crypto/bn/bn_nist.c

   1 /* crypto/bn/bn_nist.c */
   2 /*
   3  * Written by Nils Larsch for the OpenSSL project
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    openssl-core@openssl.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58
  59 #include "bn_lcl.h"
  60 #include "cryptlib.h"
  61
  62 #define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
  63 #define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
  64 #define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
  65 #define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
  66 #define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
  67
  68 /* pre-computed tables are "carry-less" values of modulus*(i+1) */
  69 #if BN_BITS2 == 64
  70 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
  71         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
  72         {0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
  73         {0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
  74         };
  75 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
  76         {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
  77          0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
  78         {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
  79          0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
  80         };
  81 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
  82         {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
  83          0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
  84         {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
  85          0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
  86         {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
  87          0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
  88         {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
  89          0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
  90         {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
  91          0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
  92         };
  93 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
  94         {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
  95          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
  96         {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
  97          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
  98         {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
  99          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 100         {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
 101          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 102         {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
 103          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
 104         };
 105 static const BN_ULONG _nist_p_521[] =
 106         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 107         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 108         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 109         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 110         0x00000000000001FFULL};
 111 #elif BN_BITS2 == 32
 112 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
 113         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 114         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 115         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 116         };
 117 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
 118         {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
 119          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 120         {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
 121          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
 122         };
 123 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
 124         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
 125          0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
 126         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
 127          0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
 128         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
 129          0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
 130         {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
 131          0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
 132         {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
 133          0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
 134         };
 135 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
 136         {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
 137          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 138         {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
 139          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 140         {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
 141          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 142         {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
 143          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 144         {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
 145          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
 146         };
 147 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 148         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 149         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 150         0xFFFFFFFF,0x000001FF};
 151 #else
 152 #error "unsupported BN_BITS2"
 153 #endif
 154
 155 const BIGNUM *BN_get0_nist_prime_192(void)
 156         {
 157         static BIGNUM const_nist_192 = { (BN_ULONG *)_nist_p_192[0],
 158                 BN_NIST_192_TOP, BN_NIST_192_TOP, 0, BN_FLG_STATIC_DATA };
 159         return &const_nist_192;
 160         }
 161
 162 const BIGNUM *BN_get0_nist_prime_224(void)
 163         {
 164         static BIGNUM const_nist_224 = { (BN_ULONG *)_nist_p_224[0],
 165                 BN_NIST_224_TOP, BN_NIST_224_TOP, 0, BN_FLG_STATIC_DATA };
 166         return &const_nist_224;
 167         }
 168
 169 const BIGNUM *BN_get0_nist_prime_256(void)
 170         {
 171         static BIGNUM const_nist_256 = { (BN_ULONG *)_nist_p_256[0],
 172                 BN_NIST_256_TOP, BN_NIST_256_TOP, 0, BN_FLG_STATIC_DATA };
 173         return &const_nist_256;
 174         }
 175
 176 const BIGNUM *BN_get0_nist_prime_384(void)
 177         {
 178         static BIGNUM const_nist_384 = { (BN_ULONG *)_nist_p_384[0],
 179                 BN_NIST_384_TOP, BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA };
 180         return &const_nist_384;
 181         }
 182
 183 const BIGNUM *BN_get0_nist_prime_521(void)
 184         {
 185         static BIGNUM const_nist_521 = { (BN_ULONG *)_nist_p_521,
 186                 BN_NIST_521_TOP, BN_NIST_521_TOP, 0, BN_FLG_STATIC_DATA };
 187         return &const_nist_521;
 188         }
 189
 190 #define BN_NIST_ADD_ONE(a)      while (!(*(a)=(*(a)+1)&BN_MASK2)) ++(a);
 191
 192 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
 193         {
 194         int i;
 195         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 196         for (i = (top); i != 0; i--)
 197                 *_tmp1++ = *_tmp2++;
 198         for (i = (max) - (top); i != 0; i--)
 199                 *_tmp1++ = (BN_ULONG) 0;
 200         }
 201
 202 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 203         {
 204         int i;
 205         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 206         for (i = (top); i != 0; i--)
 207                 *_tmp1++ = *_tmp2++;
 208         }
 209
 210 #if BN_BITS2 == 64
 211 #define bn_cp_64(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 212 #define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 213 /*
 214  * two following macros are implemented under assumption that they
 215  * are called in a sequence with *ascending* n, i.e. as they are...
 216  */
 217 #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))\
 218                                                 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
 219 #define bn_32_set_0(to, n)              (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
 220 #define bn_cp_32(to,n,from,m)           ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
 221 #else
 222 #define bn_cp_64(to, n, from, m) \
 223         { \
 224         bn_cp_32(to, (n)*2, from, (m)*2); \
 225         bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
 226         }
 227 #define bn_64_set_0(to, n) \
 228         { \
 229         bn_32_set_0(to, (n)*2); \
 230         bn_32_set_0(to, (n)*2+1); \
 231         }
 232 #if BN_BITS2 == 32
 233 #define bn_cp_32(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
 234 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 235 #endif
 236 #endif /* BN_BITS2 != 64 */
 237
 238
 239 #define nist_set_192(to, from, a1, a2, a3) \
 240         { \
 241         bn_cp_64(to, 0, from, (a3) - 3) \
 242         bn_cp_64(to, 1, from, (a2) - 3) \
 243         bn_cp_64(to, 2, from, (a1) - 3) \
 244         }
 245
 246 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 247         BN_CTX *ctx)
 248         {
 249         int      top = a->top, i;
 250         int      carry;
 251         register BN_ULONG *r_d, *a_d = a->d;
 252         BN_ULONG t_d[BN_NIST_192_TOP],
 253                  buf[BN_NIST_192_TOP],
 254                  c_d[BN_NIST_192_TOP],
 255                 *res;
 256         size_t   mask;
 257
 258         i = BN_ucmp(field, a);
 259         if (i == 0)
 260                 {
 261                 BN_zero(r);
 262                 return 1;
 263                 }
 264         else if (i > 0)
 265                 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
 266
 267         if (top == BN_NIST_192_TOP)
 268                 return BN_usub(r, a, field);
 269
 270         if (r != a)
 271                 {
 272                 if (!bn_wexpand(r, BN_NIST_192_TOP))
 273                         return 0;
 274                 r_d = r->d;
 275                 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
 276                 }
 277         else
 278                 r_d = a_d;
 279
 280         nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
 281
 282         nist_set_192(t_d, buf, 0, 3, 3);
 283         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 284         nist_set_192(t_d, buf, 4, 4, 0);
 285         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 286         nist_set_192(t_d, buf, 5, 5, 5)
 287         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 288
 289         if (carry > 0)
 290                 carry = bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
 291         else
 292                 carry = 1;
 293
 294         /*
 295          * we need 'if (carry==0 || result>=modulus) result-=modulus;'
 296          * as comparison implies subtraction, we can write
 297          * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
 298          * this is what happens below, but without explicit if:-) a.
 299          */
 300         mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
 301         mask &= 0-(size_t)carry;
 302         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 303         nist_cp_bn(r_d, res, BN_NIST_192_TOP);
 304         r->top = BN_NIST_192_TOP;
 305         bn_correct_top(r);
 306
 307         return 1;
 308         }
 309
 310 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
 311
 312 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 313         { \
 314         bn_cp_32(to, 0, from, (a7) - 7) \
 315         bn_cp_32(to, 1, from, (a6) - 7) \
 316         bn_cp_32(to, 2, from, (a5) - 7) \
 317         bn_cp_32(to, 3, from, (a4) - 7) \
 318         bn_cp_32(to, 4, from, (a3) - 7) \
 319         bn_cp_32(to, 5, from, (a2) - 7) \
 320         bn_cp_32(to, 6, from, (a1) - 7) \
 321         }
 322
 323 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 324         BN_CTX *ctx)
 325         {
 326         int     top = a->top, i;
 327         int     carry;
 328         BN_ULONG *r_d, *a_d = a->d;
 329         BN_ULONG t_d[BN_NIST_224_TOP],
 330                  buf[BN_NIST_224_TOP],
 331                  c_d[BN_NIST_224_TOP],
 332                 *res;
 333         size_t   mask;
 334         union { bn_addsub_f f; size_t p; } u;
 335
 336         i = BN_ucmp(field, a);
 337         if (i == 0)
 338                 {
 339                 BN_zero(r);
 340                 return 1;
 341                 }
 342         else if (i > 0)
 343                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 344
 345         if (top == BN_NIST_224_TOP)
 346                 return BN_usub(r, a, field);
 347
 348         if (r != a)
 349                 {
 350                 if (!bn_wexpand(r, BN_NIST_224_TOP))
 351                         return 0;
 352                 r_d = r->d;
 353                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
 354                 }
 355         else
 356                 r_d = a_d;
 357
 358 #if BN_BITS2==64
 359         /* copy upper 256 bits of 448 bit number ... */
 360         nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
 361         /* ... and right shift by 32 to obtain upper 224 bits */
 362         nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
 363         /* truncate lower part to 224 bits too */
 364         r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
 365 #else
 366         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
 367 #endif
 368         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 369         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 370         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
 371         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 372         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
 373         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 374         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
 375         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 376
 377 #if BN_BITS2==64
 378         carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
 379 #endif
 380         u.f = bn_sub_words;
 381         if (carry > 0)
 382                 {
 383                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
 384 #if BN_BITS2==64
 385                 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
 386 #endif
 387                 }
 388         else if (carry < 0)
 389                 {
 390                 /* it's a bit more comlicated logic in this case.
 391                  * if bn_add_words yields no carry, then result
 392                  * has to be adjusted by unconditionally *adding*
 393                  * the modulus. but if it does, then result has
 394                  * to be compared to the modulus and conditionally
 395                  * adjusted by *subtracting* the latter. */
 396                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
 397                 mask = 0-(size_t)carry;
 398                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 399                 }
 400         else
 401                 carry = 1;
 402
 403         /* otherwise it's effectively same as in BN_nist_mod_192... */
 404         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
 405         mask &= 0-(size_t)carry;
 406         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 407         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
 408         r->top = BN_NIST_224_TOP;
 409         bn_correct_top(r);
 410
 411         return 1;
 412         }
 413
 414 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 415         { \
 416         bn_cp_32(to, 0, from, (a8) - 8) \
 417         bn_cp_32(to, 1, from, (a7) - 8) \
 418         bn_cp_32(to, 2, from, (a6) - 8) \
 419         bn_cp_32(to, 3, from, (a5) - 8) \
 420         bn_cp_32(to, 4, from, (a4) - 8) \
 421         bn_cp_32(to, 5, from, (a3) - 8) \
 422         bn_cp_32(to, 6, from, (a2) - 8) \
 423         bn_cp_32(to, 7, from, (a1) - 8) \
 424         }
 425
 426 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 427         BN_CTX *ctx)
 428         {
 429         int     i, top = a->top;
 430         int     carry = 0;
 431         register BN_ULONG *a_d = a->d, *r_d;
 432         BN_ULONG t_d[BN_NIST_256_TOP],
 433                  buf[BN_NIST_256_TOP],
 434                  c_d[BN_NIST_256_TOP],
 435                 *res;
 436         size_t   mask;
 437         union { bn_addsub_f f; size_t p; } u;
 438
 439         i = BN_ucmp(field, a);
 440         if (i == 0)
 441                 {
 442                 BN_zero(r);
 443                 return 1;
 444                 }
 445         else if (i > 0)
 446                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 447
 448         if (top == BN_NIST_256_TOP)
 449                 return BN_usub(r, a, field);
 450
 451         if (r != a)
 452                 {
 453                 if (!bn_wexpand(r, BN_NIST_256_TOP))
 454                         return 0;
 455                 r_d = r->d;
 456                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
 457                 }
 458         else
 459                 r_d = a_d;
 460
 461         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
 462
 463         /*S1*/
 464         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 465         /*S2*/
 466         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
 467         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
 468         /* left shift */
 469                 {
 470                 register BN_ULONG *ap,t,c;
 471                 ap = t_d;
 472                 c=0;
 473                 for (i = BN_NIST_256_TOP; i != 0; --i)
 474                         {
 475                         t= *ap;
 476                         *(ap++)=((t<<1)|c)&BN_MASK2;
 477                         c=(t & BN_TBIT)?1:0;
 478                         }
 479                 carry <<= 1;
 480                 carry  |= c;
 481                 }
 482         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 483         /*S3*/
 484         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
 485         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 486         /*S4*/
 487         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
 488         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 489         /*D1*/
 490         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
 491         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 492         /*D2*/
 493         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
 494         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 495         /*D3*/
 496         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
 497         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 498         /*D4*/
 499         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
 500         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 501
 502         /* see BN_nist_mod_224 for explanation */
 503         u.f = bn_sub_words;
 504         if (carry > 0)
 505                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
 506         else if (carry < 0)
 507                 {
 508                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
 509                 mask = 0-(size_t)carry;
 510                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 511                 }
 512         else
 513                 carry = 1;
 514
 515         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
 516         mask &= 0-(size_t)carry;
 517         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 518         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
 519         r->top = BN_NIST_256_TOP;
 520         bn_correct_top(r);
 521
 522         return 1;
 523         }
 524
 525 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 526         { \
 527         bn_cp_32(to, 0, from,  (a12) - 12) \
 528         bn_cp_32(to, 1, from,  (a11) - 12) \
 529         bn_cp_32(to, 2, from,  (a10) - 12) \
 530         bn_cp_32(to, 3, from,  (a9) - 12)  \
 531         bn_cp_32(to, 4, from,  (a8) - 12)  \
 532         bn_cp_32(to, 5, from,  (a7) - 12)  \
 533         bn_cp_32(to, 6, from,  (a6) - 12)  \
 534         bn_cp_32(to, 7, from,  (a5) - 12)  \
 535         bn_cp_32(to, 8, from,  (a4) - 12)  \
 536         bn_cp_32(to, 9, from,  (a3) - 12)  \
 537         bn_cp_32(to, 10, from, (a2) - 12)  \
 538         bn_cp_32(to, 11, from, (a1) - 12)  \
 539         }
 540
 541 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 542         BN_CTX *ctx)
 543         {
 544         int     i, top = a->top;
 545         int     carry = 0;
 546         register BN_ULONG *r_d, *a_d = a->d;
 547         BN_ULONG t_d[BN_NIST_384_TOP],
 548                  buf[BN_NIST_384_TOP],
 549                  c_d[BN_NIST_384_TOP],
 550                 *res;
 551         size_t   mask;
 552         union { bn_addsub_f f; size_t p; } u;
 553
 554         i = BN_ucmp(field, a);
 555         if (i == 0)
 556                 {
 557                 BN_zero(r);
 558                 return 1;
 559                 }
 560         else if (i > 0)
 561                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 562
 563         if (top == BN_NIST_384_TOP)
 564                 return BN_usub(r, a, field);
 565
 566         if (r != a)
 567                 {
 568                 if (!bn_wexpand(r, BN_NIST_384_TOP))
 569                         return 0;
 570                 r_d = r->d;
 571                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
 572                 }
 573         else
 574                 r_d = a_d;
 575
 576         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
 577
 578         /*S1*/
 579         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
 580                 /* left shift */
 581                 {
 582                 register BN_ULONG *ap,t,c;
 583                 ap = t_d;
 584                 c=0;
 585                 for (i = 3; i != 0; --i)
 586                         {
 587                         t= *ap;
 588                         *(ap++)=((t<<1)|c)&BN_MASK2;
 589                         c=(t & BN_TBIT)?1:0;
 590                         }
 591                 *ap=c;
 592                 }
 593         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 594                 t_d, BN_NIST_256_TOP);
 595         /*S2 */
 596         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
 597         /*S3*/
 598         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
 599         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 600         /*S4*/
 601         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
 602         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 603         /*S5*/
 604         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
 605         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 606         /*S6*/
 607         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
 608         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 609         /*D1*/
 610         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
 611         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 612         /*D2*/
 613         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
 614         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 615         /*D3*/
 616         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
 617         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 618
 619         /* see BN_nist_mod_224 for explanation */
 620         u.f = bn_sub_words;
 621         if (carry > 0)
 622                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
 623         else if (carry < 0)
 624                 {
 625                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
 626                 mask = 0-(size_t)carry;
 627                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
 628                 }
 629         else
 630                 carry = 1;
 631
 632         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
 633         mask &= 0-(size_t)carry;
 634         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 635         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
 636         r->top = BN_NIST_384_TOP;
 637         bn_correct_top(r);
 638
 639         return 1;
 640         }
 641
 642 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 643         BN_CTX *ctx)
 644         {
 645 #if BN_BITS2 == 64
 646 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 647 #elif BN_BITS2 == 32
 648 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 649 #endif
 650         int     top, ret = 0;
 651         BN_ULONG *r_d;
 652         BIGNUM  *tmp;
 653
 654         /* check whether a reduction is necessary */
 655         top = a->top;
 656         if (top < BN_NIST_521_TOP  || ( top == BN_NIST_521_TOP &&
 657            (!(a->d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))))
 658                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 659
 660         BN_CTX_start(ctx);
 661         tmp = BN_CTX_get(ctx);
 662         if (!tmp)
 663                 goto err;
 664
 665         if (!bn_wexpand(tmp, BN_NIST_521_TOP))
 666                 goto err;
 667         nist_cp_bn(tmp->d, a->d, BN_NIST_521_TOP);
 668
 669         tmp->top = BN_NIST_521_TOP;
 670         tmp->d[BN_NIST_521_TOP-1]  &= BN_NIST_521_TOP_MASK;
 671         bn_correct_top(tmp);
 672
 673         if (!BN_rshift(r, a, 521))
 674                 goto err;
 675
 676         if (!BN_uadd(r, tmp, r))
 677                 goto err;
 678         top = r->top;
 679         r_d = r->d;
 680         if (top == BN_NIST_521_TOP  &&
 681            (r_d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))
 682                 {
 683                 BN_NIST_ADD_ONE(r_d)
 684                 r->d[BN_NIST_521_TOP-1] &= BN_NIST_521_TOP_MASK;
 685                 }
 686         bn_correct_top(r);
 687
 688         ret = 1;
 689 err:
 690         BN_CTX_end(ctx);
 691
 692         bn_check_top(r);
 693         return ret;
 694         }