/* $OpenBSD: bn.h,v 1.39 2019/08/25 19:23:59 schwarze Exp $ */
/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 *
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 *
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 *
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */
/* ====================================================================
 * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */
/* ====================================================================
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
 *
 * Portions of the attached software ("Contribution") are developed by
 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
 *
 * The Contribution is licensed pursuant to the Eric Young open source
 * license provided above.
 *
 * The binary polynomial arithmetic software is originally written by
 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
 *
 */

#ifndef HEADER_BN_H
#define HEADER_BN_H

#include <stdio.h>
#include <stdlib.h>

#include <openssl/opensslconf.h>

#include <openssl/ossl_typ.h>
#include <openssl/crypto.h>
#include <openssl/bio.h>

#ifdef  __cplusplus
extern "C" {
#endif

/* These preprocessor symbols control various aspects of the bignum headers and
 * library code. They're not defined by any "normal" configuration, as they are
 * intended for development and testing purposes. NB: defining all three can be
 * useful for debugging application code as well as openssl itself.
 *
 * BN_DEBUG - turn on various debugging alterations to the bignum code
 * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
 * mismanagement of bignum internals. You must also define BN_DEBUG.
 */
/* #define BN_DEBUG */
/* #define BN_DEBUG_RAND */

#ifndef OPENSSL_SMALL_FOOTPRINT
#define BN_MUL_COMBA
#define BN_SQR_COMBA
#define BN_RECURSION
#endif

/* This next option uses the C libraries (2 word)/(1 word) function.
 * If it is not defined, I use my C version (which is slower).
 * The reason for this flag is that when the particular C compiler
 * library routine is used, and the library is linked with a different
 * compiler, the library is missing.  This mostly happens when the
 * library is built with gcc and then linked using normal cc.  This would
 * be a common occurrence because gcc normally produces code that is
 * 2 times faster than system compilers for the big number stuff.
 * For machines with only one compiler (or shared libraries), this should
 * be on.  Again this in only really a problem on machines
 * using "long long's", are 32bit, and are not using my assembler code. */
/* #define BN_DIV2W */

#ifdef _LP64
#undef	BN_LLONG
#define BN_ULONG	unsigned long
#define BN_LONG		long
#define BN_BITS		128
#define BN_BYTES	8
#define BN_BITS2	64
#define BN_BITS4	32
#define BN_MASK2	(0xffffffffffffffffL)
#define BN_MASK2l	(0xffffffffL)
#define BN_MASK2h	(0xffffffff00000000L)
#define BN_MASK2h1	(0xffffffff80000000L)
#define BN_TBIT		(0x8000000000000000L)
#define BN_DEC_CONV	(10000000000000000000UL)
#define BN_DEC_FMT1	"%lu"
#define BN_DEC_FMT2	"%019lu"
#define BN_DEC_NUM	19
#define BN_HEX_FMT1	"%lX"
#define BN_HEX_FMT2	"%016lX"
#else
#define BN_ULLONG	unsigned long long
#define	BN_LLONG
#define BN_ULONG	unsigned int
#define BN_LONG		int
#define BN_BITS		64
#define BN_BYTES	4
#define BN_BITS2	32
#define BN_BITS4	16
#define BN_MASK		(0xffffffffffffffffLL)
#define BN_MASK2	(0xffffffffL)
#define BN_MASK2l	(0xffff)
#define BN_MASK2h1	(0xffff8000L)
#define BN_MASK2h	(0xffff0000L)
#define BN_TBIT		(0x80000000L)
#define BN_DEC_CONV	(1000000000L)
#define BN_DEC_FMT1	"%u"
#define BN_DEC_FMT2	"%09u"
#define BN_DEC_NUM	9
#define BN_HEX_FMT1	"%X"
#define BN_HEX_FMT2	"%08X"
#endif

#define BN_FLG_MALLOCED		0x01
#define BN_FLG_STATIC_DATA	0x02
#define BN_FLG_CONSTTIME	0x04 /* 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.
                                      */

#ifndef OPENSSL_NO_DEPRECATED
#define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME /* deprecated name for the flag */
                                      /* avoid leaking exponent information through timings
                                      * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
#endif

#ifndef OPENSSL_NO_DEPRECATED
#define BN_FLG_FREE		0x8000	/* used for debuging */
#endif
#define BN_set_flags(b,n)	((b)->flags|=(n))
#define BN_get_flags(b,n)	((b)->flags&(n))

/* get a clone of a BIGNUM with changed flags, for *temporary* use only
 * (the two BIGNUMs cannot not be used in parallel!) */
#define BN_with_flags(dest,b,n)  ((dest)->d=(b)->d, \
                                  (dest)->top=(b)->top, \
                                  (dest)->dmax=(b)->dmax, \
                                  (dest)->neg=(b)->neg, \
                                  (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
                                                 |  ((b)->flags & ~BN_FLG_MALLOCED) \
                                                 |  BN_FLG_STATIC_DATA \
                                                 |  (n)))

struct bignum_st {
	BN_ULONG *d;	/* Pointer to an array of 'BN_BITS2' bit chunks. */
	int top;	/* Index of last used d +1. */
	/* The next are internal book keeping for bn_expand. */
	int dmax;	/* Size of the d array. */
	int neg;	/* one if the number is negative */
	int flags;
};

/* Used for montgomery multiplication */
struct bn_mont_ctx_st {
	int ri;        /* number of bits in R */
	BIGNUM RR;     /* used to convert to montgomery form */
	BIGNUM N;      /* The modulus */
	BIGNUM Ni;     /* R*(1/R mod N) - N*Ni = 1
	                * (Ni is only stored for bignum algorithm) */
	BN_ULONG n0[2];/* least significant word(s) of Ni;
	                  (type changed with 0.9.9, was "BN_ULONG n0;" before) */
	int flags;
};

/* Used for reciprocal division/mod functions
 * It cannot be shared between threads
 */
struct bn_recp_ctx_st {
	BIGNUM N;	/* the divisor */
	BIGNUM Nr;	/* the reciprocal */
	int num_bits;
	int shift;
	int flags;
};

/* Used for slow "generation" functions. */
struct bn_gencb_st {
	unsigned int ver;	/* To handle binary (in)compatibility */
	void *arg;		/* callback-specific data */
	union {
		/* if(ver==1) - handles old style callbacks */
		void (*cb_1)(int, int, void *);
		/* if(ver==2) - new callback style */
		int (*cb_2)(int, int, BN_GENCB *);
	} cb;
};

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

/* Wrapper function to make using BN_GENCB easier,  */
int BN_GENCB_call(BN_GENCB *cb, int a, int b);
/* Macro to populate a BN_GENCB structure with an "old"-style callback */
#define BN_GENCB_set_old(gencb, callback, cb_arg) { \
		BN_GENCB *tmp_gencb = (gencb); \
		tmp_gencb->ver = 1; \
		tmp_gencb->arg = (cb_arg); \
		tmp_gencb->cb.cb_1 = (callback); }
/* Macro to populate a BN_GENCB structure with a "new"-style callback */
#define BN_GENCB_set(gencb, callback, cb_arg) { \
		BN_GENCB *tmp_gencb = (gencb); \
		tmp_gencb->ver = 2; \
		tmp_gencb->arg = (cb_arg); \
		tmp_gencb->cb.cb_2 = (callback); }

#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)

/* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
#define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
				(((w) == 0) && ((a)->top == 0)))
#define BN_is_zero(a)       ((a)->top == 0)
#define BN_is_one(a)        (BN_abs_is_word((a),1) && !(a)->neg)
#define BN_is_word(a,w)     (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
#define BN_is_odd(a)	    (((a)->top > 0) && ((a)->d[0] & 1))

#define BN_one(a)	(BN_set_word((a),1))
#define BN_zero_ex(a) \
	do { \
		BIGNUM *_tmp_bn = (a); \
		_tmp_bn->top = 0; \
		_tmp_bn->neg = 0; \
	} while(0)

#ifdef OPENSSL_NO_DEPRECATED
#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);
#ifndef OPENSSL_NO_DEPRECATED
void	BN_CTX_init(BN_CTX *c);
#endif
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_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
int	BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
int	BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
int	BN_num_bits(const BIGNUM *a);
int	BN_num_bits_word(BN_ULONG);
BIGNUM *BN_new(void);
void	BN_init(BIGNUM *);
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);
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  a  pointer to the BIGNUM object
 * \return 1 if a < 0 and 0 otherwise
 */
#define BN_is_negative(a) ((a)->neg != 0)

#ifndef LIBRESSL_INTERNAL
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))
#endif
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);

#ifndef LIBRESSL_INTERNAL
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);
#endif
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);
int	BN_print_fp(FILE *fp, const BIGNUM *a);
int	BN_print(BIO *fp, 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);
#ifndef LIBRESSL_INTERNAL
int	BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
#endif
int	BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
#ifndef LIBRESSL_INTERNAL
BIGNUM *BN_mod_inverse(BIGNUM *ret,
    const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
#endif
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 */
#ifndef OPENSSL_NO_DEPRECATED
BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
    const BIGNUM *add, const BIGNUM *rem,
    void (*callback)(int, int, void *), void *cb_arg);
int	BN_is_prime(const BIGNUM *p, int nchecks,
    void (*callback)(int, int, void *),
    BN_CTX *ctx, void *cb_arg);
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);
#endif /* !defined(OPENSSL_NO_DEPRECATED) */

/* 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 );
void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
    BN_MONT_CTX *mont, BN_CTX *ctx);
#define BN_to_montgomery(r,a,mont,ctx)	BN_mod_mul_montgomery(\
	(r),(a),&((mont)->RR),(mont),(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, int 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 *);
#ifndef OPENSSL_NO_DEPRECATED
unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
#endif
CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
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);

#ifndef OPENSSL_NO_DEPRECATED
void BN_set_params(int mul, int high, int low, int mont);
int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
#endif

void	BN_RECP_CTX_init(BN_RECP_CTX *recp);
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.
 */

int	BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
#define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
int	BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
int
BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
	const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
int
BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
	BN_CTX *ctx); /* r = (a * a) mod p */
int
BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
	BN_CTX *ctx); /* r = (1 / 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 = (a ^ b) mod p */
int
BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
	BN_CTX *ctx); /* r = sqrt(a) mod p */
int	BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
	BN_CTX *ctx); /* r^2 + r = a mod p */
#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.
 */
int	BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
/* r = a mod p */
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
	const int p[], BN_CTX *ctx); /* r = (a * b) mod p */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
	BN_CTX *ctx); /* r = (a * a) mod p */
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
	BN_CTX *ctx); /* r = (1 / 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 = (a ^ b) mod p */
int	BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
	const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
int	BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
	const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
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);

/* Primes from RFC 2409 */
BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
BIGNUM *BN_get_rfc2409_prime_768(BIGNUM *bn);
BIGNUM *BN_get_rfc2409_prime_1024(BIGNUM *bn);

/* Primes from RFC 3526 */
BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
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);

/* BEGIN ERROR CODES */
/* The following lines are auto generated by the script mkerr.pl. Any changes
 * made after this point may be overwritten when the script is next run.
 */
void ERR_load_BN_strings(void);

/* Error codes for the BN functions. */

/* Function codes. */
#define BN_F_BNRAND					 127
#define BN_F_BN_BLINDING_CONVERT_EX			 100
#define BN_F_BN_BLINDING_CREATE_PARAM			 128
#define BN_F_BN_BLINDING_INVERT_EX			 101
#define BN_F_BN_BLINDING_NEW				 102
#define BN_F_BN_BLINDING_UPDATE				 103
#define BN_F_BN_BN2DEC					 104
#define BN_F_BN_BN2HEX					 105
#define BN_F_BN_CTX_GET					 116
#define BN_F_BN_CTX_NEW					 106
#define BN_F_BN_CTX_START				 129
#define BN_F_BN_DIV					 107
#define BN_F_BN_DIV_NO_BRANCH				 138
#define BN_F_BN_DIV_RECP				 130
#define BN_F_BN_EXP					 123
#define BN_F_BN_EXPAND2					 108
#define BN_F_BN_GENERATE_PRIME_EX			 140
#define BN_F_BN_EXPAND_INTERNAL				 120
#define BN_F_BN_GF2M_MOD				 131
#define BN_F_BN_GF2M_MOD_EXP				 132
#define BN_F_BN_GF2M_MOD_MUL				 133
#define BN_F_BN_GF2M_MOD_SOLVE_QUAD			 134
#define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR			 135
#define BN_F_BN_GF2M_MOD_SQR				 136
#define BN_F_BN_GF2M_MOD_SQRT				 137
#define BN_F_BN_MOD_EXP2_MONT				 118
#define BN_F_BN_MOD_EXP_MONT				 109
#define BN_F_BN_MOD_EXP_MONT_CONSTTIME			 124
#define BN_F_BN_MOD_EXP_MONT_WORD			 117
#define BN_F_BN_MOD_EXP_RECP				 125
#define BN_F_BN_MOD_EXP_SIMPLE				 126
#define BN_F_BN_MOD_INVERSE				 110
#define BN_F_BN_MOD_INVERSE_NO_BRANCH			 139
#define BN_F_BN_MOD_LSHIFT_QUICK			 119
#define BN_F_BN_MOD_MUL_RECIPROCAL			 111
#define BN_F_BN_MOD_SQRT				 121
#define BN_F_BN_MPI2BN					 112
#define BN_F_BN_NEW					 113
#define BN_F_BN_RAND					 114
#define BN_F_BN_RAND_RANGE				 122
#define BN_F_BN_USUB					 115

/* Reason codes. */
#define BN_R_ARG2_LT_ARG3				 100
#define BN_R_BAD_RECIPROCAL				 101
#define BN_R_BIGNUM_TOO_LONG				 114
#define BN_R_BITS_TOO_SMALL				 117
#define BN_R_CALLED_WITH_EVEN_MODULUS			 102
#define BN_R_DIV_BY_ZERO				 103
#define BN_R_ENCODING_ERROR				 104
#define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA		 105
#define BN_R_INPUT_NOT_REDUCED				 110
#define BN_R_INVALID_LENGTH				 106
#define BN_R_INVALID_RANGE				 115
#define BN_R_NOT_A_SQUARE				 111
#define BN_R_NOT_INITIALIZED				 107
#define BN_R_NO_INVERSE					 108
#define BN_R_NO_SOLUTION				 116
#define BN_R_P_IS_NOT_PRIME				 112
#define BN_R_TOO_MANY_ITERATIONS			 113
#define BN_R_TOO_MANY_TEMPORARY_VARIABLES		 109

#ifdef  __cplusplus
}
#endif
#endif
