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 #if BN_BITS2 == 64
  69 static const BN_ULONG _nist_p_192[] =
  70         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,
  71         0xFFFFFFFFFFFFFFFFULL};
  72 static const BN_ULONG _nist_p_224[] =
  73         {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
  74         0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL};
  75 static const BN_ULONG _nist_p_256[] =
  76         {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
  77         0x0000000000000000ULL,0xFFFFFFFF00000001ULL};
  78 static const BN_ULONG _nist_p_384[] =
  79         {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,
  80         0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL,
  81         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL};
  82 static const BN_ULONG _nist_p_521[] =
  83         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
  84         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
  85         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
  86         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
  87         0x00000000000001FFULL};
  88 #elif BN_BITS2 == 32
  89 static const BN_ULONG _nist_p_192[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,
  90         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
  91 static const BN_ULONG _nist_p_224[] = {0x00000001,0x00000000,0x00000000,
  92         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
  93 static const BN_ULONG _nist_p_256[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
  94         0x00000000,0x00000000,0x00000000,0x00000001,0xFFFFFFFF};
  95 static const BN_ULONG _nist_p_384[] = {0xFFFFFFFF,0x00000000,0x00000000,
  96         0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
  97         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
  98 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
  99         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 100         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 101         0xFFFFFFFF,0x000001FF};
 102 #elif BN_BITS2 == 16
 103 static const BN_ULONG _nist_p_192[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFE,
 104         0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
 105 static const BN_ULONG _nist_p_224[] = {0x0001,0x0000,0x0000,0x0000,0x0000,
 106         0x0000,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
 107 static const BN_ULONG _nist_p_256[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
 108         0xFFFF,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0001,0x0000,0xFFFF,
 109         0xFFFF};
 110 static const BN_ULONG _nist_p_384[] = {0xFFFF,0xFFFF,0x0000,0x0000,0x0000,
 111         0x0000,0xFFFF,0xFFFF,0xFFFE,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
 112         0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
 113 static const BN_ULONG _nist_p_521[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
 114         0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
 115         0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
 116         0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0x01FF};
 117 #elif BN_BITS2 == 8
 118 static const BN_ULONG _nist_p_192[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 119         0xFE,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 120         0xFF,0xFF};
 121 static const BN_ULONG _nist_p_224[] = {0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
 122         0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 123         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF};
 124 static const BN_ULONG _nist_p_256[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 125         0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
 126         0x00,0x00,0x01,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF};
 127 static const BN_ULONG _nist_p_384[] = {0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
 128         0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0xFF,
 129         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 130         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF};
 131 static const BN_ULONG _nist_p_521[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 132         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 133         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 134         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 135         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
 136         0xFF,0x01};
 137 #endif
 138
 139 const BIGNUM *BN_get0_nist_prime_192(void)
 140         {
 141         static BIGNUM const_nist_192 = { (BN_ULONG *)_nist_p_192,
 142                 BN_NIST_192_TOP, BN_NIST_192_TOP, 0, BN_FLG_STATIC_DATA };
 143         return &const_nist_192;
 144         }
 145
 146 const BIGNUM *BN_get0_nist_prime_224(void)
 147         {
 148         static BIGNUM const_nist_224 = { (BN_ULONG *)_nist_p_224,
 149                 BN_NIST_224_TOP, BN_NIST_224_TOP, 0, BN_FLG_STATIC_DATA };
 150         return &const_nist_224;
 151         }
 152
 153 const BIGNUM *BN_get0_nist_prime_256(void)
 154         {
 155         static BIGNUM const_nist_256 = { (BN_ULONG *)_nist_p_256,
 156                 BN_NIST_256_TOP, BN_NIST_256_TOP, 0, BN_FLG_STATIC_DATA };
 157         return &const_nist_256;
 158         }
 159
 160 const BIGNUM *BN_get0_nist_prime_384(void)
 161         {
 162         static BIGNUM const_nist_384 = { (BN_ULONG *)_nist_p_384,
 163                 BN_NIST_384_TOP, BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA };
 164         return &const_nist_384;
 165         }
 166
 167 const BIGNUM *BN_get0_nist_prime_521(void)
 168         {
 169         static BIGNUM const_nist_521 = { (BN_ULONG *)_nist_p_521,
 170                 BN_NIST_521_TOP, BN_NIST_521_TOP, 0, BN_FLG_STATIC_DATA };
 171         return &const_nist_521;
 172         }
 173
 174 /* some misc internal functions */
 175 static BN_ULONG _256_data[BN_NIST_256_TOP*6];
 176 static int _is_set_256_data = 0;
 177 static void _init_256_data(void);
 178
 179 static BN_ULONG _384_data[BN_NIST_384_TOP*8];
 180 static int _is_set_384_data = 0;
 181 static void _init_384_data(void);
 182
 183 #define BN_NIST_ADD_ONE(a)      while (!(++(*(a)))) ++(a);
 184
 185 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
 186         {
 187         int i;
 188         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 189         for (i = (top); i != 0; i--)
 190                 *_tmp1++ = *_tmp2++;
 191         for (i = (max) - (top); i != 0; i--)
 192                 *_tmp1++ = (BN_ULONG) 0;
 193         }
 194
 195 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 196         {
 197         int i;
 198         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
 199         for (i = (top); i != 0; i--)
 200                 *_tmp1++ = *_tmp2++;
 201         }
 202
 203 #if BN_BITS2 == 64
 204 #define bn_cp_64(to, n, from, m)        (to)[n] = (from)[m];
 205 #define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 206 /* TBD */
 207 #define bn_cp_32(to, n, from, m)        (to)[n] = (from)[m];
 208 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 209 #else
 210 #define bn_cp_64(to, n, from, m) \
 211         { \
 212         bn_cp_32(to, (n)*2, from, (m)*2); \
 213         bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
 214         }
 215 #define bn_64_set_0(to, n) \
 216         { \
 217         bn_32_set_0(to, (n)*2); \
 218         bn_32_set_0(to, (n)*2+1); \
 219         }
 220 #if BN_BITS2 == 32
 221 #define bn_cp_32(to, n, from, m)        (to)[n] = (from)[m];
 222 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
 223 #elif BN_BITS2 == 16
 224 #define bn_cp_32(to, n, from, m) \
 225         { \
 226         (to)[(n)*2]   = (from)[(m)*2];  \
 227         (to)[(n)*2+1] = (from)[(m)*2+1];\
 228         }
 229 #define bn_32_set_0(to, n) { (to)[(n)*2] = 0; (to)[(n)*2+1] = 0; }
 230 #elif BN_BITS2 == 8
 231 #define bn_cp_32(to, n, from, m) \
 232         { \
 233         (to)[(n)*4]   = (from)[(m)*4];  \
 234         (to)[(n)*4+1] = (from)[(m)*4+1];\
 235         (to)[(n)*4+2] = (from)[(m)*4+2];\
 236         (to)[(n)*4+3] = (from)[(m)*4+3];\
 237         }
 238 #define bn_32_set_0(to, n) \
 239         { (to)[(n)*4]   = (BN_ULONG)0; (to)[(n)*4+1] = (BN_ULONG)0; \
 240           (to)[(n)*4+2] = (BN_ULONG)0; (to)[(n)*4+3] = (BN_ULONG)0; }
 241 #endif
 242 #endif /* BN_BITS2 != 64 */
 243
 244
 245 #define nist_set_192(to, from, a1, a2, a3) \
 246         { \
 247         if (a3 != 0) bn_cp_64(to, 0, from, (a3) - 3) else bn_64_set_0(to, 0)\
 248         bn_cp_64(to, 1, from, (a2) - 3) \
 249         if (a1 != 0) bn_cp_64(to, 2, from, (a1) - 3) else bn_64_set_0(to, 2)\
 250         }
 251
 252 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 253         BN_CTX *ctx)
 254         {
 255         int      top = a->top, i;
 256         BN_ULONG carry = 0;
 257         register BN_ULONG *r_d, *a_d = a->d;
 258         BN_ULONG t_d[BN_NIST_192_TOP],
 259                  buf[BN_NIST_192_TOP];
 260
 261         i = BN_ucmp(field, a);
 262         if (i == 0)
 263                 {
 264                 BN_zero(r);
 265                 return 1;
 266                 }
 267         else if (i > 0)
 268                 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
 269
 270         if (top == BN_NIST_192_TOP)
 271                 return BN_usub(r, a, field);
 272
 273         if (r != a)
 274                 {
 275                 if (!bn_wexpand(r, BN_NIST_192_TOP))
 276                         return 0;
 277                 r_d = r->d;
 278                 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
 279                 }
 280         else
 281                 r_d = a_d;
 282
 283         nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
 284
 285         nist_set_192(t_d, buf, 0, 3, 3);
 286         if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
 287                 ++carry;
 288
 289         nist_set_192(t_d, buf, 4, 4, 0);
 290         if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
 291                 ++carry;
 292
 293         nist_set_192(t_d, buf, 5, 5, 5)
 294         if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
 295                 ++carry;
 296
 297         while (carry)
 298                 {
 299                 if (bn_sub_words(r_d, r_d, _nist_p_192, BN_NIST_192_TOP))
 300                         --carry;
 301                 }
 302         r->top = BN_NIST_192_TOP;
 303         bn_correct_top(r);
 304         if (BN_ucmp(r, field) >= 0)
 305                 {
 306                 bn_sub_words(r_d, r_d, _nist_p_192, BN_NIST_192_TOP);
 307                 bn_correct_top(r);
 308                 }
 309
 310         bn_check_top(r);
 311         return 1;
 312         }
 313
 314 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 315         { \
 316         if (a7 != 0) bn_cp_32(to, 0, from, (a7) - 7) else bn_32_set_0(to, 0)\
 317         if (a6 != 0) bn_cp_32(to, 1, from, (a6) - 7) else bn_32_set_0(to, 1)\
 318         if (a5 != 0) bn_cp_32(to, 2, from, (a5) - 7) else bn_32_set_0(to, 2)\
 319         if (a4 != 0) bn_cp_32(to, 3, from, (a4) - 7) else bn_32_set_0(to, 3)\
 320         if (a3 != 0) bn_cp_32(to, 4, from, (a3) - 7) else bn_32_set_0(to, 4)\
 321         if (a2 != 0) bn_cp_32(to, 5, from, (a2) - 7) else bn_32_set_0(to, 5)\
 322         if (a1 != 0) bn_cp_32(to, 6, from, (a1) - 7) else bn_32_set_0(to, 6)\
 323         }
 324
 325 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 326         BN_CTX *ctx)
 327         {
 328 #if BN_BITS2 != 64
 329         int     top = a->top, i;
 330         int     carry = 0;
 331         BN_ULONG *r_d, *a_d = a->d;
 332         BN_ULONG t_d[BN_NIST_224_TOP],
 333                  buf[BN_NIST_224_TOP];
 334
 335         i = BN_ucmp(field, a);
 336         if (i == 0)
 337                 {
 338                 BN_zero(r);
 339                 return 1;
 340                 }
 341         else if (i > 0)
 342                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 343
 344         if (top == BN_NIST_224_TOP)
 345                 return BN_usub(r, a, field);
 346
 347         if (r != a)
 348                 {
 349                 if (!bn_wexpand(r, BN_NIST_224_TOP))
 350                         return 0;
 351                 r_d = r->d;
 352                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
 353                 }
 354         else
 355                 r_d = a_d;
 356
 357         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
 358
 359         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 360         if (bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP))
 361                 ++carry;
 362         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
 363         if (bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP))
 364                 ++carry;
 365         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
 366         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
 367                 --carry;
 368         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
 369         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
 370                 --carry;
 371
 372         if (carry > 0)
 373                 while (carry)
 374                         {
 375                         if (bn_sub_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP))
 376                                 --carry;
 377                         }
 378         else if (carry < 0)
 379                 while (carry)
 380                         {
 381                         if (bn_add_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP))
 382                                 ++carry;
 383                         }
 384
 385         r->top = BN_NIST_224_TOP;
 386         bn_correct_top(r);
 387         if (BN_ucmp(r, field) >= 0)
 388                 {
 389                 bn_sub_words(r_d, r_d, _nist_p_224, BN_NIST_224_TOP);
 390                 bn_correct_top(r);
 391                 }
 392         bn_check_top(r);
 393         return 1;
 394 #else
 395         return 0;
 396 #endif
 397         }
 398
 399 static void _init_256_data(void)
 400         {
 401         int     i;
 402         BN_ULONG *tmp1 = _256_data;
 403         const BN_ULONG *tmp2 = tmp1;
 404
 405         memcpy(tmp1, _nist_p_256, BN_NIST_256_TOP * sizeof(BN_ULONG));
 406         tmp1 += BN_NIST_256_TOP;
 407
 408         for (i=0; i<5; i++)
 409                 {
 410                 bn_add_words(tmp1, _nist_p_256, tmp2, BN_NIST_256_TOP);
 411                 tmp2  = tmp1;
 412                 tmp1 += BN_NIST_256_TOP;
 413                 }
 414         _is_set_256_data = 1;
 415         }
 416
 417 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 418         { \
 419         if (a8 != 0) bn_cp_32(to, 0, from, (a8) - 8) else bn_32_set_0(to, 0)\
 420         if (a7 != 0) bn_cp_32(to, 1, from, (a7) - 8) else bn_32_set_0(to, 1)\
 421         if (a6 != 0) bn_cp_32(to, 2, from, (a6) - 8) else bn_32_set_0(to, 2)\
 422         if (a5 != 0) bn_cp_32(to, 3, from, (a5) - 8) else bn_32_set_0(to, 3)\
 423         if (a4 != 0) bn_cp_32(to, 4, from, (a4) - 8) else bn_32_set_0(to, 4)\
 424         if (a3 != 0) bn_cp_32(to, 5, from, (a3) - 8) else bn_32_set_0(to, 5)\
 425         if (a2 != 0) bn_cp_32(to, 6, from, (a2) - 8) else bn_32_set_0(to, 6)\
 426         if (a1 != 0) bn_cp_32(to, 7, from, (a1) - 8) else bn_32_set_0(to, 7)\
 427         }
 428
 429 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 430         BN_CTX *ctx)
 431         {
 432 #if BN_BITS2 != 64
 433         int     i, top = a->top;
 434         int     carry = 0;
 435         register BN_ULONG *a_d = a->d, *r_d;
 436         BN_ULONG t_d[BN_NIST_256_TOP],
 437                  t_d2[BN_NIST_256_TOP],
 438                  buf[BN_NIST_256_TOP];
 439
 440         if (!_is_set_256_data)
 441                 {
 442                 CRYPTO_w_lock(CRYPTO_LOCK_BN);
 443
 444                 if (!_is_set_256_data)
 445                         _init_256_data();
 446
 447                 CRYPTO_w_unlock(CRYPTO_LOCK_BN);
 448                 }
 449
 450         i = BN_ucmp(field, a);
 451         if (i == 0)
 452                 {
 453                 BN_zero(r);
 454                 return 1;
 455                 }
 456         else if (i > 0)
 457                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 458
 459         if (top == BN_NIST_256_TOP)
 460                 return BN_usub(r, a, field);
 461
 462         if (r != a)
 463                 {
 464                 if (!bn_wexpand(r, BN_NIST_256_TOP))
 465                         return 0;
 466                 r_d = r->d;
 467                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
 468                 }
 469         else
 470                 r_d = a_d;
 471
 472         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
 473
 474         /*S1*/
 475         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 476         /*S2*/
 477         nist_set_256(t_d2,buf, 0, 15, 14, 13, 12, 0, 0, 0);
 478         if (bn_add_words(t_d, t_d, t_d2, BN_NIST_256_TOP))
 479                 carry = 2;
 480         /* left shift */
 481                 {
 482                 register BN_ULONG *ap,t,c;
 483                 ap = t_d;
 484                 c=0;
 485                 for (i = BN_NIST_256_TOP; i != 0; --i)
 486                         {
 487                         t= *ap;
 488                         *(ap++)=((t<<1)|c)&BN_MASK2;
 489                         c=(t & BN_TBIT)?1:0;
 490                         }
 491                 if (c)
 492                         ++carry;
 493                 }
 494
 495         if (bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 496                 ++carry;
 497         /*S3*/
 498         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
 499         if (bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 500                 ++carry;
 501         /*S4*/
 502         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
 503         if (bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 504                 ++carry;
 505         /*D1*/
 506         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
 507         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 508                 --carry;
 509         /*D2*/
 510         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
 511         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 512                 --carry;
 513         /*D3*/
 514         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
 515         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 516                 --carry;
 517         /*D4*/
 518         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
 519         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
 520                 --carry;
 521
 522         if (carry)
 523                 {
 524                 if (carry > 0)
 525                         bn_sub_words(r_d, r_d, _256_data + BN_NIST_256_TOP *
 526                                 --carry, BN_NIST_256_TOP);
 527                 else
 528                         {
 529                         carry = -carry;
 530                         bn_add_words(r_d, r_d, _256_data + BN_NIST_256_TOP *
 531                                 --carry, BN_NIST_256_TOP);
 532                         }
 533                 }
 534
 535         r->top = BN_NIST_256_TOP;
 536         bn_correct_top(r);
 537         if (BN_ucmp(r, field) >= 0)
 538                 {
 539                 bn_sub_words(r_d, r_d, _nist_p_256, BN_NIST_256_TOP);
 540                 bn_correct_top(r);
 541                 }
 542         bn_check_top(r);
 543         return 1;
 544 #else
 545         return 0;
 546 #endif
 547         }
 548
 549 static void _init_384_data(void)
 550         {
 551         int     i;
 552         BN_ULONG *tmp1 = _384_data;
 553         const BN_ULONG *tmp2 = tmp1;
 554
 555         memcpy(tmp1, _nist_p_384, BN_NIST_384_TOP * sizeof(BN_ULONG));
 556         tmp1 += BN_NIST_384_TOP;
 557
 558         for (i=0; i<7; i++)
 559                 {
 560                 bn_add_words(tmp1, _nist_p_384, tmp2, BN_NIST_384_TOP);
 561                 tmp2  = tmp1;
 562                 tmp1 += BN_NIST_384_TOP;
 563                 }
 564         _is_set_384_data = 1;
 565         }
 566
 567 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 568         { \
 569         if (a12 != 0) bn_cp_32(to, 0, from,  (a12) - 12) else bn_32_set_0(to, 0)\
 570         if (a11 != 0) bn_cp_32(to, 1, from,  (a11) - 12) else bn_32_set_0(to, 1)\
 571         if (a10 != 0) bn_cp_32(to, 2, from,  (a10) - 12) else bn_32_set_0(to, 2)\
 572         if (a9 != 0)  bn_cp_32(to, 3, from,  (a9) - 12)  else bn_32_set_0(to, 3)\
 573         if (a8 != 0)  bn_cp_32(to, 4, from,  (a8) - 12)  else bn_32_set_0(to, 4)\
 574         if (a7 != 0)  bn_cp_32(to, 5, from,  (a7) - 12)  else bn_32_set_0(to, 5)\
 575         if (a6 != 0)  bn_cp_32(to, 6, from,  (a6) - 12)  else bn_32_set_0(to, 6)\
 576         if (a5 != 0)  bn_cp_32(to, 7, from,  (a5) - 12)  else bn_32_set_0(to, 7)\
 577         if (a4 != 0)  bn_cp_32(to, 8, from,  (a4) - 12)  else bn_32_set_0(to, 8)\
 578         if (a3 != 0)  bn_cp_32(to, 9, from,  (a3) - 12)  else bn_32_set_0(to, 9)\
 579         if (a2 != 0)  bn_cp_32(to, 10, from, (a2) - 12)  else bn_32_set_0(to, 10)\
 580         if (a1 != 0)  bn_cp_32(to, 11, from, (a1) - 12)  else bn_32_set_0(to, 11)\
 581         }
 582
 583 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 584         BN_CTX *ctx)
 585         {
 586 #if BN_BITS2 != 64
 587         int     i, top = a->top;
 588         int     carry = 0;
 589         register BN_ULONG *r_d, *a_d = a->d;
 590         BN_ULONG t_d[BN_NIST_384_TOP],
 591                  buf[BN_NIST_384_TOP];
 592
 593         if (!_is_set_384_data)
 594                 {
 595                 CRYPTO_w_lock(CRYPTO_LOCK_BN);
 596
 597                 if (!_is_set_384_data)
 598                         _init_384_data();
 599
 600                 CRYPTO_w_unlock(CRYPTO_LOCK_BN);
 601                 }
 602
 603         i = BN_ucmp(field, a);
 604         if (i == 0)
 605                 {
 606                 BN_zero(r);
 607                 return 1;
 608                 }
 609         else if (i > 0)
 610                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 611
 612         if (top == BN_NIST_384_TOP)
 613                 return BN_usub(r, a, field);
 614
 615         if (r != a)
 616                 {
 617                 if (!bn_wexpand(r, BN_NIST_384_TOP))
 618                         return 0;
 619                 r_d = r->d;
 620                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
 621                 }
 622         else
 623                 r_d = a_d;
 624
 625         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
 626
 627         /*S1*/
 628         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
 629                 /* left shift */
 630                 {
 631                 register BN_ULONG *ap,t,c;
 632                 ap = t_d;
 633                 c=0;
 634                 for (i = BN_NIST_256_TOP; i != 0; --i)
 635                         {
 636                         t= *ap;
 637                         *(ap++)=((t<<1)|c)&BN_MASK2;
 638                         c=(t & BN_TBIT)?1:0;
 639                         }
 640                 }
 641         if (bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 642                 t_d, BN_NIST_256_TOP))
 643                 ++carry;
 644         /*S2 */
 645         if (bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP))
 646                 ++carry;
 647         /*S3*/
 648         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
 649         if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
 650                 ++carry;
 651         /*S4*/
 652         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
 653         if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
 654                 ++carry;
 655         /*S5*/
 656         nist_set_256(t_d, buf, 0, 0, 0, 0, 23-4, 22-4, 21-4, 20-4);
 657         if (bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
 658                 t_d, BN_NIST_256_TOP))
 659                 ++carry;
 660         /*S6*/
 661         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
 662         if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
 663                 ++carry;
 664         /*D1*/
 665         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
 666         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
 667                 --carry;
 668         /*D2*/
 669         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
 670         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
 671                 --carry;
 672         /*D3*/
 673         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
 674         if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
 675                 --carry;
 676
 677         if (carry)
 678                 {
 679                 if (carry > 0)
 680                         bn_sub_words(r_d, r_d, _384_data + BN_NIST_384_TOP *
 681                                 --carry, BN_NIST_384_TOP);
 682                 else
 683                         {
 684                         carry = -carry;
 685                         bn_add_words(r_d, r_d, _384_data + BN_NIST_384_TOP *
 686                                 --carry, BN_NIST_384_TOP);
 687                         }
 688                 }
 689
 690         r->top = BN_NIST_384_TOP;
 691         bn_correct_top(r);
 692         if (BN_ucmp(r, field) >= 0)
 693                 {
 694                 bn_sub_words(r_d, r_d, _nist_p_384, BN_NIST_384_TOP);
 695                 bn_correct_top(r);
 696                 }
 697         bn_check_top(r);
 698         return 1;
 699 #else
 700         return 0;
 701 #endif
 702         }
 703
 704 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 705         BN_CTX *ctx)
 706         {
 707 #if BN_BITS2 == 64
 708 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 709 #elif BN_BITS2 == 32
 710 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 711 #elif BN_BITS2 == 16
 712 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
 713 #elif BN_BITS2 == 8
 714 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1
 715 #endif
 716         int     top, ret = 0;
 717         BN_ULONG *r_d;
 718         BIGNUM  *tmp;
 719
 720         /* check whether a reduction is necessary */
 721         top = a->top;
 722         if (top < BN_NIST_521_TOP  || ( top == BN_NIST_521_TOP &&
 723            (!(a->d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))))
 724                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
 725
 726         BN_CTX_start(ctx);
 727         tmp = BN_CTX_get(ctx);
 728         if (!tmp)
 729                 goto err;
 730
 731         if (!bn_wexpand(tmp, BN_NIST_521_TOP))
 732                 goto err;
 733         nist_cp_bn(tmp->d, a->d, BN_NIST_521_TOP);
 734
 735         tmp->top = BN_NIST_521_TOP;
 736         tmp->d[BN_NIST_521_TOP-1]  &= BN_NIST_521_TOP_MASK;
 737         bn_correct_top(tmp);
 738
 739         if (!BN_rshift(r, a, 521))
 740                 goto err;
 741
 742         if (!BN_uadd(r, tmp, r))
 743                 goto err;
 744         top = r->top;
 745         r_d = r->d;
 746         if (top == BN_NIST_521_TOP  &&
 747            (r_d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))
 748                 {
 749                 BN_NIST_ADD_ONE(r_d)
 750                 r_d[BN_NIST_521_TOP-1] &= BN_NIST_521_TOP_MASK;
 751                 }
 752         bn_correct_top(r);
 753
 754         ret = 1;
 755 err:
 756         BN_CTX_end(ctx);
 757
 758         bn_check_top(r);
 759         return ret;
 760         }