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         if (BN_ucmp(field, r) <= 0)
 349                 {
 350                 if (!BN_usub(r, r, field)) return 0;
 351                 }
 352
 353         return 1;
 354         }
 355
 356 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
 357
 358 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 359         { \
 360         bn_cp_32(to, 0, from, (a7) - 7) \
 361         bn_cp_32(to, 1, from, (a6) - 7) \
 362         bn_cp_32(to, 2, from, (a5) - 7) \
 363         bn_cp_32(to, 3, from, (a4) - 7) \
 364         bn_cp_32(to, 4, from, (a3) - 7) \
 365         bn_cp_32(to, 5, from, (a2) - 7) \
 366         bn_cp_32(to, 6, from, (a1) - 7) \
 367         }
 368
 369 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 370         BN_CTX *ctx)
 371         {
 372         int     top = a->top, i;
 373         int     carry;
 374         BN_ULONG *r_d, *a_d = a->d;
 375         BN_ULONG t_d[BN_NIST_224_TOP],
 376                  buf[BN_NIST_224_TOP],
 377                  c_d[BN_NIST_224_TOP],
 378                 *res;
 379         size_t   mask;
 380         union { bn_addsub_f f; size_t p; } u;
 381
 382         field = &_bignum_nist_p_224; /* just to make sure */
 383
 384         if (BN_is_negative(a) || a->top > 2*BN_NIST_224_TOP)
 385                 return BN_nnmod(r, field, a, ctx);
 386
 387         i = BN_ucmp(field, a);
 388         if (i == 0)
 389                 {
 390                 BN_zero(r);
 391                 return 1;
 392                 }
 393         else if (i > 0)
 394                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 395
 396         if (r != a)
 397                 {
 398                 if (!bn_wexpand(r, BN_NIST_224_TOP))
 399                         return 0;
 400                 r_d = r->d;
 401                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
 402                 }
 403         else
 404                 r_d = a_d;
 405
 406 #if BN_BITS2==64
 407         /* copy upper 256 bits of 448 bit number ... */
 408         nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
 409         /* ... and right shift by 32 to obtain upper 224 bits */
 410         nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
 411         /* truncate lower part to 224 bits too */
 412         r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
 413 #else
 414         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
 415 #endif
 416         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 417         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 418         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
 419         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 420         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
 421         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 422         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
 423         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 424
 425 #if BN_BITS2==64
 426         carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
 427 #endif
 428         u.f = bn_sub_words;
 429         if (carry > 0)
 430                 {
 431                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
 432 #if BN_BITS2==64
 433                 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
 434 #endif
 435                 }
 436         else if (carry < 0)
 437                 {
 438                 /* it's a bit more comlicated logic in this case.
 439                  * if bn_add_words yields no carry, then result
 440                  * has to be adjusted by unconditionally *adding*
 441                  * the modulus. but if it does, then result has
 442                  * to be compared to the modulus and conditionally
 443                  * adjusted by *subtracting* the latter. */
 444                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
 445                 mask = 0-(size_t)carry;
 446                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 447                 }
 448         else
 449                 carry = 1;
 450
 451         /* otherwise it's effectively same as in BN_nist_mod_192... */
 452         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
 453         mask &= 0-(size_t)carry;
 454         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 455         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
 456         r->top = BN_NIST_224_TOP;
 457         bn_correct_top(r);
 458
 459         if (BN_ucmp(field, r) <= 0)
 460                 {
 461                 if (!BN_usub(r, r, field)) return 0;
 462                 }
 463
 464         return 1;
 465         }
 466
 467 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 468         { \
 469         bn_cp_32(to, 0, from, (a8) - 8) \
 470         bn_cp_32(to, 1, from, (a7) - 8) \
 471         bn_cp_32(to, 2, from, (a6) - 8) \
 472         bn_cp_32(to, 3, from, (a5) - 8) \
 473         bn_cp_32(to, 4, from, (a4) - 8) \
 474         bn_cp_32(to, 5, from, (a3) - 8) \
 475         bn_cp_32(to, 6, from, (a2) - 8) \
 476         bn_cp_32(to, 7, from, (a1) - 8) \
 477         }
 478
 479 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 480         BN_CTX *ctx)
 481         {
 482         int     i, top = a->top;
 483         int     carry = 0;
 484         register BN_ULONG *a_d = a->d, *r_d;
 485         BN_ULONG t_d[BN_NIST_256_TOP],
 486                  buf[BN_NIST_256_TOP],
 487                  c_d[BN_NIST_256_TOP],
 488                 *res;
 489         size_t   mask;
 490         union { bn_addsub_f f; size_t p; } u;
 491
 492         field = &_bignum_nist_p_256; /* just to make sure */
 493
 494         if (BN_is_negative(a) || a->top > 2*BN_NIST_256_TOP)
 495                 return BN_nnmod(r, field, a, ctx);
 496
 497         i = BN_ucmp(field, a);
 498         if (i == 0)
 499                 {
 500                 BN_zero(r);
 501                 return 1;
 502                 }
 503         else if (i > 0)
 504                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 505
 506         if (r != a)
 507                 {
 508                 if (!bn_wexpand(r, BN_NIST_256_TOP))
 509                         return 0;
 510                 r_d = r->d;
 511                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
 512                 }
 513         else
 514                 r_d = a_d;
 515
 516         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
 517
 518         /*S1*/
 519         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 520         /*S2*/
 521         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
 522         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
 523         /* left shift */
 524                 {
 525                 register BN_ULONG *ap,t,c;
 526                 ap = t_d;
 527                 c=0;
 528                 for (i = BN_NIST_256_TOP; i != 0; --i)
 529                         {
 530                         t= *ap;
 531                         *(ap++)=((t<<1)|c)&BN_MASK2;
 532                         c=(t & BN_TBIT)?1:0;
 533                         }
 534                 carry <<= 1;
 535                 carry  |= c;
 536                 }
 537         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 538         /*S3*/
 539         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
 540         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 541         /*S4*/
 542         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
 543         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 544         /*D1*/
 545         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
 546         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 547         /*D2*/
 548         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
 549         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 550         /*D3*/
 551         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
 552         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 553         /*D4*/
 554         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
 555         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 556
 557         /* see BN_nist_mod_224 for explanation */
 558         u.f = bn_sub_words;
 559         if (carry > 0)
 560                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
 561         else if (carry < 0)
 562                 {
 563                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
 564                 mask = 0-(size_t)carry;
 565                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 566                 }
 567         else
 568                 carry = 1;
 569
 570         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
 571         mask &= 0-(size_t)carry;
 572         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 573         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
 574         r->top = BN_NIST_256_TOP;
 575         bn_correct_top(r);
 576
 577         if (BN_ucmp(field, r) <= 0)
 578                 {
 579                 if (!BN_usub(r, r, field)) return 0;
 580                 }
 581
 582         return 1;
 583         }
 584
 585 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 586         { \
 587         bn_cp_32(to, 0, from,  (a12) - 12) \
 588         bn_cp_32(to, 1, from,  (a11) - 12) \
 589         bn_cp_32(to, 2, from,  (a10) - 12) \
 590         bn_cp_32(to, 3, from,  (a9) - 12)  \
 591         bn_cp_32(to, 4, from,  (a8) - 12)  \
 592         bn_cp_32(to, 5, from,  (a7) - 12)  \
 593         bn_cp_32(to, 6, from,  (a6) - 12)  \
 594         bn_cp_32(to, 7, from,  (a5) - 12)  \
 595         bn_cp_32(to, 8, from,  (a4) - 12)  \
 596         bn_cp_32(to, 9, from,  (a3) - 12)  \
 597         bn_cp_32(to, 10, from, (a2) - 12)  \
 598         bn_cp_32(to, 11, from, (a1) - 12)  \
 599         }
 600
 601 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 602         BN_CTX *ctx)
 603         {
 604         int     i, top = a->top;
 605         int     carry = 0;
 606         register BN_ULONG *r_d, *a_d = a->d;
 607         BN_ULONG t_d[BN_NIST_384_TOP],
 608                  buf[BN_NIST_384_TOP],
 609                  c_d[BN_NIST_384_TOP],
 610                 *res;
 611         size_t   mask;
 612         union { bn_addsub_f f; size_t p; } u;
 613
 614         field = &_bignum_nist_p_384; /* just to make sure */
 615
 616         if (BN_is_negative(a) || a->top > 2*BN_NIST_384_TOP)
 617                 return BN_nnmod(r, field, a, ctx);
 618
 619         i = BN_ucmp(field, a);
 620         if (i == 0)
 621                 {
 622                 BN_zero(r);
 623                 return 1;
 624                 }
 625         else if (i > 0)
 626                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 627
 628         if (r != a)
 629                 {
 630                 if (!bn_wexpand(r, BN_NIST_384_TOP))
 631                         return 0;
 632                 r_d = r->d;
 633                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
 634                 }
 635         else
 636                 r_d = a_d;
 637
 638         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
 639
 640         /*S1*/
 641         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
 642                 /* left shift */
 643                 {
 644                 register BN_ULONG *ap,t,c;
 645                 ap = t_d;
 646                 c=0;
 647                 for (i = 3; i != 0; --i)
 648                         {
 649                         t= *ap;
 650                         *(ap++)=((t<<1)|c)&BN_MASK2;
 651                         c=(t & BN_TBIT)?1:0;
 652                         }
 653                 *ap=c;
 654                 }
 655         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 656                 t_d, BN_NIST_256_TOP);
 657         /*S2 */
 658         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
 659         /*S3*/
 660         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
 661         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 662         /*S4*/
 663         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
 664         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 665         /*S5*/
 666         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
 667         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 668         /*S6*/
 669         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
 670         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 671         /*D1*/
 672         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
 673         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 674         /*D2*/
 675         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
 676         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 677         /*D3*/
 678         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
 679         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 680
 681         /* see BN_nist_mod_224 for explanation */
 682         u.f = bn_sub_words;
 683         if (carry > 0)
 684                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
 685         else if (carry < 0)
 686                 {
 687                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
 688                 mask = 0-(size_t)carry;
 689                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 690                 }
 691         else
 692                 carry = 1;
 693
 694         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
 695         mask &= 0-(size_t)carry;
 696         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 697         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
 698         r->top = BN_NIST_384_TOP;
 699         bn_correct_top(r);
 700
 701         if (BN_ucmp(field, r) <= 0)
 702                 {
 703                 if (!BN_usub(r, r, field)) return 0;
 704                 }
 705
 706         return 1;
 707         }
 708
 709 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 710         BN_CTX *ctx)
 711         {
 712 #if BN_BITS2 == 64
 713 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 714 #elif BN_BITS2 == 32
 715 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 716 #endif
 717         int     top, ret = 0;
 718         BIGNUM  *tmp;
 719
 720         field = &_bignum_nist_p_521; /* just to make sure */
 721
 722         if (BN_is_negative(a))
 723                 return BN_nnmod(r, field, a, ctx);
 724
 725         /* check whether a reduction is necessary */
 726         top = a->top;
 727         if (top < BN_NIST_521_TOP  || ( top == BN_NIST_521_TOP &&
 728             (!(a->d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))))
 729                 {
 730                 int i = BN_ucmp(field, a);
 731                 if (i == 0)
 732                         {
 733                         BN_zero(r);
 734                         return 1;
 735                         }
 736                 else
 737                         {
 738 #ifdef BN_DEBUG
 739                         OPENSSL_assert(i > 0); /* because 'field' is 1111...1111 */
 740 #endif
 741                         return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 742                         }
 743                 }
 744
 745         if (BN_num_bits(a) > 2*521)
 746                 return BN_nnmod(r, field, a, ctx);
 747
 748         BN_CTX_start(ctx);
 749         tmp = BN_CTX_get(ctx);
 750         if (!tmp)
 751                 goto err;
 752
 753         if (!bn_wexpand(tmp, BN_NIST_521_TOP))
 754                 goto err;
 755         nist_cp_bn(tmp->d, a->d, BN_NIST_521_TOP);
 756
 757         tmp->top = BN_NIST_521_TOP;
 758         tmp->d[BN_NIST_521_TOP-1]  &= BN_NIST_521_TOP_MASK;
 759         bn_correct_top(tmp);
 760
 761         if (!BN_rshift(r, a, 521))
 762                 goto err;
 763
 764         if (!BN_uadd(r, tmp, r))
 765                 goto err;
 766
 767         if (BN_ucmp(field, r) <= 0)
 768                 {
 769                 if (!BN_usub(r, r, field)) goto err;
 770                 }
 771
 772         ret = 1;
 773 err:
 774         BN_CTX_end(ctx);
 775
 776         bn_check_top(r);
 777         return ret;
 778         }