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Edit File : bn.h \| Size : 21.62 KB
/* * Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html / #ifndef HEADER_BN_H # define HEADER_BN_H # include <openssl/e_os2.h> # ifndef OPENSSL_NO_STDIO # include <stdio.h> # endif # include <openssl/opensslconf.h> # include <openssl/ossl_typ.h> # include <openssl/crypto.h> # include <openssl/bnerr.h> #ifdef __cplusplus extern "C" { #endif / * 64-bit processor with LP64 ABI / # ifdef SIXTY_FOUR_BIT_LONG # define BN_ULONG unsigned long # define BN_BYTES 8 # endif / * 64-bit processor other than LP64 ABI / # ifdef SIXTY_FOUR_BIT # define BN_ULONG unsigned long long # define BN_BYTES 8 # endif # ifdef THIRTY_TWO_BIT # define BN_ULONG unsigned int # define BN_BYTES 4 # endif # define BN_BITS2 (BN_BYTES 8) # define BN_BITS (BN_BITS2 * 2) # define BN_TBIT ((BN_ULONG)1 << (BN_BITS2 - 1)) # define BN_FLG_MALLOCED 0x01 # define BN_FLG_STATIC_DATA 0x02 /* * avoid leaking exponent information through timing, * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime, * BN_div() will call BN_div_no_branch, * BN_mod_inverse() will call bn_mod_inverse_no_branch. / # define BN_FLG_CONSTTIME 0x04 # define BN_FLG_SECURE 0x08 # if OPENSSL_API_COMPAT < 0x00908000L / deprecated name for the flag / # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME # define BN_FLG_FREE 0x8000 / used for debugging / # endif void BN_set_flags(BIGNUM b, int n); int BN_get_flags(const BIGNUM b, int n); / Values for \|top\| in BN_rand() / #define BN_RAND_TOP_ANY -1 #define BN_RAND_TOP_ONE 0 #define BN_RAND_TOP_TWO 1 / Values for \|bottom\| in BN_rand() / #define BN_RAND_BOTTOM_ANY 0 #define BN_RAND_BOTTOM_ODD 1 / * get a clone of a BIGNUM with changed flags, for temporary use only (the * two BIGNUMs cannot be used in parallel!). Also only for read only use. The * value \|dest\| should be a newly allocated BIGNUM obtained via BN_new() that * has not been otherwise initialised or used. / void BN_with_flags(BIGNUM dest, const BIGNUM b, int flags); / Wrapper function to make using BN_GENCB easier / int BN_GENCB_call(BN_GENCB cb, int a, int b); BN_GENCB BN_GENCB_new(void); void BN_GENCB_free(BN_GENCB cb); /* Populate a BN_GENCB structure with an "old"-style callback / void BN_GENCB_set_old(BN_GENCB gencb, void (callback) (int, int, void ), void cb_arg); / Populate a BN_GENCB structure with a "new"-style callback / void BN_GENCB_set(BN_GENCB gencb, int (callback) (int, int, BN_GENCB ), void cb_arg); void BN_GENCB_get_arg(BN_GENCB cb); # define BN_prime_checks 0 / default: select number of iterations based * on the size of the number / / * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations * that will be done for checking that a random number is probably prime. The * error rate for accepting a composite number as prime depends on the size of * the prime \|b\|. The error rates used are for calculating an RSA key with 2 primes, * and so the level is what you would expect for a key of double the size of the * prime. * * This table is generated using the algorithm of FIPS PUB 186-4 * Digital Signature Standard (DSS), section F.1, page 117. * (https://dx.doi.org/10.6028/NIST.FIPS.186-4) * * The following magma script was used to generate the output: * securitybits:=125; * k:=1024; * for t:=1 to 65 do * for M:=3 to Floor(2Sqrt(k-1)-1) do S:=0; * // Sum over m * for m:=3 to M do * s:=0; * // Sum over j * for j:=2 to m do * s+:=(RealField(32)!2)^-(j+(k-1)/j); * end for; * S+:=2^(m-(m-1)t)s; * end for; * A:=2^(k-2-Mt); B:=8(Pi(RealField(32))^2-6)/32^(k-2)S; pkt:=2.00743Log(2)k2^-k(A+B); * seclevel:=Floor(-Log(2,pkt)); * if seclevel ge securitybits then * printf "k: %5o, security: %o bits (t: %o, M: %o)\n",k,seclevel,t,M; * break; * end if; * end for; * if seclevel ge securitybits then break; end if; * end for; * * It can be run online at: * http://magma.maths.usyd.edu.au/calc * * And will output: * k: 1024, security: 129 bits (t: 6, M: 23) * * k is the number of bits of the prime, securitybits is the level we want to * reach. * * prime length \| RSA key size \| # MR tests \| security level * -------------+--------------\|------------+--------------- * (b) >= 6394 \| >= 12788 \| 3 \| 256 bit * (b) >= 3747 \| >= 7494 \| 3 \| 192 bit * (b) >= 1345 \| >= 2690 \| 4 \| 128 bit * (b) >= 1080 \| >= 2160 \| 5 \| 128 bit * (b) >= 852 \| >= 1704 \| 5 \| 112 bit * (b) >= 476 \| >= 952 \| 5 \| 80 bit * (b) >= 400 \| >= 800 \| 6 \| 80 bit * (b) >= 347 \| >= 694 \| 7 \| 80 bit * (b) >= 308 \| >= 616 \| 8 \| 80 bit * (b) >= 55 \| >= 110 \| 27 \| 64 bit * (b) >= 6 \| >= 12 \| 34 \| 64 bit / # define BN_prime_checks_for_size(b) ((b) >= 3747 ? 3 : \ (b) >= 1345 ? 4 : \ (b) >= 476 ? 5 : \ (b) >= 400 ? 6 : \ (b) >= 347 ? 7 : \ (b) >= 308 ? 8 : \ (b) >= 55 ? 27 : \ / b >= 6 / 34) # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8) int BN_abs_is_word(const BIGNUM a, const BN_ULONG w); int BN_is_zero(const BIGNUM a); int BN_is_one(const BIGNUM a); int BN_is_word(const BIGNUM a, const BN_ULONG w); int BN_is_odd(const BIGNUM a); # define BN_one(a) (BN_set_word((a),1)) void BN_zero_ex(BIGNUM a); # if OPENSSL_API_COMPAT >= 0x00908000L # define BN_zero(a) BN_zero_ex(a) # else # define BN_zero(a) (BN_set_word((a),0)) # endif const BIGNUM BN_value_one(void); char BN_options(void); BN_CTX BN_CTX_new(void); BN_CTX BN_CTX_secure_new(void); void BN_CTX_free(BN_CTX c); void BN_CTX_start(BN_CTX ctx); BIGNUM BN_CTX_get(BN_CTX ctx); void BN_CTX_end(BN_CTX ctx); int BN_rand(BIGNUM rnd, int bits, int top, int bottom); int BN_priv_rand(BIGNUM rnd, int bits, int top, int bottom); int BN_rand_range(BIGNUM rnd, const BIGNUM range); int BN_priv_rand_range(BIGNUM rnd, const BIGNUM range); int BN_pseudo_rand(BIGNUM rnd, int bits, int top, int bottom); int BN_pseudo_rand_range(BIGNUM rnd, const BIGNUM range); int BN_num_bits(const BIGNUM a); int BN_num_bits_word(BN_ULONG l); int BN_security_bits(int L, int N); BIGNUM BN_new(void); BIGNUM BN_secure_new(void); void BN_clear_free(BIGNUM a); BIGNUM BN_copy(BIGNUM a, const BIGNUM b); void BN_swap(BIGNUM a, BIGNUM b); BIGNUM BN_bin2bn(const unsigned char s, int len, BIGNUM ret); int BN_bn2bin(const BIGNUM a, unsigned char to); int BN_bn2binpad(const BIGNUM a, unsigned char to, int tolen); BIGNUM BN_lebin2bn(const unsigned char s, int len, BIGNUM ret); int BN_bn2lebinpad(const BIGNUM a, unsigned char to, int tolen); BIGNUM BN_mpi2bn(const unsigned char s, int len, BIGNUM ret); int BN_bn2mpi(const BIGNUM a, unsigned char to); int BN_sub(BIGNUM r, const BIGNUM a, const BIGNUM b); int BN_usub(BIGNUM r, const BIGNUM a, const BIGNUM b); int BN_uadd(BIGNUM r, const BIGNUM a, const BIGNUM b); int BN_add(BIGNUM r, const BIGNUM a, const BIGNUM b); int BN_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, BN_CTX ctx); int BN_sqr(BIGNUM r, const BIGNUM a, BN_CTX ctx); /** BN_set_negative sets sign of a BIGNUM * \param b pointer to the BIGNUM object * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise / void BN_set_negative(BIGNUM b, int n); /** BN_is_negative returns 1 if the BIGNUM is negative * \param b pointer to the BIGNUM object * \return 1 if a < 0 and 0 otherwise / int BN_is_negative(const BIGNUM b); int BN_div(BIGNUM dv, BIGNUM rem, const BIGNUM m, const BIGNUM d, BN_CTX ctx); # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx)) int BN_nnmod(BIGNUM r, const BIGNUM m, const BIGNUM d, BN_CTX ctx); int BN_mod_add(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m, BN_CTX ctx); int BN_mod_add_quick(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m); int BN_mod_sub(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m, BN_CTX ctx); int BN_mod_sub_quick(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m); int BN_mod_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM m, BN_CTX ctx); int BN_mod_sqr(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx); int BN_mod_lshift1(BIGNUM r, const BIGNUM a, const BIGNUM m, BN_CTX ctx); int BN_mod_lshift1_quick(BIGNUM r, const BIGNUM a, const BIGNUM m); int BN_mod_lshift(BIGNUM r, const BIGNUM a, int n, const BIGNUM m, BN_CTX ctx); int BN_mod_lshift_quick(BIGNUM r, const BIGNUM a, int n, const BIGNUM m); BN_ULONG BN_mod_word(const BIGNUM a, BN_ULONG w); BN_ULONG BN_div_word(BIGNUM a, BN_ULONG w); int BN_mul_word(BIGNUM a, BN_ULONG w); int BN_add_word(BIGNUM a, BN_ULONG w); int BN_sub_word(BIGNUM a, BN_ULONG w); int BN_set_word(BIGNUM a, BN_ULONG w); BN_ULONG BN_get_word(const BIGNUM a); int BN_cmp(const BIGNUM a, const BIGNUM b); void BN_free(BIGNUM a); int BN_is_bit_set(const BIGNUM a, int n); int BN_lshift(BIGNUM r, const BIGNUM a, int n); int BN_lshift1(BIGNUM r, const BIGNUM a); int BN_exp(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); int BN_mod_exp(BIGNUM r, const BIGNUM a, const BIGNUM p, const BIGNUM m, BN_CTX ctx); int BN_mod_exp_mont(BIGNUM r, const BIGNUM a, const BIGNUM p, const BIGNUM m, BN_CTX ctx, BN_MONT_CTX m_ctx); int BN_mod_exp_mont_consttime(BIGNUM rr, const BIGNUM a, const BIGNUM p, const BIGNUM m, BN_CTX ctx, BN_MONT_CTX in_mont); int BN_mod_exp_mont_word(BIGNUM r, BN_ULONG a, const BIGNUM p, const BIGNUM m, BN_CTX ctx, BN_MONT_CTX m_ctx); int BN_mod_exp2_mont(BIGNUM r, const BIGNUM a1, const BIGNUM p1, const BIGNUM a2, const BIGNUM p2, const BIGNUM m, BN_CTX ctx, BN_MONT_CTX m_ctx); int BN_mod_exp_simple(BIGNUM r, const BIGNUM a, const BIGNUM p, const BIGNUM m, BN_CTX ctx); int BN_mask_bits(BIGNUM a, int n); # ifndef OPENSSL_NO_STDIO int BN_print_fp(FILE fp, const BIGNUM a); # endif int BN_print(BIO bio, const BIGNUM a); int BN_reciprocal(BIGNUM r, const BIGNUM m, int len, BN_CTX ctx); int BN_rshift(BIGNUM r, const BIGNUM a, int n); int BN_rshift1(BIGNUM r, const BIGNUM a); void BN_clear(BIGNUM a); BIGNUM BN_dup(const BIGNUM a); int BN_ucmp(const BIGNUM a, const BIGNUM b); int BN_set_bit(BIGNUM a, int n); int BN_clear_bit(BIGNUM a, int n); char BN_bn2hex(const BIGNUM a); char BN_bn2dec(const BIGNUM a); int BN_hex2bn(BIGNUM a, const char str); int BN_dec2bn(BIGNUM *a, const char str); int BN_asc2bn(BIGNUM *a, const char str); int BN_gcd(BIGNUM r, const BIGNUM a, const BIGNUM b, BN_CTX ctx); int BN_kronecker(const BIGNUM a, const BIGNUM b, BN_CTX ctx); / returns * -2 for * error / BIGNUM BN_mod_inverse(BIGNUM ret, const BIGNUM a, const BIGNUM n, BN_CTX ctx); BIGNUM BN_mod_sqrt(BIGNUM ret, const BIGNUM a, const BIGNUM n, BN_CTX ctx); void BN_consttime_swap(BN_ULONG swap, BIGNUM a, BIGNUM b, int nwords); / Deprecated versions / DEPRECATEDIN_0_9_8(BIGNUM BN_generate_prime(BIGNUM ret, int bits, int safe, const BIGNUM add, const BIGNUM rem, void (callback) (int, int, void ), void cb_arg)) DEPRECATEDIN_0_9_8(int BN_is_prime(const BIGNUM p, int nchecks, void (callback) (int, int, void ), BN_CTX ctx, void cb_arg)) DEPRECATEDIN_0_9_8(int BN_is_prime_fasttest(const BIGNUM p, int nchecks, void (callback) (int, int, void ), BN_CTX ctx, void cb_arg, int do_trial_division)) /* Newer versions / int BN_generate_prime_ex(BIGNUM ret, int bits, int safe, const BIGNUM add, const BIGNUM rem, BN_GENCB cb); int BN_is_prime_ex(const BIGNUM p, int nchecks, BN_CTX ctx, BN_GENCB cb); int BN_is_prime_fasttest_ex(const BIGNUM p, int nchecks, BN_CTX ctx, int do_trial_division, BN_GENCB cb); int BN_X931_generate_Xpq(BIGNUM Xp, BIGNUM Xq, int nbits, BN_CTX ctx); int BN_X931_derive_prime_ex(BIGNUM p, BIGNUM p1, BIGNUM p2, const BIGNUM Xp, const BIGNUM Xp1, const BIGNUM Xp2, const BIGNUM e, BN_CTX ctx, BN_GENCB cb); int BN_X931_generate_prime_ex(BIGNUM p, BIGNUM p1, BIGNUM p2, BIGNUM Xp1, BIGNUM Xp2, const BIGNUM Xp, const BIGNUM e, BN_CTX ctx, BN_GENCB cb); BN_MONT_CTX BN_MONT_CTX_new(void); int BN_mod_mul_montgomery(BIGNUM r, const BIGNUM a, const BIGNUM b, BN_MONT_CTX mont, BN_CTX ctx); int BN_to_montgomery(BIGNUM r, const BIGNUM a, BN_MONT_CTX mont, BN_CTX ctx); int BN_from_montgomery(BIGNUM r, const BIGNUM a, BN_MONT_CTX mont, BN_CTX ctx); void BN_MONT_CTX_free(BN_MONT_CTX mont); int BN_MONT_CTX_set(BN_MONT_CTX mont, const BIGNUM mod, BN_CTX ctx); BN_MONT_CTX BN_MONT_CTX_copy(BN_MONT_CTX to, BN_MONT_CTX from); BN_MONT_CTX BN_MONT_CTX_set_locked(BN_MONT_CTX *pmont, CRYPTO_RWLOCK lock, const BIGNUM mod, BN_CTX ctx); /* BN_BLINDING flags / # define BN_BLINDING_NO_UPDATE 0x00000001 # define BN_BLINDING_NO_RECREATE 0x00000002 BN_BLINDING BN_BLINDING_new(const BIGNUM A, const BIGNUM Ai, BIGNUM mod); void BN_BLINDING_free(BN_BLINDING b); int BN_BLINDING_update(BN_BLINDING b, BN_CTX ctx); int BN_BLINDING_convert(BIGNUM n, BN_BLINDING b, BN_CTX ctx); int BN_BLINDING_invert(BIGNUM n, BN_BLINDING b, BN_CTX ctx); int BN_BLINDING_convert_ex(BIGNUM n, BIGNUM r, BN_BLINDING b, BN_CTX ); int BN_BLINDING_invert_ex(BIGNUM n, const BIGNUM r, BN_BLINDING b, BN_CTX ); int BN_BLINDING_is_current_thread(BN_BLINDING b); void BN_BLINDING_set_current_thread(BN_BLINDING b); int BN_BLINDING_lock(BN_BLINDING b); int BN_BLINDING_unlock(BN_BLINDING b); unsigned long BN_BLINDING_get_flags(const BN_BLINDING ); void BN_BLINDING_set_flags(BN_BLINDING , unsigned long); BN_BLINDING BN_BLINDING_create_param(BN_BLINDING b, const BIGNUM e, BIGNUM m, BN_CTX ctx, int (bn_mod_exp) (BIGNUM r, const BIGNUM a, const BIGNUM p, const BIGNUM m, BN_CTX ctx, BN_MONT_CTX m_ctx), BN_MONT_CTX m_ctx); DEPRECATEDIN_0_9_8(void BN_set_params(int mul, int high, int low, int mont)) DEPRECATEDIN_0_9_8(int BN_get_params(int which)) / 0, mul, 1 high, 2 low, 3 * mont / BN_RECP_CTX BN_RECP_CTX_new(void); void BN_RECP_CTX_free(BN_RECP_CTX recp); int BN_RECP_CTX_set(BN_RECP_CTX recp, const BIGNUM rdiv, BN_CTX ctx); int BN_mod_mul_reciprocal(BIGNUM r, const BIGNUM x, const BIGNUM y, BN_RECP_CTX recp, BN_CTX ctx); int BN_mod_exp_recp(BIGNUM r, const BIGNUM a, const BIGNUM p, const BIGNUM m, BN_CTX ctx); int BN_div_recp(BIGNUM dv, BIGNUM rem, const BIGNUM m, BN_RECP_CTX recp, BN_CTX ctx); # ifndef OPENSSL_NO_EC2M / * Functions for arithmetic over binary polynomials represented by BIGNUMs. * The BIGNUM::neg property of BIGNUMs representing binary polynomials is * ignored. Note that input arguments are not const so that their bit arrays * can be expanded to the appropriate size if needed. / / * r = a + b / int BN_GF2m_add(BIGNUM r, const BIGNUM a, const BIGNUM b); # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b) /* * r=a mod p / int BN_GF2m_mod(BIGNUM r, const BIGNUM a, const BIGNUM p); /* r = (a * b) mod p / int BN_GF2m_mod_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM p, BN_CTX ctx); /* r = (a * a) mod p / int BN_GF2m_mod_sqr(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); / r = (1 / b) mod p / int BN_GF2m_mod_inv(BIGNUM r, const BIGNUM b, const BIGNUM p, BN_CTX ctx); / r = (a / b) mod p / int BN_GF2m_mod_div(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM p, BN_CTX ctx); /* r = (a ^ b) mod p / int BN_GF2m_mod_exp(BIGNUM r, const BIGNUM a, const BIGNUM b, const BIGNUM p, BN_CTX ctx); /* r = sqrt(a) mod p / int BN_GF2m_mod_sqrt(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); / r^2 + r = a mod p / int BN_GF2m_mod_solve_quad(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b)) /- * Some functions allow for representation of the irreducible polynomials * as an unsigned int[], say p. The irreducible f(t) is then of the form: * t^p[0] + t^p[1] + ... + t^p[k] * where m = p[0] > p[1] > ... > p[k] = 0. / / r = a mod p / int BN_GF2m_mod_arr(BIGNUM r, const BIGNUM a, const int p[]); / r = (a * b) mod p / int BN_GF2m_mod_mul_arr(BIGNUM r, const BIGNUM a, const BIGNUM b, const int p[], BN_CTX ctx); / r = (a * a) mod p / int BN_GF2m_mod_sqr_arr(BIGNUM r, const BIGNUM a, const int p[], BN_CTX ctx); /* r = (1 / b) mod p / int BN_GF2m_mod_inv_arr(BIGNUM r, const BIGNUM b, const int p[], BN_CTX ctx); /* r = (a / b) mod p / int BN_GF2m_mod_div_arr(BIGNUM r, const BIGNUM a, const BIGNUM b, const int p[], BN_CTX ctx); / r = (a ^ b) mod p / int BN_GF2m_mod_exp_arr(BIGNUM r, const BIGNUM a, const BIGNUM b, const int p[], BN_CTX ctx); / r = sqrt(a) mod p / int BN_GF2m_mod_sqrt_arr(BIGNUM r, const BIGNUM a, const int p[], BN_CTX ctx); /* r^2 + r = a mod p / int BN_GF2m_mod_solve_quad_arr(BIGNUM r, const BIGNUM a, const int p[], BN_CTX ctx); int BN_GF2m_poly2arr(const BIGNUM a, int p[], int max); int BN_GF2m_arr2poly(const int p[], BIGNUM a); # endif /* * faster mod functions for the 'NIST primes' 0 <= a < p^2 / int BN_nist_mod_192(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); int BN_nist_mod_224(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); int BN_nist_mod_256(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); int BN_nist_mod_384(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); int BN_nist_mod_521(BIGNUM r, const BIGNUM a, const BIGNUM p, BN_CTX ctx); const BIGNUM BN_get0_nist_prime_192(void); const BIGNUM BN_get0_nist_prime_224(void); const BIGNUM BN_get0_nist_prime_256(void); const BIGNUM BN_get0_nist_prime_384(void); const BIGNUM BN_get0_nist_prime_521(void); int (BN_nist_mod_func(const BIGNUM p)) (BIGNUM r, const BIGNUM a, const BIGNUM field, BN_CTX ctx); int BN_generate_dsa_nonce(BIGNUM out, const BIGNUM range, const BIGNUM priv, const unsigned char message, size_t message_len, BN_CTX ctx); / Primes from RFC 2409 / BIGNUM BN_get_rfc2409_prime_768(BIGNUM bn); BIGNUM BN_get_rfc2409_prime_1024(BIGNUM bn); / Primes from RFC 3526 / BIGNUM BN_get_rfc3526_prime_1536(BIGNUM bn); BIGNUM BN_get_rfc3526_prime_2048(BIGNUM bn); BIGNUM BN_get_rfc3526_prime_3072(BIGNUM bn); BIGNUM BN_get_rfc3526_prime_4096(BIGNUM bn); BIGNUM BN_get_rfc3526_prime_6144(BIGNUM bn); BIGNUM BN_get_rfc3526_prime_8192(BIGNUM bn); # if OPENSSL_API_COMPAT < 0x10100000L # define get_rfc2409_prime_768 BN_get_rfc2409_prime_768 # define get_rfc2409_prime_1024 BN_get_rfc2409_prime_1024 # define get_rfc3526_prime_1536 BN_get_rfc3526_prime_1536 # define get_rfc3526_prime_2048 BN_get_rfc3526_prime_2048 # define get_rfc3526_prime_3072 BN_get_rfc3526_prime_3072 # define get_rfc3526_prime_4096 BN_get_rfc3526_prime_4096 # define get_rfc3526_prime_6144 BN_get_rfc3526_prime_6144 # define get_rfc3526_prime_8192 BN_get_rfc3526_prime_8192 # endif int BN_bntest_rand(BIGNUM rnd, int bits, int top, int bottom); # ifdef __cplusplus } # endif #endif Back

Edit File : bn.h | Size : 21.62 KB

/*
 * Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved.
 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
 *
 * Licensed under the OpenSSL license (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

#ifndef HEADER_BN_H
# define HEADER_BN_H

# include <openssl/e_os2.h>
# ifndef OPENSSL_NO_STDIO
#  include <stdio.h>
# endif
# include <openssl/opensslconf.h>
# include <openssl/ossl_typ.h>
# include <openssl/crypto.h>
# include <openssl/bnerr.h>

#ifdef  __cplusplus
extern "C" {
#endif

/*
 * 64-bit processor with LP64 ABI
 */
# ifdef SIXTY_FOUR_BIT_LONG
#  define BN_ULONG        unsigned long
#  define BN_BYTES        8
# endif

/*
 * 64-bit processor other than LP64 ABI
 */
# ifdef SIXTY_FOUR_BIT
#  define BN_ULONG        unsigned long long
#  define BN_BYTES        8
# endif

# ifdef THIRTY_TWO_BIT
#  define BN_ULONG        unsigned int
#  define BN_BYTES        4
# endif

# define BN_BITS2       (BN_BYTES * 8)
# define BN_BITS        (BN_BITS2 * 2)
# define BN_TBIT        ((BN_ULONG)1 << (BN_BITS2 - 1))

# define BN_FLG_MALLOCED         0x01
# define BN_FLG_STATIC_DATA      0x02

/*
 * avoid leaking exponent information through timing,
 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
 * BN_div() will call BN_div_no_branch,
 * BN_mod_inverse() will call bn_mod_inverse_no_branch.
 */
# define BN_FLG_CONSTTIME        0x04
# define BN_FLG_SECURE           0x08

# if OPENSSL_API_COMPAT < 0x00908000L
/* deprecated name for the flag */
#  define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
#  define BN_FLG_FREE            0x8000 /* used for debugging */
# endif

void BN_set_flags(BIGNUM *b, int n);
int BN_get_flags(const BIGNUM *b, int n);

/* Values for |top| in BN_rand() */
#define BN_RAND_TOP_ANY    -1
#define BN_RAND_TOP_ONE     0
#define BN_RAND_TOP_TWO     1

/* Values for |bottom| in BN_rand() */
#define BN_RAND_BOTTOM_ANY  0
#define BN_RAND_BOTTOM_ODD  1

/*
 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
 * two BIGNUMs cannot be used in parallel!). Also only for *read only* use. The
 * value |dest| should be a newly allocated BIGNUM obtained via BN_new() that
 * has not been otherwise initialised or used.
 */
void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags);

/* Wrapper function to make using BN_GENCB easier */
int BN_GENCB_call(BN_GENCB *cb, int a, int b);

BN_GENCB *BN_GENCB_new(void);
void BN_GENCB_free(BN_GENCB *cb);

/* Populate a BN_GENCB structure with an "old"-style callback */
void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
                      void *cb_arg);

/* Populate a BN_GENCB structure with a "new"-style callback */
void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
                  void *cb_arg);

void *BN_GENCB_get_arg(BN_GENCB *cb);

# define BN_prime_checks 0      /* default: select number of iterations based
                                 * on the size of the number */

/*
 * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations
 * that will be done for checking that a random number is probably prime. The
 * error rate for accepting a composite number as prime depends on the size of
 * the prime |b|. The error rates used are for calculating an RSA key with 2 primes,
 * and so the level is what you would expect for a key of double the size of the
 * prime.
 *
 * This table is generated using the algorithm of FIPS PUB 186-4
 * Digital Signature Standard (DSS), section F.1, page 117.
 * (https://dx.doi.org/10.6028/NIST.FIPS.186-4)
 *
 * The following magma script was used to generate the output:
 * securitybits:=125;
 * k:=1024;
 * for t:=1 to 65 do
 *   for M:=3 to Floor(2*Sqrt(k-1)-1) do
 *     S:=0;
 *     // Sum over m
 *     for m:=3 to M do
 *       s:=0;
 *       // Sum over j
 *       for j:=2 to m do
 *         s+:=(RealField(32)!2)^-(j+(k-1)/j);
 *       end for;
 *       S+:=2^(m-(m-1)*t)*s;
 *     end for;
 *     A:=2^(k-2-M*t);
 *     B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S;
 *     pkt:=2.00743*Log(2)*k*2^-k*(A+B);
 *     seclevel:=Floor(-Log(2,pkt));
 *     if seclevel ge securitybits then
 *       printf "k: %5o, security: %o bits  (t: %o, M: %o)\n",k,seclevel,t,M;
 *       break;
 *     end if;
 *   end for;
 *   if seclevel ge securitybits then break; end if;
 * end for;
 *
 * It can be run online at:
 * http://magma.maths.usyd.edu.au/calc
 *
 * And will output:
 * k:  1024, security: 129 bits  (t: 6, M: 23)
 *
 * k is the number of bits of the prime, securitybits is the level we want to
 * reach.
 *
 * prime length | RSA key size | # MR tests | security level
 * -------------+--------------|------------+---------------
 *  (b) >= 6394 |     >= 12788 |          3 |        256 bit
 *  (b) >= 3747 |     >=  7494 |          3 |        192 bit
 *  (b) >= 1345 |     >=  2690 |          4 |        128 bit
 *  (b) >= 1080 |     >=  2160 |          5 |        128 bit
 *  (b) >=  852 |     >=  1704 |          5 |        112 bit
 *  (b) >=  476 |     >=   952 |          5 |         80 bit
 *  (b) >=  400 |     >=   800 |          6 |         80 bit
 *  (b) >=  347 |     >=   694 |          7 |         80 bit
 *  (b) >=  308 |     >=   616 |          8 |         80 bit
 *  (b) >=   55 |     >=   110 |         27 |         64 bit
 *  (b) >=    6 |     >=    12 |         34 |         64 bit
 */

# define BN_prime_checks_for_size(b) ((b) >= 3747 ?  3 : \
                                (b) >=  1345 ?  4 : \
                                (b) >=  476 ?  5 : \
                                (b) >=  400 ?  6 : \
                                (b) >=  347 ?  7 : \
                                (b) >=  308 ?  8 : \
                                (b) >=  55  ? 27 : \
                                /* b >= 6 */ 34)

# define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)

int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w);
int BN_is_zero(const BIGNUM *a);
int BN_is_one(const BIGNUM *a);
int BN_is_word(const BIGNUM *a, const BN_ULONG w);
int BN_is_odd(const BIGNUM *a);

# define BN_one(a)       (BN_set_word((a),1))

void BN_zero_ex(BIGNUM *a);

# if OPENSSL_API_COMPAT >= 0x00908000L
#  define BN_zero(a)      BN_zero_ex(a)
# else
#  define BN_zero(a)      (BN_set_word((a),0))
# endif

const BIGNUM *BN_value_one(void);
char *BN_options(void);
BN_CTX *BN_CTX_new(void);
BN_CTX *BN_CTX_secure_new(void);
void BN_CTX_free(BN_CTX *c);
void BN_CTX_start(BN_CTX *ctx);
BIGNUM *BN_CTX_get(BN_CTX *ctx);
void BN_CTX_end(BN_CTX *ctx);
int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_priv_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
int BN_priv_rand_range(BIGNUM *rnd, const BIGNUM *range);
int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
int BN_num_bits(const BIGNUM *a);
int BN_num_bits_word(BN_ULONG l);
int BN_security_bits(int L, int N);
BIGNUM *BN_new(void);
BIGNUM *BN_secure_new(void);
void BN_clear_free(BIGNUM *a);
BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
void BN_swap(BIGNUM *a, BIGNUM *b);
BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
int BN_bn2bin(const BIGNUM *a, unsigned char *to);
int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen);
BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret);
int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen);
BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
/** BN_set_negative sets sign of a BIGNUM
 * \param  b  pointer to the BIGNUM object
 * \param  n  0 if the BIGNUM b should be positive and a value != 0 otherwise
 */
void BN_set_negative(BIGNUM *b, int n);
/** BN_is_negative returns 1 if the BIGNUM is negative
 * \param  b  pointer to the BIGNUM object
 * \return 1 if a < 0 and 0 otherwise
 */
int BN_is_negative(const BIGNUM *b);

int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
           BN_CTX *ctx);
# define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
               BN_CTX *ctx);
int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                     const BIGNUM *m);
int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
               BN_CTX *ctx);
int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                     const BIGNUM *m);
int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
               BN_CTX *ctx);
int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
                  BN_CTX *ctx);
int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);

BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
int BN_mul_word(BIGNUM *a, BN_ULONG w);
int BN_add_word(BIGNUM *a, BN_ULONG w);
int BN_sub_word(BIGNUM *a, BN_ULONG w);
int BN_set_word(BIGNUM *a, BN_ULONG w);
BN_ULONG BN_get_word(const BIGNUM *a);

int BN_cmp(const BIGNUM *a, const BIGNUM *b);
void BN_free(BIGNUM *a);
int BN_is_bit_set(const BIGNUM *a, int n);
int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
int BN_lshift1(BIGNUM *r, const BIGNUM *a);
int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);

int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
               const BIGNUM *m, BN_CTX *ctx);
int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                              const BIGNUM *m, BN_CTX *ctx,
                              BN_MONT_CTX *in_mont);
int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
                         const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
                     const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
                     BN_CTX *ctx, BN_MONT_CTX *m_ctx);
int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                      const BIGNUM *m, BN_CTX *ctx);

int BN_mask_bits(BIGNUM *a, int n);
# ifndef OPENSSL_NO_STDIO
int BN_print_fp(FILE *fp, const BIGNUM *a);
# endif
int BN_print(BIO *bio, const BIGNUM *a);
int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
int BN_rshift1(BIGNUM *r, const BIGNUM *a);
void BN_clear(BIGNUM *a);
BIGNUM *BN_dup(const BIGNUM *a);
int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
int BN_set_bit(BIGNUM *a, int n);
int BN_clear_bit(BIGNUM *a, int n);
char *BN_bn2hex(const BIGNUM *a);
char *BN_bn2dec(const BIGNUM *a);
int BN_hex2bn(BIGNUM **a, const char *str);
int BN_dec2bn(BIGNUM **a, const char *str);
int BN_asc2bn(BIGNUM **a, const char *str);
int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
                                                                  * -2 for
                                                                  * error */
BIGNUM *BN_mod_inverse(BIGNUM *ret,
                       const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
BIGNUM *BN_mod_sqrt(BIGNUM *ret,
                    const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);

void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);

/* Deprecated versions */
DEPRECATEDIN_0_9_8(BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
                                             const BIGNUM *add,
                                             const BIGNUM *rem,
                                             void (*callback) (int, int,
                                                               void *),
                                             void *cb_arg))
DEPRECATEDIN_0_9_8(int
                   BN_is_prime(const BIGNUM *p, int nchecks,
                               void (*callback) (int, int, void *),
                               BN_CTX *ctx, void *cb_arg))
DEPRECATEDIN_0_9_8(int
                   BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
                                        void (*callback) (int, int, void *),
                                        BN_CTX *ctx, void *cb_arg,
                                        int do_trial_division))

/* Newer versions */
int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
                         const BIGNUM *rem, BN_GENCB *cb);
int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
                            int do_trial_division, BN_GENCB *cb);

int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);

int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
                            const BIGNUM *Xp, const BIGNUM *Xp1,
                            const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
                            BN_GENCB *cb);
int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
                              BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
                              BN_CTX *ctx, BN_GENCB *cb);

BN_MONT_CTX *BN_MONT_CTX_new(void);
int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                          BN_MONT_CTX *mont, BN_CTX *ctx);
int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
                     BN_CTX *ctx);
int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
                       BN_CTX *ctx);
void BN_MONT_CTX_free(BN_MONT_CTX *mont);
int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
                                    const BIGNUM *mod, BN_CTX *ctx);

/* BN_BLINDING flags */
# define BN_BLINDING_NO_UPDATE   0x00000001
# define BN_BLINDING_NO_RECREATE 0x00000002

BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
void BN_BLINDING_free(BN_BLINDING *b);
int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
                          BN_CTX *);

int BN_BLINDING_is_current_thread(BN_BLINDING *b);
void BN_BLINDING_set_current_thread(BN_BLINDING *b);
int BN_BLINDING_lock(BN_BLINDING *b);
int BN_BLINDING_unlock(BN_BLINDING *b);

unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
                                      const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
                                      int (*bn_mod_exp) (BIGNUM *r,
                                                         const BIGNUM *a,
                                                         const BIGNUM *p,
                                                         const BIGNUM *m,
                                                         BN_CTX *ctx,
                                                         BN_MONT_CTX *m_ctx),
                                      BN_MONT_CTX *m_ctx);

DEPRECATEDIN_0_9_8(void BN_set_params(int mul, int high, int low, int mont))
DEPRECATEDIN_0_9_8(int BN_get_params(int which)) /* 0, mul, 1 high, 2 low, 3
                                                  * mont */

BN_RECP_CTX *BN_RECP_CTX_new(void);
void BN_RECP_CTX_free(BN_RECP_CTX *recp);
int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
                          BN_RECP_CTX *recp, BN_CTX *ctx);
int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                    const BIGNUM *m, BN_CTX *ctx);
int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
                BN_RECP_CTX *recp, BN_CTX *ctx);

# ifndef OPENSSL_NO_EC2M

/*
 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
 * ignored. Note that input arguments are not const so that their bit arrays
 * can be expanded to the appropriate size if needed.
 */

/*
 * r = a + b
 */
int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
#  define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
/*
 * r=a mod p
 */
int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
/* r = (a * b) mod p */
int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                    const BIGNUM *p, BN_CTX *ctx);
/* r = (a * a) mod p */
int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
/* r = (1 / b) mod p */
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
/* r = (a / b) mod p */
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                    const BIGNUM *p, BN_CTX *ctx);
/* r = (a ^ b) mod p */
int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                    const BIGNUM *p, BN_CTX *ctx);
/* r = sqrt(a) mod p */
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                     BN_CTX *ctx);
/* r^2 + r = a mod p */
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                           BN_CTX *ctx);
#  define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
/*-
 * Some functions allow for representation of the irreducible polynomials
 * as an unsigned int[], say p.  The irreducible f(t) is then of the form:
 *     t^p[0] + t^p[1] + ... + t^p[k]
 * where m = p[0] > p[1] > ... > p[k] = 0.
 */
/* r = a mod p */
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
/* r = (a * b) mod p */
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                        const int p[], BN_CTX *ctx);
/* r = (a * a) mod p */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
                        BN_CTX *ctx);
/* r = (1 / b) mod p */
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
                        BN_CTX *ctx);
/* r = (a / b) mod p */
int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                        const int p[], BN_CTX *ctx);
/* r = (a ^ b) mod p */
int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                        const int p[], BN_CTX *ctx);
/* r = sqrt(a) mod p */
int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
                         const int p[], BN_CTX *ctx);
/* r^2 + r = a mod p */
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
                               const int p[], BN_CTX *ctx);
int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
int BN_GF2m_arr2poly(const int p[], BIGNUM *a);

# endif

/*
 * faster mod functions for the 'NIST primes' 0 <= a < p^2
 */
int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);

const BIGNUM *BN_get0_nist_prime_192(void);
const BIGNUM *BN_get0_nist_prime_224(void);
const BIGNUM *BN_get0_nist_prime_256(void);
const BIGNUM *BN_get0_nist_prime_384(void);
const BIGNUM *BN_get0_nist_prime_521(void);

int (*BN_nist_mod_func(const BIGNUM *p)) (BIGNUM *r, const BIGNUM *a,
                                          const BIGNUM *field, BN_CTX *ctx);

int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
                          const BIGNUM *priv, const unsigned char *message,
                          size_t message_len, BN_CTX *ctx);

/* Primes from RFC 2409 */
BIGNUM *BN_get_rfc2409_prime_768(BIGNUM *bn);
BIGNUM *BN_get_rfc2409_prime_1024(BIGNUM *bn);

/* Primes from RFC 3526 */
BIGNUM *BN_get_rfc3526_prime_1536(BIGNUM *bn);
BIGNUM *BN_get_rfc3526_prime_2048(BIGNUM *bn);
BIGNUM *BN_get_rfc3526_prime_3072(BIGNUM *bn);
BIGNUM *BN_get_rfc3526_prime_4096(BIGNUM *bn);
BIGNUM *BN_get_rfc3526_prime_6144(BIGNUM *bn);
BIGNUM *BN_get_rfc3526_prime_8192(BIGNUM *bn);

# if OPENSSL_API_COMPAT < 0x10100000L
#  define get_rfc2409_prime_768 BN_get_rfc2409_prime_768
#  define get_rfc2409_prime_1024 BN_get_rfc2409_prime_1024
#  define get_rfc3526_prime_1536 BN_get_rfc3526_prime_1536
#  define get_rfc3526_prime_2048 BN_get_rfc3526_prime_2048
#  define get_rfc3526_prime_3072 BN_get_rfc3526_prime_3072
#  define get_rfc3526_prime_4096 BN_get_rfc3526_prime_4096
#  define get_rfc3526_prime_6144 BN_get_rfc3526_prime_6144
#  define get_rfc3526_prime_8192 BN_get_rfc3526_prime_8192
# endif

int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);

# ifdef  __cplusplus
}
# endif
#endif

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