679         return ret;
 680         }