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
  63 #define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
  64 #define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
  65 #define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
  66 #define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
  67 #define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
  68
  69 /* pre-computed tables are "carry-less" values of modulus*(i+1) */
  70 #if BN_BITS2 == 64
  71 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
  72         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
  73         {0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
  74         {0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
  75         };
  76 static const BN_ULONG _nist_p_192_sqr[] = {
  77         0x0000000000000001ULL,0x0000000000000002ULL,0x0000000000000001ULL,
  78         0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL
  79         };
  80 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
  81         {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
  82          0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
  83         {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
  84          0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
  85         };
  86 static const BN_ULONG _nist_p_224_sqr[] = {
  87         0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
  88         0xFFFFFFFFFFFFFFFFULL,0x0000000200000000ULL,
  89         0x0000000000000000ULL,0xFFFFFFFFFFFFFFFEULL,
  90         0xFFFFFFFFFFFFFFFFULL
  91         };
  92 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
  93         {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
  94          0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
  95         {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
  96          0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
  97         {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
  98          0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
  99         {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
 100          0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
 101         {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
 102          0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
 103         };
 104 static const BN_ULONG _nist_p_256_sqr[] = {
 105         0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
 106         0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFEULL,
 107         0x00000001FFFFFFFEULL,0x00000001FFFFFFFEULL,
 108         0xFFFFFFFE00000001ULL,0xFFFFFFFE00000002ULL
 109         };
 110 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
 111         {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
 112          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 113         {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
 114          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 115         {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
 116          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 117         {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
 118          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 119         {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
 120          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 121         };
 122 static const BN_ULONG _nist_p_384_sqr[] = {
 123         0xFFFFFFFE00000001ULL,0x0000000200000000ULL,0xFFFFFFFE00000000ULL,
 124         0x0000000200000000ULL,0x0000000000000001ULL,0x0000000000000000ULL,
 125         0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
 126         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL
 127         };
 128 static const BN_ULONG _nist_p_521[] =
 129         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 130         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 131         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 132         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 133         0x00000000000001FFULL};
 134 static const BN_ULONG _nist_p_521_sqr[] = {
 135         0x0000000000000001ULL,0x0000000000000000ULL,0x0000000000000000ULL,
 136         0x0000000000000000ULL,0x0000000000000000ULL,0x0000000000000000ULL,
 137         0x0000000000000000ULL,0x0000000000000000ULL,0xFFFFFFFFFFFFFC00ULL,
 138         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 139         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 140         0xFFFFFFFFFFFFFFFFULL,0x000000000003FFFFULL
 141         };
 142 #elif BN_BITS2 == 32
 143 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
 144         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 145         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 146         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 147         };
 148 static const BN_ULONG _nist_p_192_sqr[] = {
 149         0x00000001,0x00000000,0x00000002,0x00000000,0x00000001,0x00000000,
 150         0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
 151         };
 152 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
 153         {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
 154          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 155         {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
 156          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 157         };
 158 static const BN_ULONG _nist_p_224_sqr[] = {
 159         0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
 160         0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000002,
 161         0x00000000,0x00000000,0xFFFFFFFE,0xFFFFFFFF,
 162         0xFFFFFFFF,0xFFFFFFFF
 163         };
 164 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
 165         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
 166          0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
 167         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
 168          0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
 169         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
 170          0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
 171         {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
 172          0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
 173         {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
 174          0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
 175         };
 176 static const BN_ULONG _nist_p_256_sqr[] = {
 177         0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
 178         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0x00000001,
 179         0xFFFFFFFE,0x00000001,0xFFFFFFFE,0x00000001,
 180         0x00000001,0xFFFFFFFE,0x00000002,0xFFFFFFFE
 181         };
 182 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
 183         {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
 184          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 185         {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
 186          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 187         {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
 188          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 189         {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
 190          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 191         {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
 192          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 193         };
 194 static const BN_ULONG _nist_p_384_sqr[] = {
 195         0x00000001,0xFFFFFFFE,0x00000000,0x00000002,0x00000000,0xFFFFFFFE,
 196         0x00000000,0x00000002,0x00000001,0x00000000,0x00000000,0x00000000,
 197         0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
 198         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
 199         };
 200 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 201         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 202         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 203         0xFFFFFFFF,0x000001FF};
 204 static const BN_ULONG _nist_p_521_sqr[] = {
 205         0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
 206         0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
 207         0x00000000,0x00000000,0x00000000,0x00000000,0xFFFFFC00,0xFFFFFFFF,
 208         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 209         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 210         0xFFFFFFFF,0xFFFFFFFF,0x0003FFFF
 211         };
 212 #else
 213 #error "unsupported BN_BITS2"
 214 #endif
 215
 216
 217 static const BIGNUM _bignum_nist_p_192 =
 218         {
 219         (BN_ULONG *)_nist_p_192[0],
 220         BN_NIST_192_TOP,
 221         BN_NIST_192_TOP,
 222         0,
 223         BN_FLG_STATIC_DATA
 224         };
 225
 226 static const BIGNUM _bignum_nist_p_224 =
 227         {
 228         (BN_ULONG *)_nist_p_224[0],
 229         BN_NIST_224_TOP,
 230         BN_NIST_224_TOP,
 231         0,
 232         BN_FLG_STATIC_DATA
 233         };
 234
 235 static const BIGNUM _bignum_nist_p_256 =
 236         {
 237         (BN_ULONG *)_nist_p_256[0],
 238         BN_NIST_256_TOP,
 239         BN_NIST_256_TOP,
 240         0,
 241         BN_FLG_STATIC_DATA
 242         };
 243
 244 static const BIGNUM _bignum_nist_p_384 =
 245         {
 246         (BN_ULONG *)_nist_p_384[0],
 247         BN_NIST_384_TOP,
 248         BN_NIST_384_TOP,
 249         0,
 250         BN_FLG_STATIC_DATA
 251         };
 252
 253 static const BIGNUM _bignum_nist_p_521 =
 254         {
 255         (BN_ULONG *)_nist_p_521,
 256         BN_NIST_521_TOP,
 257         BN_NIST_521_TOP,
 258         0,
 259         BN_FLG_STATIC_DATA
 260         };
 261
 262
 263 const BIGNUM *BN_get0_nist_prime_192(void)
 264         {
 265         return &_bignum_nist_p_192;
 266         }
 267
 268 const BIGNUM *BN_get0_nist_prime_224(void)
 269         {
 270         return &_bignum_nist_p_224;
 271         }
 272
 273 const BIGNUM *BN_get0_nist_prime_256(void)
 274         {
 275         return &_bignum_nist_p_256;
 276         }
 277
 278 const BIGNUM *BN_get0_nist_prime_384(void)
 279         {
 280         return &_bignum_nist_p_384;
 281         }
 282
 283 const BIGNUM *BN_get0_nist_prime_521(void)
 284         {
 285         return &_bignum_nist_p_521;
 286         }
 287
 288
 289 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
 290         {
 291         int i;
 292         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 293
 294 #ifdef BN_DEBUG
 295         OPENSSL_assert(top <= max);
 296 #endif
 297         for (i = (top); i != 0; i--)
 298                 *_tmp1++ = *_tmp2++;
 299         for (i = (max) - (top); i != 0; i--)
 300                 *_tmp1++ = (BN_ULONG) 0;
 301         }
 302
 303 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 304         {
 305         int i;
 306         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 307         for (i = (top); i != 0; i--)
 308                 *_tmp1++ = *_tmp2++;
 309         }
 310
 311 #if BN_BITS2 == 64
 312 #define bn_cp_64(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 313 #define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 314 /*
 315  * two following macros are implemented under assumption that they
 316  * are called in a sequence with *ascending* n, i.e. as they are...
 317  */
 318 #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))\
 319                                                 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
 320 #define bn_32_set_0(to, n)              (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
 321 #define bn_cp_32(to,n,from,m)           ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
 322 #else
 323 #define bn_cp_64(to, n, from, m) \
 324         { \
 325         bn_cp_32(to, (n)*2, from, (m)*2); \
 326         bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
 327         }
 328 #define bn_64_set_0(to, n) \
 329         { \
 330         bn_32_set_0(to, (n)*2); \
 331         bn_32_set_0(to, (n)*2+1); \
 332         }
 333 #if BN_BITS2 == 32
 334 #define bn_cp_32(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 335 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 336 #endif
 337 #endif /* BN_BITS2 != 64 */
 338
 339
 340 #define nist_set_192(to, from, a1, a2, a3) \
 341         { \
 342         bn_cp_64(to, 0, from, (a3) - 3) \
 343         bn_cp_64(to, 1, from, (a2) - 3) \
 344         bn_cp_64(to, 2, from, (a1) - 3) \
 345         }
 346
 347 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 348         BN_CTX *ctx)
 349         {
 350         int      top = a->top, i;
 351         int      carry;
 352         register BN_ULONG *r_d, *a_d = a->d;
 353         BN_ULONG t_d[BN_NIST_192_TOP],
 354                  buf[BN_NIST_192_TOP],
 355                  c_d[BN_NIST_192_TOP],
 356                 *res;
 357         size_t   mask;
 358         static const BIGNUM _bignum_nist_p_192_sqr = {
 359                 (BN_ULONG *)_nist_p_192_sqr,
 360                 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
 361                 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
 362                 0,BN_FLG_STATIC_DATA };
 363
 364         field = &_bignum_nist_p_192; /* just to make sure */
 365
 366         if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
 367                 return BN_nnmod(r, a, field, ctx);
 368
 369         i = BN_ucmp(field, a);
 370         if (i == 0)
 371                 {
 372                 BN_zero(r);
 373                 return 1;
 374                 }
 375         else if (i > 0)
 376                 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
 377
 378         if (r != a)
 379                 {
 380                 if (!bn_wexpand(r, BN_NIST_192_TOP))
 381                         return 0;
 382                 r_d = r->d;
 383                 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
 384                 }
 385         else
 386                 r_d = a_d;
 387
 388         nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
 389
 390         nist_set_192(t_d, buf, 0, 3, 3);
 391         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 392         nist_set_192(t_d, buf, 4, 4, 0);
 393         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 394         nist_set_192(t_d, buf, 5, 5, 5)
 395         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 396
 397         if (carry > 0)
 398                 carry = bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
 399         else
 400                 carry = 1;
 401
 402         /*
 403          * we need 'if (carry==0 || result>=modulus) result-=modulus;'
 404          * as comparison implies subtraction, we can write
 405          * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
 406          * this is what happens below, but without explicit if:-) a.
 407          */
 408         mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
 409         mask &= 0-(size_t)carry;
 410         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 411         nist_cp_bn(r_d, res, BN_NIST_192_TOP);
 412         r->top = BN_NIST_192_TOP;
 413         bn_correct_top(r);
 414
 415         return 1;
 416         }
 417
 418 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *, const BN_ULONG *, const BN_ULONG *,
 419                                 size_t);
 420
 421 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 422         { \
 423         bn_cp_32(to, 0, from, (a7) - 7) \
 424         bn_cp_32(to, 1, from, (a6) - 7) \
 425         bn_cp_32(to, 2, from, (a5) - 7) \
 426         bn_cp_32(to, 3, from, (a4) - 7) \
 427         bn_cp_32(to, 4, from, (a3) - 7) \
 428         bn_cp_32(to, 5, from, (a2) - 7) \
 429         bn_cp_32(to, 6, from, (a1) - 7) \
 430         }
 431
 432 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 433                     BN_CTX *ctx)
 434         {
 435         int     top = a->top, i;
 436         int     carry;
 437         BN_ULONG *r_d, *a_d = a->d;
 438         BN_ULONG t_d[BN_NIST_224_TOP],
 439                  buf[BN_NIST_224_TOP],
 440                  c_d[BN_NIST_224_TOP],
 441                 *res;
 442         size_t   mask;
 443         union { bn_addsub_f f; size_t p; } u;
 444         static const BIGNUM _bignum_nist_p_224_sqr = {
 445                 (BN_ULONG *)_nist_p_224_sqr,
 446                 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
 447                 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
 448                 0,BN_FLG_STATIC_DATA };
 449
 450
 451         field = &_bignum_nist_p_224; /* just to make sure */
 452
 453         if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
 454                 return BN_nnmod(r, a, field, ctx);
 455
 456         i = BN_ucmp(field, a);
 457         if (i == 0)
 458                 {
 459                 BN_zero(r);
 460                 return 1;
 461                 }
 462         else if (i > 0)
 463                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 464
 465         if (r != a)
 466                 {
 467                 if (!bn_wexpand(r, BN_NIST_224_TOP))
 468                         return 0;
 469                 r_d = r->d;
 470                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
 471                 }
 472         else
 473                 r_d = a_d;
 474
 475 #if BN_BITS2==64
 476         /* copy upper 256 bits of 448 bit number ... */
 477         nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
 478         /* ... and right shift by 32 to obtain upper 224 bits */
 479         nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
 480         /* truncate lower part to 224 bits too */
 481         r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
 482 #else
 483         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
 484 #endif
 485         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 486         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 487         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
 488         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 489         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
 490         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 491         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
 492         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 493
 494 #if BN_BITS2==64
 495         carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
 496 #endif
 497         u.f = bn_sub_words;
 498         if (carry > 0)
 499                 {
 500                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
 501 #if BN_BITS2==64
 502                 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
 503 #endif
 504                 }
 505         else if (carry < 0)
 506                 {
 507                 /* it's a bit more comlicated logic in this case.
 508                  * if bn_add_words yields no carry, then result
 509                  * has to be adjusted by unconditionally *adding*
 510                  * the modulus. but if it does, then result has
 511                  * to be compared to the modulus and conditionally
 512                  * adjusted by *subtracting* the latter. */
 513                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
 514                 mask = 0-(size_t)carry;
 515                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 516                 }
 517         else
 518                 carry = 1;
 519
 520         /* otherwise it's effectively same as in BN_nist_mod_192... */
 521         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
 522         mask &= 0-(size_t)carry;
 523         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 524         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
 525         r->top = BN_NIST_224_TOP;
 526         bn_correct_top(r);
 527
 528         return 1;
 529         }
 530
 531 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 532         { \
 533         bn_cp_32(to, 0, from, (a8) - 8) \
 534         bn_cp_32(to, 1, from, (a7) - 8) \
 535         bn_cp_32(to, 2, from, (a6) - 8) \
 536         bn_cp_32(to, 3, from, (a5) - 8) \
 537         bn_cp_32(to, 4, from, (a4) - 8) \
 538         bn_cp_32(to, 5, from, (a3) - 8) \
 539         bn_cp_32(to, 6, from, (a2) - 8) \
 540         bn_cp_32(to, 7, from, (a1) - 8) \
 541         }
 542
 543 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 544         BN_CTX *ctx)
 545         {
 546         int     i, top = a->top;
 547         int     carry = 0;
 548         register BN_ULONG *a_d = a->d, *r_d;
 549         BN_ULONG t_d[BN_NIST_256_TOP],
 550                  buf[BN_NIST_256_TOP],
 551                  c_d[BN_NIST_256_TOP],
 552                 *res;
 553         size_t   mask;
 554         union { bn_addsub_f f; size_t p; } u;
 555         static const BIGNUM _bignum_nist_p_256_sqr = {
 556                 (BN_ULONG *)_nist_p_256_sqr,
 557                 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
 558                 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
 559                 0,BN_FLG_STATIC_DATA };
 560
 561         field = &_bignum_nist_p_256; /* just to make sure */
 562
 563         if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
 564                 return BN_nnmod(r, a, field, ctx);
 565
 566         i = BN_ucmp(field, a);
 567         if (i == 0)
 568                 {
 569                 BN_zero(r);
 570                 return 1;
 571                 }
 572         else if (i > 0)
 573                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 574
 575         if (r != a)
 576                 {
 577                 if (!bn_wexpand(r, BN_NIST_256_TOP))
 578                         return 0;
 579                 r_d = r->d;
 580                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
 581                 }
 582         else
 583                 r_d = a_d;
 584
 585         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
 586
 587         /*S1*/
 588         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 589         /*S2*/
 590         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
 591         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
 592         /* left shift */
 593                 {
 594                 register BN_ULONG *ap,t,c;
 595                 ap = t_d;
 596                 c=0;
 597                 for (i = BN_NIST_256_TOP; i != 0; --i)
 598                         {
 599                         t= *ap;
 600                         *(ap++)=((t<<1)|c)&BN_MASK2;
 601                         c=(t & BN_TBIT)?1:0;
 602                         }
 603                 carry <<= 1;
 604                 carry  |= c;
 605                 }
 606         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 607         /*S3*/
 608         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
 609         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 610         /*S4*/
 611         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
 612         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 613         /*D1*/
 614         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
 615         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 616         /*D2*/
 617         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
 618         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 619         /*D3*/
 620         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
 621         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 622         /*D4*/
 623         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
 624         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 625
 626         /* see BN_nist_mod_224 for explanation */
 627         u.f = bn_sub_words;
 628         if (carry > 0)
 629                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
 630         else if (carry < 0)
 631                 {
 632                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
 633                 mask = 0-(size_t)carry;
 634                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 635                 }
 636         else
 637                 carry = 1;
 638
 639         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
 640         mask &= 0-(size_t)carry;
 641         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 642         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
 643         r->top = BN_NIST_256_TOP;
 644         bn_correct_top(r);
 645
 646         return 1;
 647         }
 648
 649 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 650         { \
 651         bn_cp_32(to, 0, from,  (a12) - 12) \
 652         bn_cp_32(to, 1, from,  (a11) - 12) \
 653         bn_cp_32(to, 2, from,  (a10) - 12) \
 654         bn_cp_32(to, 3, from,  (a9) - 12)  \
 655         bn_cp_32(to, 4, from,  (a8) - 12)  \
 656         bn_cp_32(to, 5, from,  (a7) - 12)  \
 657         bn_cp_32(to, 6, from,  (a6) - 12)  \
 658         bn_cp_32(to, 7, from,  (a5) - 12)  \
 659         bn_cp_32(to, 8, from,  (a4) - 12)  \
 660         bn_cp_32(to, 9, from,  (a3) - 12)  \
 661         bn_cp_32(to, 10, from, (a2) - 12)  \
 662         bn_cp_32(to, 11, from, (a1) - 12)  \
 663         }
 664
 665 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 666         BN_CTX *ctx)
 667         {
 668         int     i, top = a->top;
 669         int     carry = 0;
 670         register BN_ULONG *r_d, *a_d = a->d;
 671         BN_ULONG t_d[BN_NIST_384_TOP],
 672                  buf[BN_NIST_384_TOP],
 673                  c_d[BN_NIST_384_TOP],
 674                 *res;
 675         size_t   mask;
 676         union { bn_addsub_f f; size_t p; } u;
 677         static const BIGNUM _bignum_nist_p_384_sqr = {
 678                 (BN_ULONG *)_nist_p_384_sqr,
 679                 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
 680                 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
 681                 0,BN_FLG_STATIC_DATA };
 682
 683
 684         field = &_bignum_nist_p_384; /* just to make sure */
 685
 686         if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
 687                 return BN_nnmod(r, a, field, ctx);
 688
 689         i = BN_ucmp(field, a);
 690         if (i == 0)
 691                 {
 692                 BN_zero(r);
 693                 return 1;
 694                 }
 695         else if (i > 0)
 696                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 697
 698         if (r != a)
 699                 {
 700                 if (!bn_wexpand(r, BN_NIST_384_TOP))
 701                         return 0;
 702                 r_d = r->d;
 703                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
 704                 }
 705         else
 706                 r_d = a_d;
 707
 708         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
 709
 710         /*S1*/
 711         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
 712                 /* left shift */
 713                 {
 714                 register BN_ULONG *ap,t,c;
 715                 ap = t_d;
 716                 c=0;
 717                 for (i = 3; i != 0; --i)
 718                         {
 719                         t= *ap;
 720                         *(ap++)=((t<<1)|c)&BN_MASK2;
 721                         c=(t & BN_TBIT)?1:0;
 722                         }
 723                 *ap=c;
 724                 }
 725         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 726                 t_d, BN_NIST_256_TOP);
 727         /*S2 */
 728         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
 729         /*S3*/
 730         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
 731         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 732         /*S4*/
 733         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
 734         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 735         /*S5*/
 736         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
 737         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 738         /*S6*/
 739         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
 740         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 741         /*D1*/
 742         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
 743         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 744         /*D2*/
 745         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
 746         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 747         /*D3*/
 748         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
 749         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 750
 751         /* see BN_nist_mod_224 for explanation */
 752         u.f = bn_sub_words;
 753         if (carry > 0)
 754                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
 755         else if (carry < 0)
 756                 {
 757                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
 758                 mask = 0-(size_t)carry;
 759                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 760                 }
 761         else
 762                 carry = 1;
 763
 764         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
 765         mask &= 0-(size_t)carry;
 766         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 767         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
 768         r->top = BN_NIST_384_TOP;
 769         bn_correct_top(r);
 770
 771         return 1;
 772         }
 773
 774 #define BN_NIST_521_RSHIFT      (521%BN_BITS2)
 775 #define BN_NIST_521_LSHIFT      (BN_BITS2-BN_NIST_521_RSHIFT)
 776 #define BN_NIST_521_TOP_MASK    ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
 777
 778 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 779         BN_CTX *ctx)
 780         {
 781         int     top = a->top, i;
 782         BN_ULONG *r_d, *a_d = a->d,
 783                  t_d[BN_NIST_521_TOP],
 784                  val,tmp,*res;
 785         size_t  mask;
 786         static const BIGNUM _bignum_nist_p_521_sqr = {
 787                 (BN_ULONG *)_nist_p_521_sqr,
 788                 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
 789                 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
 790                 0,BN_FLG_STATIC_DATA };
 791
 792         field = &_bignum_nist_p_521; /* just to make sure */
 793
 794         if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
 795                 return BN_nnmod(r, a, field, ctx);
 796
 797         i = BN_ucmp(field, a);
 798         if (i == 0)
 799                 {
 800                 BN_zero(r);
 801                 return 1;
 802                 }
 803         else if (i > 0)
 804                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 805
 806         if (r != a)
 807                 {
 808                 if (!bn_wexpand(r,BN_NIST_521_TOP))
 809                         return 0;
 810                 r_d = r->d;
 811                 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
 812                 }
 813         else
 814                 r_d = a_d;
 815
 816         /* upper 521 bits, copy ... */
 817         nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
 818         /* ... and right shift */
 819         for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
 820                 {
 821                 tmp = val>>BN_NIST_521_RSHIFT;
 822                 val = t_d[i+1];
 823                 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
 824                 }
 825         t_d[i] = val>>BN_NIST_521_RSHIFT;
 826         /* lower 521 bits */
 827         r_d[i] &= BN_NIST_521_TOP_MASK;
 828
 829         bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
 830         mask = 0-(size_t)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
 831         res  = (BN_ULONG *)(((size_t)t_d&~mask) | ((size_t)r_d&mask));
 832         nist_cp_bn(r_d,res,BN_NIST_521_TOP);
 833         r->top = BN_NIST_521_TOP;
 834         bn_correct_top(r);
 835
 836         return 1;
 837         }