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/* crypto/bn/bn.h */
/* 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) 1998-2018 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 <limits.h>
# include <openssl/e_os2.h>
# ifndef OPENSSL_NO_FP_API
# include <stdio.h> /* FILE */
# endif
# include <openssl/ossl_typ.h>
# include <openssl/crypto.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.
*/
# if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
defined(OPENSSL_SYS_WIN32) || defined(linux)
# ifndef BN_DIV2W
# define BN_DIV2W
# endif
# endif
/*
* assuming long is 64bit - this is the DEC Alpha unsigned long long is only
* 64 bits :-(, don't define BN_LLONG for the DEC Alpha
*/
# ifdef SIXTY_FOUR_BIT_LONG
# define BN_ULLONG unsigned long long
# 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_MASK (0xffffffffffffffffffffffffffffffffLL)
# 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"
# endif
/*
* This is where the long long data type is 64 bits, but long is 32. For
* machines where there are 64bit registers, this is the mode to use. IRIX,
* on R4000 and above should use this mode, along with the relevant assembler
* code :-). Do NOT define BN_LLONG.
*/
# ifdef SIXTY_FOUR_BIT
# undef BN_LLONG
# undef BN_ULLONG
# define BN_ULONG unsigned long long
# define BN_LONG long long
# define BN_BITS 128
# define BN_BYTES 8
# define BN_BITS2 64
# define BN_BITS4 32
# define BN_MASK2 (0xffffffffffffffffLL)
# define BN_MASK2l (0xffffffffL)
# define BN_MASK2h (0xffffffff00000000LL)
# define BN_MASK2h1 (0xffffffff80000000LL)
# define BN_TBIT (0x8000000000000000LL)
# define BN_DEC_CONV (10000000000000000000ULL)
# define BN_DEC_FMT1 "%llu"
# define BN_DEC_FMT2 "%019llu"
# define BN_DEC_NUM 19
# define BN_HEX_FMT1 "%llX"
# define BN_HEX_FMT2 "%016llX"
# endif
# ifdef THIRTY_TWO_BIT
# ifdef BN_LLONG
# if defined(_WIN32) && !defined(__GNUC__)
# define BN_ULLONG unsigned __int64
# define BN_MASK (0xffffffffffffffffI64)
# else
# define BN_ULLONG unsigned long long
# define BN_MASK (0xffffffffffffffffLL)
# endif
# endif
# 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_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_DEFAULT_BITS 1280
# 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
# ifdef OPENSSL_NO_DEPRECATED
/* deprecated name for the flag */
# define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
/*
* 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)))
/* Already declared in ossl_typ.h */
# if 0
typedef struct bignum_st BIGNUM;
/* Used for temp variables (declaration hidden in bn_lcl.h) */
typedef struct bignum_ctx BN_CTX;
typedef struct bn_blinding_st BN_BLINDING;
typedef struct bn_mont_ctx_st BN_MONT_CTX;
typedef struct bn_recp_ctx_st BN_RECP_CTX;
typedef struct bn_gencb_st BN_GENCB;
# endif
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;
};
/* 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)
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_FP_API
int BN_print_fp(FILE *fp, const BIGNUM *a);
# endif
# ifdef HEADER_BIO_H
int BN_print(BIO *fp, const BIGNUM *a);
# else
int BN_print(void *fp, const BIGNUM *a);
# endif
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 */
# 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.
*/
/*
* 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);
/* library internal functions */
# define bn_expand(a,bits) \
( \
bits > (INT_MAX - BN_BITS2 + 1) ? \
NULL \
: \
(((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax) ? \
(a) \
: \
bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2) \
)
# define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
BIGNUM *bn_expand2(BIGNUM *a, int words);
# ifndef OPENSSL_NO_DEPRECATED
BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
# endif
/*-
* Bignum consistency macros
* There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
* bignum data after direct manipulations on the data. There is also an
* "internal" macro, bn_check_top(), for verifying that there are no leading
* zeroes. Unfortunately, some auditing is required due to the fact that
* bn_fix_top() has become an overabused duct-tape because bignum data is
* occasionally passed around in an inconsistent state. So the following
* changes have been made to sort this out;
* - bn_fix_top()s implementation has been moved to bn_correct_top()
* - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
* bn_check_top() is as before.
* - if BN_DEBUG *is* defined;
* - bn_check_top() tries to pollute unused words even if the bignum 'top' is
* consistent. (ed: only if BN_DEBUG_RAND is defined)
* - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
* The idea is to have debug builds flag up inconsistent bignums when they
* occur. If that occurs in a bn_fix_top(), we examine the code in question; if
* the use of bn_fix_top() was appropriate (ie. it follows directly after code
* that manipulates the bignum) it is converted to bn_correct_top(), and if it
* was not appropriate, we convert it permanently to bn_check_top() and track
* down the cause of the bug. Eventually, no internal code should be using the
* bn_fix_top() macro. External applications and libraries should try this with
* their own code too, both in terms of building against the openssl headers
* with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
* defined. This not only improves external code, it provides more test
* coverage for openssl's own code.
*/
# ifdef BN_DEBUG
/* We only need assert() when debugging */
# include <assert.h>
/*
* The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with
* bn_correct_top, in other words such vectors are permitted to have zeros
* in most significant limbs. Such vectors are used internally to achieve
* execution time invariance for critical operations with private keys.
* It's BN_DEBUG-only flag, because user application is not supposed to
* observe it anyway. Moreover, optimizing compiler would actually remove
* all operations manipulating the bit in question in non-BN_DEBUG build.
*/
# define BN_FLG_FIXED_TOP 0x10000
# ifdef BN_DEBUG_RAND
/* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
# ifndef RAND_pseudo_bytes
int RAND_pseudo_bytes(unsigned char *buf, int num);
# define BN_DEBUG_TRIX
# endif
# define bn_pollute(a) \
do { \
const BIGNUM *_bnum1 = (a); \
if(_bnum1->top < _bnum1->dmax) { \
unsigned char _tmp_char; \
/* We cast away const without the compiler knowing, any \
* *genuinely* constant variables that aren't mutable \
* wouldn't be constructed with top!=dmax. */ \
BN_ULONG *_not_const; \
memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
/* Debug only - safe to ignore error return */ \
RAND_pseudo_bytes(&_tmp_char, 1); \
memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
(_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
} \
} while(0)
# ifdef BN_DEBUG_TRIX
# undef RAND_pseudo_bytes
# endif
# else
# define bn_pollute(a)
# endif
# define bn_check_top(a) \
do { \
const BIGNUM *_bnum2 = (a); \
if (_bnum2 != NULL) { \
int _top = _bnum2->top; \
assert((_top == 0) || \
(_bnum2->flags & BN_FLG_FIXED_TOP) || \
(_bnum2->d[_top - 1] != 0)); \
bn_pollute(_bnum2); \
} \
} while(0)
# define bn_fix_top(a) bn_check_top(a)
# define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
# define bn_wcheck_size(bn, words) \
do { \
const BIGNUM *_bnum2 = (bn); \
assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
/* avoid unused variable warning with NDEBUG */ \
(void)(_bnum2); \
} while(0)
# else /* !BN_DEBUG */
# define BN_FLG_FIXED_TOP 0
# define bn_pollute(a)
# define bn_check_top(a)
# define bn_fix_top(a) bn_correct_top(a)
# define bn_check_size(bn, bits)
# define bn_wcheck_size(bn, words)
# endif
# define bn_correct_top(a) \
{ \
BN_ULONG *ftl; \
int tmp_top = (a)->top; \
if (tmp_top > 0) \
{ \
for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
if (*(ftl--)) break; \
(a)->top = tmp_top; \
} \
if ((a)->top == 0) \
(a)->neg = 0; \
bn_pollute(a); \
}
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
BN_ULONG w);
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
int num);
BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
int num);
/* Primes from RFC 2409 */
BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
BIGNUM *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);
int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
/* 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_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_LSHIFT 145
# 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_RSHIFT 146
# 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 118
# 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_INVALID_SHIFT 119
# 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