swh:1:snp:dc2a5002442a00b1c0eda7c65d04ea7455e166cd
Tip revision: 20d7295cb0529882306c370f5dd895f412bbf59b authored by Matt Caswell on 05 November 2020, 14:03:50 UTC
Prepare for release of 3.0 alpha 8
Prepare for release of 3.0 alpha 8
Tip revision: 20d7295
bn.h
/*
* Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
*
* Licensed under the Apache License 2.0 (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 OPENSSL_BN_H
# define OPENSSL_BN_H
# pragma once
# include <openssl/macros.h>
# ifndef OPENSSL_NO_DEPRECATED_3_0
# define HEADER_BN_H
# endif
# include <openssl/e_os2.h>
# ifndef OPENSSL_NO_STDIO
# include <stdio.h>
# endif
# include <openssl/opensslconf.h>
# include <openssl/types.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
# ifndef OPENSSL_NO_DEPRECATED_0_9_8
/* 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);
# ifndef OPENSSL_NO_DEPRECATED_3_0
# 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)
# endif
# 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_LEVEL > 908
# 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_ex(OSSL_LIB_CTX *ctx);
BN_CTX *BN_CTX_new(void);
BN_CTX *BN_CTX_secure_new_ex(OSSL_LIB_CTX *ctx);
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_ex(BIGNUM *rnd, int bits, int top, int bottom, BN_CTX *ctx);
int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_priv_rand_ex(BIGNUM *rnd, int bits, int top, int bottom, BN_CTX *ctx);
int BN_priv_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_rand_range_ex(BIGNUM *r, const BIGNUM *range, BN_CTX *ctx);
int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
int BN_priv_rand_range_ex(BIGNUM *r, const BIGNUM *range, BN_CTX *ctx);
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_native2bn(const unsigned char *s, int len, BIGNUM *ret);
int BN_bn2nativepad(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))
DEPRECATEDIN_3_0(int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb))
DEPRECATEDIN_3_0(int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb))
/* Newer versions */
int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
BN_CTX *ctx);
int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
const BIGNUM *rem, BN_GENCB *cb);
int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, 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);
# ifndef OPENSSL_NO_DH
/* 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);
# ifndef OPENSSL_NO_DEPRECATED_1_1_0
# 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
# endif
int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
# ifdef __cplusplus
}
# endif
#endif
