1 /* 2 * Copyright 1995-2020 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 540