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_224[][BN_NIST_224_TOP] = {
  77         {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
  78          0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
  79         {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
  80          0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
  81         };
  82 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
  83         {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
  84          0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
  85         {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
  86          0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
  87         {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
  88          0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
  89         {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
  90          0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
  91         {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
  92          0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
  93         };
  94 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
  95         {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
  96          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
  97         {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
  98          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
  99         {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
 100          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 101         {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
 102          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 103         {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
 104          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 105         };
 106 static const BN_ULONG _nist_p_521[] =
 107         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 108         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 109         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 110         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 111         0x00000000000001FFULL};
 112 #elif BN_BITS2 == 32
 113 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
 114         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 115         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 116         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 117         };
 118 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
 119         {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
 120          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 121         {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
 122          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 123         };
 124 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
 125         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
 126          0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
 127         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
 128          0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
 129         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
 130          0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
 131         {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
 132          0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
 133         {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
 134          0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
 135         };
 136 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
 137         {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
 138          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 139         {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
 140          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 141         {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
 142          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 143         {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
 144          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 145         {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
 146          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 147         };
 148 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 149         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 150         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 151         0xFFFFFFFF,0x000001FF};
 152 #else
 153 #error "unsupported BN_BITS2"
 154 #endif
 155
 156
 157 static const BIGNUM _bignum_nist_p_192 =
 158         {
 159         (BN_ULONG *)_nist_p_192[0],
 160         BN_NIST_192_TOP,
 161         BN_NIST_192_TOP,
 162         0,
 163         BN_FLG_STATIC_DATA
 164         };
 165
 166 static const BIGNUM _bignum_nist_p_224 =
 167         {
 168         (BN_ULONG *)_nist_p_224[0],
 169         BN_NIST_224_TOP,
 170         BN_NIST_224_TOP,
 171         0,
 172         BN_FLG_STATIC_DATA
 173         };
 174
 175 static const BIGNUM _bignum_nist_p_256 =
 176         {
 177         (BN_ULONG *)_nist_p_256[0],
 178         BN_NIST_256_TOP,
 179         BN_NIST_256_TOP,
 180         0,
 181         BN_FLG_STATIC_DATA
 182         };
 183
 184 static const BIGNUM _bignum_nist_p_384 =
 185         {
 186         (BN_ULONG *)_nist_p_384[0],
 187         BN_NIST_384_TOP,
 188         BN_NIST_384_TOP,
 189         0,
 190         BN_FLG_STATIC_DATA
 191         };
 192
 193 static const BIGNUM _bignum_nist_p_521 =
 194         {
 195         (BN_ULONG *)_nist_p_521,
 196         BN_NIST_521_TOP,
 197         BN_NIST_521_TOP,
 198         0,
 199         BN_FLG_STATIC_DATA
 200         };
 201
 202
 203 const BIGNUM *BN_get0_nist_prime_192(void)
 204         {
 205         return &_bignum_nist_p_192;
 206         }
 207
 208 const BIGNUM *BN_get0_nist_prime_224(void)
 209         {
 210         return &_bignum_nist_p_224;
 211         }
 212
 213 const BIGNUM *BN_get0_nist_prime_256(void)
 214         {
 215         return &_bignum_nist_p_256;
 216         }
 217
 218 const BIGNUM *BN_get0_nist_prime_384(void)
 219         {
 220         return &_bignum_nist_p_384;
 221         }
 222
 223 const BIGNUM *BN_get0_nist_prime_521(void)
 224         {
 225         return &_bignum_nist_p_521;
 226         }
 227
 228
 229 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
 230         {
 231         int i;
 232         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 233
 234         OPENSSL_assert(top <= max);
 235         for (i = (top); i != 0; i--)
 236                 *_tmp1++ = *_tmp2++;
 237         for (i = (max) - (top); i != 0; i--)
 238                 *_tmp1++ = (BN_ULONG) 0;
 239         }
 240
 241 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 242         {
 243         int i;
 244         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 245         for (i = (top); i != 0; i--)
 246                 *_tmp1++ = *_tmp2++;
 247         }
 248
 249 #if BN_BITS2 == 64
 250 #define bn_cp_64(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 251 #define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 252 /*
 253  * two following macros are implemented under assumption that they
 254  * are called in a sequence with *ascending* n, i.e. as they are...
 255  */
 256 #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))\
 257                                                 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
 258 #define bn_32_set_0(to, n)              (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
 259 #define bn_cp_32(to,n,from,m)           ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
 260 #else
 261 #define bn_cp_64(to, n, from, m) \
 262         { \
 263         bn_cp_32(to, (n)*2, from, (m)*2); \
 264         bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
 265         }
 266 #define bn_64_set_0(to, n) \
 267         { \
 268         bn_32_set_0(to, (n)*2); \
 269         bn_32_set_0(to, (n)*2+1); \
 270         }
 271 #if BN_BITS2 == 32
 272 #define bn_cp_32(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 273 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 274 #endif
 275 #endif /* BN_BITS2 != 64 */
 276
 277
 278 #define nist_set_192(to, from, a1, a2, a3) \
 279         { \
 280         bn_cp_64(to, 0, from, (a3) - 3) \
 281         bn_cp_64(to, 1, from, (a2) - 3) \
 282         bn_cp_64(to, 2, from, (a1) - 3) \
 283         }
 284
 285 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 286         BN_CTX *ctx)
 287         {
 288         int      top = a->top, i;
 289         int      carry;
 290         register BN_ULONG *r_d, *a_d = a->d;
 291         BN_ULONG t_d[BN_NIST_192_TOP],
 292                  buf[BN_NIST_192_TOP],
 293                  c_d[BN_NIST_192_TOP],
 294                 *res;
 295         size_t   mask;
 296
 297         field = &_bignum_nist_p_192; /* just to make sure */
 298
 299         if (BN_is_negative(a) || a->top > 2*BN_NIST_192_TOP)
 300                 return BN_nnmod(r, field, a, ctx);
 301
 302         i = BN_ucmp(field, a);
 303         if (i == 0)
 304                 {
 305                 BN_zero(r);
 306                 return 1;
 307                 }
 308         else if (i > 0)
 309                 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
 310
 311         if (r != a)
 312                 {
 313                 if (!bn_wexpand(r, BN_NIST_192_TOP))
 314                         return 0;
 315                 r_d = r->d;
 316                 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
 317                 }
 318         else
 319                 r_d = a_d;
 320
 321         nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
 322
 323         nist_set_192(t_d, buf, 0, 3, 3);
 324         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 325         nist_set_192(t_d, buf, 4, 4, 0);
 326         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 327         nist_set_192(t_d, buf, 5, 5, 5)
 328         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 329
 330         if (carry > 0)
 331                 carry = bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
 332         else
 333                 carry = 1;
 334
 335         /*
 336          * we need 'if (carry==0 || result>=modulus) result-=modulus;'
 337          * as comparison implies subtraction, we can write
 338          * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
 339          * this is what happens below, but without explicit if:-) a.
 340          */
 341         mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
 342         mask &= 0-(size_t)carry;
 343         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 344         nist_cp_bn(r_d, res, BN_NIST_192_TOP);
 345         r->top = BN_NIST_192_TOP;
 346         bn_correct_top(r);
 347
 348         return 1;
 349         }
 350
 351 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
 352
 353 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 354         { \
 355         bn_cp_32(to, 0, from, (a7) - 7) \
 356         bn_cp_32(to, 1, from, (a6) - 7) \
 357         bn_cp_32(to, 2, from, (a5) - 7) \
 358         bn_cp_32(to, 3, from, (a4) - 7) \
 359         bn_cp_32(to, 4, from, (a3) - 7) \
 360         bn_cp_32(to, 5, from, (a2) - 7) \
 361         bn_cp_32(to, 6, from, (a1) - 7) \
 362         }
 363
 364 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 365         BN_CTX *ctx)
 366         {
 367         int     top = a->top, i;
 368         int     carry;
 369         BN_ULONG *r_d, *a_d = a->d;
 370         BN_ULONG t_d[BN_NIST_224_TOP],
 371                  buf[BN_NIST_224_TOP],
 372                  c_d[BN_NIST_224_TOP],
 373                 *res;
 374         size_t   mask;
 375         union { bn_addsub_f f; size_t p; } u;
 376
 377         field = &_bignum_nist_p_224; /* just to make sure */
 378
 379         if (BN_is_negative(a) || a->top > (2*224+BN_BITS2-1)/BN_BITS2)
 380                 return BN_nnmod(r, field, a, ctx);
 381
 382         i = BN_ucmp(field, a);
 383         if (i == 0)
 384                 {
 385                 BN_zero(r);
 386                 return 1;
 387                 }
 388         else if (i > 0)
 389                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 390
 391         if (r != a)
 392                 {
 393                 if (!bn_wexpand(r, BN_NIST_224_TOP))
 394                         return 0;
 395                 r_d = r->d;
 396                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
 397                 }
 398         else
 399                 r_d = a_d;
 400
 401 #if BN_BITS2==64
 402         /* copy upper 256 bits of 448 bit number ... */
 403         nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
 404         /* ... and right shift by 32 to obtain upper 224 bits */
 405         nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
 406         /* truncate lower part to 224 bits too */
 407         r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
 408 #else
 409         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
 410 #endif
 411         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 412         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 413         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
 414         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 415         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
 416         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 417         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
 418         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 419
 420 #if BN_BITS2==64
 421         carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
 422 #endif
 423         u.f = bn_sub_words;
 424         if (carry > 0)
 425                 {
 426                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
 427 #if BN_BITS2==64
 428                 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
 429 #endif
 430                 }
 431         else if (carry < 0)
 432                 {
 433                 /* it's a bit more comlicated logic in this case.
 434                  * if bn_add_words yields no carry, then result
 435                  * has to be adjusted by unconditionally *adding*
 436                  * the modulus. but if it does, then result has
 437                  * to be compared to the modulus and conditionally
 438                  * adjusted by *subtracting* the latter. */
 439                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
 440                 mask = 0-(size_t)carry;
 441                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 442                 }
 443         else
 444                 carry = 1;
 445
 446         /* otherwise it's effectively same as in BN_nist_mod_192... */
 447         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
 448         mask &= 0-(size_t)carry;
 449         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 450         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
 451         r->top = BN_NIST_224_TOP;
 452         bn_correct_top(r);
 453
 454         return 1;
 455         }
 456
 457 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 458         { \
 459         bn_cp_32(to, 0, from, (a8) - 8) \
 460         bn_cp_32(to, 1, from, (a7) - 8) \
 461         bn_cp_32(to, 2, from, (a6) - 8) \
 462         bn_cp_32(to, 3, from, (a5) - 8) \
 463         bn_cp_32(to, 4, from, (a4) - 8) \
 464         bn_cp_32(to, 5, from, (a3) - 8) \
 465         bn_cp_32(to, 6, from, (a2) - 8) \
 466         bn_cp_32(to, 7, from, (a1) - 8) \
 467         }
 468
 469 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 470         BN_CTX *ctx)
 471         {
 472         int     i, top = a->top;
 473         int     carry = 0;
 474         register BN_ULONG *a_d = a->d, *r_d;
 475         BN_ULONG t_d[BN_NIST_256_TOP],
 476                  buf[BN_NIST_256_TOP],
 477                  c_d[BN_NIST_256_TOP],
 478                 *res;
 479         size_t   mask;
 480         union { bn_addsub_f f; size_t p; } u;
 481
 482         field = &_bignum_nist_p_256; /* just to make sure */
 483
 484         if (BN_is_negative(a) || a->top > 2*BN_NIST_256_TOP)
 485                 return BN_nnmod(r, field, a, ctx);
 486
 487         i = BN_ucmp(field, a);
 488         if (i == 0)
 489                 {
 490                 BN_zero(r);
 491                 return 1;
 492                 }
 493         else if (i > 0)
 494                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 495
 496         if (r != a)
 497                 {
 498                 if (!bn_wexpand(r, BN_NIST_256_TOP))
 499                         return 0;
 500                 r_d = r->d;
 501                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
 502                 }
 503         else
 504                 r_d = a_d;
 505
 506         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
 507
 508         /*S1*/
 509         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 510         /*S2*/
 511         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
 512         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
 513         /* left shift */
 514                 {
 515                 register BN_ULONG *ap,t,c;
 516                 ap = t_d;
 517                 c=0;
 518                 for (i = BN_NIST_256_TOP; i != 0; --i)
 519                         {
 520                         t= *ap;
 521                         *(ap++)=((t<<1)|c)&BN_MASK2;
 522                         c=(t & BN_TBIT)?1:0;
 523                         }
 524                 carry <<= 1;
 525                 carry  |= c;
 526                 }
 527         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 528         /*S3*/
 529         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
 530         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 531         /*S4*/
 532         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
 533         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 534         /*D1*/
 535         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
 536         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 537         /*D2*/
 538         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
 539         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 540         /*D3*/
 541         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
 542         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 543         /*D4*/
 544         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
 545         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 546
 547         /* see BN_nist_mod_224 for explanation */
 548         u.f = bn_sub_words;
 549         if (carry > 0)
 550                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
 551         else if (carry < 0)
 552                 {
 553                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
 554                 mask = 0-(size_t)carry;
 555                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 556                 }
 557         else
 558                 carry = 1;
 559
 560         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
 561         mask &= 0-(size_t)carry;
 562         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 563         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
 564         r->top = BN_NIST_256_TOP;
 565         bn_correct_top(r);
 566
 567         return 1;
 568         }
 569
 570 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 571         { \
 572         bn_cp_32(to, 0, from,  (a12) - 12) \
 573         bn_cp_32(to, 1, from,  (a11) - 12) \
 574         bn_cp_32(to, 2, from,  (a10) - 12) \
 575         bn_cp_32(to, 3, from,  (a9) - 12)  \
 576         bn_cp_32(to, 4, from,  (a8) - 12)  \
 577         bn_cp_32(to, 5, from,  (a7) - 12)  \
 578         bn_cp_32(to, 6, from,  (a6) - 12)  \
 579         bn_cp_32(to, 7, from,  (a5) - 12)  \
 580         bn_cp_32(to, 8, from,  (a4) - 12)  \
 581         bn_cp_32(to, 9, from,  (a3) - 12)  \
 582         bn_cp_32(to, 10, from, (a2) - 12)  \
 583         bn_cp_32(to, 11, from, (a1) - 12)  \
 584         }
 585
 586 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 587         BN_CTX *ctx)
 588         {
 589         int     i, top = a->top;
 590         int     carry = 0;
 591         register BN_ULONG *r_d, *a_d = a->d;
 592         BN_ULONG t_d[BN_NIST_384_TOP],
 593                  buf[BN_NIST_384_TOP],
 594                  c_d[BN_NIST_384_TOP],
 595                 *res;
 596         size_t   mask;
 597         union { bn_addsub_f f; size_t p; } u;
 598
 599         field = &_bignum_nist_p_384; /* just to make sure */
 600
 601         if (BN_is_negative(a) || a->top > 2*BN_NIST_384_TOP)
 602                 return BN_nnmod(r, field, a, ctx);
 603
 604         i = BN_ucmp(field, a);
 605         if (i == 0)
 606                 {
 607                 BN_zero(r);
 608                 return 1;
 609                 }
 610         else if (i > 0)
 611                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 612
 613         if (r != a)
 614                 {
 615                 if (!bn_wexpand(r, BN_NIST_384_TOP))
 616                         return 0;
 617                 r_d = r->d;
 618                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
 619                 }
 620         else
 621                 r_d = a_d;
 622
 623         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
 624
 625         /*S1*/
 626         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
 627                 /* left shift */
 628                 {
 629                 register BN_ULONG *ap,t,c;
 630                 ap = t_d;
 631                 c=0;
 632                 for (i = 3; i != 0; --i)
 633                         {
 634                         t= *ap;
 635                         *(ap++)=((t<<1)|c)&BN_MASK2;
 636                         c=(t & BN_TBIT)?1:0;
 637                         }
 638                 *ap=c;
 639                 }
 640         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 641                 t_d, BN_NIST_256_TOP);
 642         /*S2 */
 643         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
 644         /*S3*/
 645         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
 646         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 647         /*S4*/
 648         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
 649         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 650         /*S5*/
 651         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
 652         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 653         /*S6*/
 654         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
 655         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 656         /*D1*/
 657         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
 658         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 659         /*D2*/
 660         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
 661         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 662         /*D3*/
 663         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
 664         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 665
 666         /* see BN_nist_mod_224 for explanation */
 667         u.f = bn_sub_words;
 668         if (carry > 0)
 669                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
 670         else if (carry < 0)
 671                 {
 672                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
 673                 mask = 0-(size_t)carry;
 674                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 675                 }
 676         else
 677                 carry = 1;
 678
 679         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
 680         mask &= 0-(size_t)carry;
 681         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 682         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
 683         r->top = BN_NIST_384_TOP;
 684         bn_correct_top(r);
 685
 686         return 1;
 687         }
 688
 689 #define BN_NIST_521_RSHIFT      (521%BN_BITS2)
 690 #define BN_NIST_521_LSHIFT      (BN_BITS2-BN_NIST_521_RSHIFT)
 691 #define BN_NIST_521_TOP_MASK    ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
 692
 693 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 694         BN_CTX *ctx)
 695         {
 696         int     top = a->top, i;
 697         BN_ULONG *r_d, *a_d = a->d,
 698                  t_d[BN_NIST_521_TOP],
 699                  val,tmp,*res;
 700         size_t  mask;
 701
 702         field = &_bignum_nist_p_521; /* just to make sure */
 703
 704         if (BN_is_negative(a) || BN_num_bits(a)>2*521)
 705                 return BN_nnmod(r, field, a, ctx);
 706
 707         i = BN_ucmp(field, a);
 708         if (i == 0)
 709                 {
 710                 BN_zero(r);
 711                 return 1;
 712                 }
 713         else if (i > 0)
 714                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 715
 716         if (r != a)
 717                 {
 718                 if (!bn_wexpand(r,BN_NIST_521_TOP))
 719                         return 0;
 720                 r_d = r->d;
 721                 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
 722                 }
 723         else
 724                 r_d = a_d;
 725
 726         /* upper 521 bits, copy ... */
 727         nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
 728         /* ... and right shift */
 729         for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
 730                 {
 731                 tmp = val>>BN_NIST_521_RSHIFT;
 732                 val = t_d[i+1];
 733                 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
 734                 }
 735         t_d[i] = val>>BN_NIST_521_RSHIFT;
 736         /* lower 521 bits */
 737         r_d[i] &= BN_NIST_521_TOP_MASK;
 738
 739         bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
 740         mask = 0-(size_t)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
 741         res  = (BN_ULONG *)(((size_t)t_d&~mask) | ((size_t)r_d&mask));
 742         nist_cp_bn(r_d,res,BN_NIST_521_TOP);
 743         r->top = BN_NIST_521_TOP;
 744         bn_correct_top(r);
 745
 746         return 1;
 747         }