include/openssl/bn.h

   1 /*
   2  * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
   4  *
   5  * Licensed under the OpenSSL license (the "License").  You may not use
   6  * this file except in compliance with the License.  You can obtain a copy
   7  * in the file LICENSE in the source distribution or at
   8  * https://www.openssl.org/source/license.html
   9  */
  10
  11 #ifndef HEADER_BN_H
  12 # define HEADER_BN_H
  13
  14 # include <openssl/e_os2.h>
  15 # ifndef OPENSSL_NO_STDIO
  16 #  include <stdio.h>
  17 # endif
  18 # include <openssl/opensslconf.h>
  19 # include <openssl/ossl_typ.h>
  20 # include <openssl/crypto.h>
  21 # include <openssl/bnerr.h>
  22
  23 #ifdef  __cplusplus
  24 extern "C" {
  25 #endif
  26
  27 /*
  28  * 64-bit processor with LP64 ABI
  29  */
  30 # ifdef SIXTY_FOUR_BIT_LONG
  31 #  define BN_ULONG        unsigned long
  32 #  define BN_BYTES        8
  33 # endif
  34
  35 /*
  36  * 64-bit processor other than LP64 ABI
  37  */
  38 # ifdef SIXTY_FOUR_BIT
  39 #  define BN_ULONG        unsigned long long
  40 #  define BN_BYTES        8
  41 # endif
  42
  43 # ifdef THIRTY_TWO_BIT
  44 #  define BN_ULONG        unsigned int
  45 #  define BN_BYTES        4
  46 # endif
  47
  48 # define BN_BITS2       (BN_BYTES * 8)
  49 # define BN_BITS        (BN_BITS2 * 2)
  50 # define BN_TBIT        ((BN_ULONG)1 << (BN_BITS2 - 1))
  51
  52 # define BN_FLG_MALLOCED         0x01
  53 # define BN_FLG_STATIC_DATA      0x02
  54
  55 /*
  56  * avoid leaking exponent information through timing,
  57  * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
  58  * BN_div() will call BN_div_no_branch,
  59  * BN_mod_inverse() will call BN_mod_inverse_no_branch.
  60  */
  61 # define BN_FLG_CONSTTIME        0x04
  62 # define BN_FLG_SECURE           0x08
  63
  64 # if OPENSSL_API_COMPAT < 0x00908000L
  65 /* deprecated name for the flag */
  66 #  define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
  67 #  define BN_FLG_FREE            0x8000 /* used for debugging */
  68 # endif
  69
  70 void BN_set_flags(BIGNUM *b, int n);
  71 int BN_get_flags(const BIGNUM *b, int n);
  72
  73 /* Values for |top| in BN_rand() */
  74 #define BN_RAND_TOP_ANY    -1
  75 #define BN_RAND_TOP_ONE     0
  76 #define BN_RAND_TOP_TWO     1
  77
  78 /* Values for |bottom| in BN_rand() */
  79 #define BN_RAND_BOTTOM_ANY  0
  80 #define BN_RAND_BOTTOM_ODD  1
  81
  82 /*
  83  * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
  84  * two BIGNUMs cannot be used in parallel!). Also only for *read only* use. The
  85  * value |dest| should be a newly allocated BIGNUM obtained via BN_new() that
  86  * has not been otherwise initialised or used.
  87  */
  88 void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags);
  89
  90 /* Wrapper function to make using BN_GENCB easier */
  91 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
  92
  93 BN_GENCB *BN_GENCB_new(void);
  94 void BN_GENCB_free(BN_GENCB *cb);
  95
  96 /* Populate a BN_GENCB structure with an "old"-style callback */
  97 void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
  98                       void *cb_arg);
  99
 100 /* Populate a BN_GENCB structure with a "new"-style callback */
 101 void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
 102                   void *cb_arg);
 103
 104 void *BN_GENCB_get_arg(BN_GENCB *cb);
 105
 106 # define BN_prime_checks 0      /* default: select number of iterations based
 107                                  * on the size of the number */
 108
 109 /*
 110  * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations
 111  * that will be done for checking that a random number is probably prime. The
 112  * error rate for accepting a composite number as prime depends on the size of
 113  * the prime |b|. The error rates used are for calculating an RSA key with 2 primes,
 114  * and so the level is what you would expect for a key of double the size of the
 115  * prime.
 116  *
 117  * This table is generated using the algorithm of FIPS PUB 186-4
 118  * Digital Signature Standard (DSS), section F.1, page 117.
 119  * (https://dx.doi.org/10.6028/NIST.FIPS.186-4)
 120  *
 121  * The following magma script was used to generate the output:
 122  * securitybits:=125;
 123  * k:=1024;
 124  * for t:=1 to 65 do
 125  *   for M:=3 to Floor(2*Sqrt(k-1)-1) do
 126  *     S:=0;
 127  *     // Sum over m
 128  *     for m:=3 to M do
 129  *       s:=0;
 130  *       // Sum over j
 131  *       for j:=2 to m do
 132  *         s+:=(RealField(32)!2)^-(j+(k-1)/j);
 133  *       end for;
 134  *       S+:=2^(m-(m-1)*t)*s;
 135  *     end for;
 136  *     A:=2^(k-2-M*t);
 137  *     B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S;
 138  *     pkt:=2.00743*Log(2)*k*2^-k*(A+B);
 139  *     seclevel:=Floor(-Log(2,pkt));
 140  *     if seclevel ge securitybits then
 141  *       printf "k: %5o, security: %o bits  (t: %o, M: %o)\n",k,seclevel,t,M;
 142  *       break;
 143  *     end if;
 144  *   end for;
 145  *   if seclevel ge securitybits then break; end if;
 146  * end for;
 147  *
 148  * It can be run online at:
 149  * http://magma.maths.usyd.edu.au/calc
 150  *
 151  * And will output:
 152  * k:  1024, security: 129 bits  (t: 6, M: 23)
 153  *
 154  * k is the number of bits of the prime, securitybits is the level we want to
 155  * reach.
 156  *
 157  * prime length | RSA key size | # MR tests | security level
 158  * -------------+--------------|------------+---------------
 159  *  (b) >= 6394 |     >= 12788 |          3 |        256 bit
 160  *  (b) >= 3747 |     >=  7494 |          3 |        192 bit
 161  *  (b) >= 1345 |     >=  2690 |          4 |        128 bit
 162  *  (b) >= 1080 |     >=  2160 |          5 |        128 bit
 163  *  (b) >=  852 |     >=  1704 |          5 |        112 bit
 164  *  (b) >=  476 |     >=   952 |          5 |         80 bit
 165  *  (b) >=  400 |     >=   800 |          6 |         80 bit
 166  *  (b) >=  347 |     >=   694 |          7 |         80 bit
 167  *  (b) >=  308 |     >=   616 |          8 |         80 bit
 168  *  (b) >=   55 |     >=   110 |         27 |         64 bit
 169  *  (b) >=    6 |     >=    12 |         34 |         64 bit
 170  */
 171
 172 # define BN_prime_checks_for_size(b) ((b) >= 3747 ?  3 : \
 173                                 (b) >=  1345 ?  4 : \
 174                                 (b) >=  476 ?  5 : \
 175                                 (b) >=  400 ?  6 : \
 176                                 (b) >=  347 ?  7 : \
 177                                 (b) >=  308 ?  8 : \
 178                                 (b) >=  55  ? 27 : \
 179                                 /* b >= 6 */ 34)
 180
 181 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
 182
 183 int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w);
 184 int BN_is_zero(const BIGNUM *a);
 185 int BN_is_one(const BIGNUM *a);
 186 int BN_is_word(const BIGNUM *a, const BN_ULONG w);
 187 int BN_is_odd(const BIGNUM *a);
 188
 189 # define BN_one(a)       (BN_set_word((a),1))
 190
 191 void BN_zero_ex(BIGNUM *a);
 192
 193 # if OPENSSL_API_COMPAT >= 0x00908000L
 194 #  define BN_zero(a)      BN_zero_ex(a)
 195 # else
 196 #  define BN_zero(a)      (BN_set_word((a),0))
 197 # endif
 198
 199 const BIGNUM *BN_value_one(void);
 200 char *BN_options(void);
 201 BN_CTX *BN_CTX_new(void);
 202 BN_CTX *BN_CTX_secure_new(void);
 203 void BN_CTX_free(BN_CTX *c);
 204 void BN_CTX_start(BN_CTX *ctx);
 205 BIGNUM *BN_CTX_get(BN_CTX *ctx);
 206 void BN_CTX_end(BN_CTX *ctx);
 207 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
 208 int BN_priv_rand(BIGNUM *rnd, int bits, int top, int bottom);
 209 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
 210 int BN_priv_rand_range(BIGNUM *rnd, const BIGNUM *range);
 211 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
 212 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
 213 int BN_num_bits(const BIGNUM *a);
 214 int BN_num_bits_word(BN_ULONG l);
 215 int BN_security_bits(int L, int N);
 216 BIGNUM *BN_new(void);
 217 BIGNUM *BN_secure_new(void);
 218 void BN_clear_free(BIGNUM *a);
 219 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
 220 void BN_swap(BIGNUM *a, BIGNUM *b);
 221 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
 222 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
 223 int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen);
 224 BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret);
 225 int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen);
 226 BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
 227 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
 228 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 229 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 230 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 231 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 232 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
 233 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
 234 /** BN_set_negative sets sign of a BIGNUM
 235  * \param  b  pointer to the BIGNUM object
 236  * \param  n  0 if the BIGNUM b should be positive and a value != 0 otherwise
 237  */
 238 void BN_set_negative(BIGNUM *b, int n);
 239 /** BN_is_negative returns 1 if the BIGNUM is negative
 240  * \param  b  pointer to the BIGNUM object
 241  * \return 1 if a < 0 and 0 otherwise
 242  */
 243 int BN_is_negative(const BIGNUM *b);
 244
 245 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
 246            BN_CTX *ctx);
 247 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
 248 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
 249 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
 250                BN_CTX *ctx);
 251 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 252                      const BIGNUM *m);
 253 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
 254                BN_CTX *ctx);
 255 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 256                      const BIGNUM *m);
 257 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
 258                BN_CTX *ctx);
 259 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 260 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 261 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
 262 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
 263                   BN_CTX *ctx);
 264 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
 265
 266 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
 267 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
 268 int BN_mul_word(BIGNUM *a, BN_ULONG w);
 269 int BN_add_word(BIGNUM *a, BN_ULONG w);
 270 int BN_sub_word(BIGNUM *a, BN_ULONG w);
 271 int BN_set_word(BIGNUM *a, BN_ULONG w);
 272 BN_ULONG BN_get_word(const BIGNUM *a);
 273
 274 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
 275 void BN_free(BIGNUM *a);
 276 int BN_is_bit_set(const BIGNUM *a, int n);
 277 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
 278 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
 279 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 280
 281 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 282                const BIGNUM *m, BN_CTX *ctx);
 283 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 284                     const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
 285 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 286                               const BIGNUM *m, BN_CTX *ctx,
 287                               BN_MONT_CTX *in_mont);
 288 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
 289                          const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
 290 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
 291                      const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
 292                      BN_CTX *ctx, BN_MONT_CTX *m_ctx);
 293 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 294                       const BIGNUM *m, BN_CTX *ctx);
 295
 296 int BN_mask_bits(BIGNUM *a, int n);
 297 # ifndef OPENSSL_NO_STDIO
 298 int BN_print_fp(FILE *fp, const BIGNUM *a);
 299 # endif
 300 int BN_print(BIO *bio, const BIGNUM *a);
 301 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
 302 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
 303 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
 304 void BN_clear(BIGNUM *a);
 305 BIGNUM *BN_dup(const BIGNUM *a);
 306 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
 307 int BN_set_bit(BIGNUM *a, int n);
 308 int BN_clear_bit(BIGNUM *a, int n);
 309 char *BN_bn2hex(const BIGNUM *a);
 310 char *BN_bn2dec(const BIGNUM *a);
 311 int BN_hex2bn(BIGNUM **a, const char *str);
 312 int BN_dec2bn(BIGNUM **a, const char *str);
 313 int BN_asc2bn(BIGNUM **a, const char *str);
 314 int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
 315 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
 316                                                                   * -2 for
 317                                                                   * error */
 318 BIGNUM *BN_mod_inverse(BIGNUM *ret,
 319                        const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
 320 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
 321                     const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
 322
 323 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
 324
 325 /* Deprecated versions */
 326 DEPRECATEDIN_0_9_8(BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
 327                                              const BIGNUM *add,
 328                                              const BIGNUM *rem,
 329                                              void (*callback) (int, int,
 330                                                                void *),
 331                                              void *cb_arg))
 332 DEPRECATEDIN_0_9_8(int
 333                    BN_is_prime(const BIGNUM *p, int nchecks,
 334                                void (*callback) (int, int, void *),
 335                                BN_CTX *ctx, void *cb_arg))
 336 DEPRECATEDIN_0_9_8(int
 337                    BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
 338                                         void (*callback) (int, int, void *),
 339                                         BN_CTX *ctx, void *cb_arg,
 340                                         int do_trial_division))
 341
 342 /* Newer versions */
 343 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
 344                          const BIGNUM *rem, BN_GENCB *cb);
 345 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
 346 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
 347                             int do_trial_division, BN_GENCB *cb);
 348
 349 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
 350
 351 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
 352                             const BIGNUM *Xp, const BIGNUM *Xp1,
 353                             const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
 354                             BN_GENCB *cb);
 355 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
 356                               BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
 357                               BN_CTX *ctx, BN_GENCB *cb);
 358
 359 BN_MONT_CTX *BN_MONT_CTX_new(void);
 360 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 361                           BN_MONT_CTX *mont, BN_CTX *ctx);
 362 int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
 363                      BN_CTX *ctx);
 364 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
 365                        BN_CTX *ctx);
 366 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
 367 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
 368 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
 369 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
 370                                     const BIGNUM *mod, BN_CTX *ctx);
 371
 372 /* BN_BLINDING flags */
 373 # define BN_BLINDING_NO_UPDATE   0x00000001
 374 # define BN_BLINDING_NO_RECREATE 0x00000002
 375
 376 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
 377 void BN_BLINDING_free(BN_BLINDING *b);
 378 int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
 379 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
 380 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
 381 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
 382 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
 383                           BN_CTX *);
 384
 385 int BN_BLINDING_is_current_thread(BN_BLINDING *b);
 386 void BN_BLINDING_set_current_thread(BN_BLINDING *b);
 387 int BN_BLINDING_lock(BN_BLINDING *b);
 388 int BN_BLINDING_unlock(BN_BLINDING *b);
 389
 390 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
 391 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
 392 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
 393                                       const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
 394                                       int (*bn_mod_exp) (BIGNUM *r,
 395                                                          const BIGNUM *a,
 396                                                          const BIGNUM *p,
 397                                                          const BIGNUM *m,
 398                                                          BN_CTX *ctx,
 399                                                          BN_MONT_CTX *m_ctx),
 400                                       BN_MONT_CTX *m_ctx);
 401
 402 DEPRECATEDIN_0_9_8(void BN_set_params(int mul, int high, int low, int mont))
 403 DEPRECATEDIN_0_9_8(int BN_get_params(int which)) /* 0, mul, 1 high, 2 low, 3
 404                                                   * mont */
 405
 406 BN_RECP_CTX *BN_RECP_CTX_new(void);
 407 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
 408 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
 409 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
 410                           BN_RECP_CTX *recp, BN_CTX *ctx);
 411 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 412                     const BIGNUM *m, BN_CTX *ctx);
 413 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
 414                 BN_RECP_CTX *recp, BN_CTX *ctx);
 415
 416 # ifndef OPENSSL_NO_EC2M
 417
 418 /*
 419  * Functions for arithmetic over binary polynomials represented by BIGNUMs.
 420  * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
 421  * ignored. Note that input arguments are not const so that their bit arrays
 422  * can be expanded to the appropriate size if needed.
 423  */
 424
 425 /*
 426  * r = a + b
 427  */
 428 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 429 #  define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
 430 /*
 431  * r=a mod p
 432  */
 433 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
 434 /* r = (a * b) mod p */
 435 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 436                     const BIGNUM *p, BN_CTX *ctx);
 437 /* r = (a * a) mod p */
 438 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 439 /* r = (1 / b) mod p */
 440 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
 441 /* r = (a / b) mod p */
 442 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 443                     const BIGNUM *p, BN_CTX *ctx);
 444 /* r = (a ^ b) mod p */
 445 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 446                     const BIGNUM *p, BN_CTX *ctx);
 447 /* r = sqrt(a) mod p */
 448 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 449                      BN_CTX *ctx);
 450 /* r^2 + r = a mod p */
 451 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 452                            BN_CTX *ctx);
 453 #  define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
 454 /*-
 455  * Some functions allow for representation of the irreducible polynomials
 456  * as an unsigned int[], say p.  The irreducible f(t) is then of the form:
 457  *     t^p[0] + t^p[1] + ... + t^p[k]
 458  * where m = p[0] > p[1] > ... > p[k] = 0.
 459  */
 460 /* r = a mod p */
 461 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
 462 /* r = (a * b) mod p */
 463 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 464                         const int p[], BN_CTX *ctx);
 465 /* r = (a * a) mod p */
 466 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
 467                         BN_CTX *ctx);
 468 /* r = (1 / b) mod p */
 469 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
 470                         BN_CTX *ctx);
 471 /* r = (a / b) mod p */
 472 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 473                         const int p[], BN_CTX *ctx);
 474 /* r = (a ^ b) mod p */
 475 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
 476                         const int p[], BN_CTX *ctx);
 477 /* r = sqrt(a) mod p */
 478 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
 479                          const int p[], BN_CTX *ctx);
 480 /* r^2 + r = a mod p */
 481 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
 482                                const int p[], BN_CTX *ctx);
 483 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
 484 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
 485
 486 # endif
 487
 488 /*
 489  * faster mod functions for the 'NIST primes' 0 <= a < p^2
 490  */
 491 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 492 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 493 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 494 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 495 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
 496
 497 const BIGNUM *BN_get0_nist_prime_192(void);
 498 const BIGNUM *BN_get0_nist_prime_224(void);
 499 const BIGNUM *BN_get0_nist_prime_256(void);
 500 const BIGNUM *BN_get0_nist_prime_384(void);
 501 const BIGNUM *BN_get0_nist_prime_521(void);
 502
 503 int (*BN_nist_mod_func(const BIGNUM *p)) (BIGNUM *r, const BIGNUM *a,
 504                                           const BIGNUM *field, BN_CTX *ctx);
 505
 506 int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
 507                           const BIGNUM *priv, const unsigned char *message,
 508                           size_t message_len, BN_CTX *ctx);
 509
 510 /* Primes from RFC 2409 */
 511 BIGNUM *BN_get_rfc2409_prime_768(BIGNUM *bn);
 512 BIGNUM *BN_get_rfc2409_prime_1024(BIGNUM *bn);
 513
 514 /* Primes from RFC 3526 */
 515 BIGNUM *BN_get_rfc3526_prime_1536(BIGNUM *bn);
 516 BIGNUM *BN_get_rfc3526_prime_2048(BIGNUM *bn);
 517 BIGNUM *BN_get_rfc3526_prime_3072(BIGNUM *bn);
 518 BIGNUM *BN_get_rfc3526_prime_4096(BIGNUM *bn);
 519 BIGNUM *BN_get_rfc3526_prime_6144(BIGNUM *bn);
 520 BIGNUM *BN_get_rfc3526_prime_8192(BIGNUM *bn);
 521
 522 # if OPENSSL_API_COMPAT < 0x10100000L
 523 #  define get_rfc2409_prime_768 BN_get_rfc2409_prime_768
 524 #  define get_rfc2409_prime_1024 BN_get_rfc2409_prime_1024
 525 #  define get_rfc3526_prime_1536 BN_get_rfc3526_prime_1536
 526 #  define get_rfc3526_prime_2048 BN_get_rfc3526_prime_2048
 527 #  define get_rfc3526_prime_3072 BN_get_rfc3526_prime_3072
 528 #  define get_rfc3526_prime_4096 BN_get_rfc3526_prime_4096
 529 #  define get_rfc3526_prime_6144 BN_get_rfc3526_prime_6144
 530 #  define get_rfc3526_prime_8192 BN_get_rfc3526_prime_8192
 531 # endif
 532
 533 int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
 534
 535
 536 # ifdef  __cplusplus
 537 }
 538 # endif
 539 #endif