/* $OpenBSD: bn_lcl.h,v 1.30 2018/11/05 23:52:47 tb Exp $ */
/* Copyright (C) 1995-1998 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) 1998-2000 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).
*
*/
#ifndef HEADER_BN_LCL_H
#define HEADER_BN_LCL_H
#include <openssl/opensslconf.h>
#include <openssl/bn.h>
__BEGIN_HIDDEN_DECLS
/*
* BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
*
*
* For window size 'w' (w >= 2) and a random 'b' bits exponent,
* the number of multiplications is a constant plus on average
*
* 2^(w-1) + (b-w)/(w+1);
*
* here 2^(w-1) is for precomputing the table (we actually need
* entries only for windows that have the lowest bit set), and
* (b-w)/(w+1) is an approximation for the expected number of
* w-bit windows, not counting the first one.
*
* Thus we should use
*
* w >= 6 if b > 671
* w = 5 if 671 > b > 239
* w = 4 if 239 > b > 79
* w = 3 if 79 > b > 23
* w <= 2 if 23 > b
*
* (with draws in between). Very small exponents are often selected
* with low Hamming weight, so we use w = 1 for b <= 23.
*/
#define BN_window_bits_for_exponent_size(b) \
((b) > 671 ? 6 : \
(b) > 239 ? 5 : \
(b) > 79 ? 4 : \
(b) > 23 ? 3 : 1)
/* BN_mod_exp_mont_consttime is based on the assumption that the
* L1 data cache line width of the target processor is at least
* the following value.
*/
#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
#define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
/* Window sizes optimized for fixed window size modular exponentiation
* algorithm (BN_mod_exp_mont_consttime).
*
* To achieve the security goals of BN_mode_exp_mont_consttime, the
* maximum size of the window must not exceed
* log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
*
* Window size thresholds are defined for cache line sizes of 32 and 64,
* cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A
* window size of 7 should only be used on processors that have a 128
* byte or greater cache line size.
*/
#if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
# define BN_window_bits_for_ctime_exponent_size(b) \
((b) > 937 ? 6 : \
(b) > 306 ? 5 : \
(b) > 89 ? 4 : \
(b) > 22 ? 3 : 1)
# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
#elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
# define BN_window_bits_for_ctime_exponent_size(b) \
((b) > 306 ? 5 : \
(b) > 89 ? 4 : \
(b) > 22 ? 3 : 1)
# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
#endif
/* Pentium pro 16,16,16,32,64 */
/* Alpha 16,16,16,16.64 */
#define BN_MULL_SIZE_NORMAL (16) /* 32 */
#define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */
#define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */
#define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */
#define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */
#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM)
/*
* BN_UMULT_HIGH section.
*
* No, I'm not trying to overwhelm you when stating that the
* product of N-bit numbers is 2*N bits wide:-) No, I don't expect
* you to be impressed when I say that if the compiler doesn't
* support 2*N integer type, then you have to replace every N*N
* multiplication with 4 (N/2)*(N/2) accompanied by some shifts
* and additions which unavoidably results in severe performance
* penalties. Of course provided that the hardware is capable of
* producing 2*N result... That's when you normally start
* considering assembler implementation. However! It should be
* pointed out that some CPUs (most notably Alpha, PowerPC and
* upcoming IA-64 family:-) provide *separate* instruction
* calculating the upper half of the product placing the result
* into a general purpose register. Now *if* the compiler supports
* inline assembler, then it's not impossible to implement the
* "bignum" routines (and have the compiler optimize 'em)
* exhibiting "native" performance in C. That's what BN_UMULT_HIGH
* macro is about:-)
*
* <appro@fy.chalmers.se>
*/
# if defined(__alpha)
# if defined(__GNUC__) && __GNUC__>=2
# define BN_UMULT_HIGH(a,b) ({ \
BN_ULONG ret; \
asm ("umulh %1,%2,%0" \
: "=r"(ret) \
: "r"(a), "r"(b)); \
ret; })
# endif /* compiler */
# elif defined(_ARCH_PPC) && defined(_LP64)
# if defined(__GNUC__) && __GNUC__>=2
# define BN_UMULT_HIGH(a,b) ({ \
BN_ULONG ret; \
asm ("mulhdu %0,%1,%2" \
: "=r"(ret) \
: "r"(a), "r"(b)); \
ret; })
# endif /* compiler */
# elif (defined(__x86_64) || defined(__x86_64__)) && defined(_LP64)
# if defined(__GNUC__) && __GNUC__>=2
# define BN_UMULT_HIGH(a,b) ({ \
BN_ULONG ret,discard; \
asm ("mulq %3" \
: "=a"(discard),"=d"(ret) \
: "a"(a), "g"(b) \
: "cc"); \
ret; })
# define BN_UMULT_LOHI(low,high,a,b) \
asm ("mulq %3" \
: "=a"(low),"=d"(high) \
: "a"(a),"g"(b) \
: "cc");
# endif
# elif defined(__mips) && defined(_LP64)
# if defined(__GNUC__) && __GNUC__>=2
# if __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 4) /* "h" constraint is no more since 4.4 */
# define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
# define BN_UMULT_LOHI(low,high,a,b) ({ \
__uint128_t ret=(__uint128_t)(a)*(b); \
(high)=ret>>64; (low)=ret; })
# else
# define BN_UMULT_HIGH(a,b) ({ \
BN_ULONG ret; \
asm ("dmultu %1,%2" \
: "=h"(ret) \
: "r"(a), "r"(b) : "l"); \
ret; })
# define BN_UMULT_LOHI(low,high,a,b)\
asm ("dmultu %2,%3" \
: "=l"(low),"=h"(high) \
: "r"(a), "r"(b));
# endif
# endif
# endif /* cpu */
#endif /* OPENSSL_NO_ASM */
/*************************************************************
* Using the long long type
*/
#define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
#define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
#ifdef BN_DEBUG_RAND
#define bn_clear_top2max(a) \
{ \
int ind = (a)->dmax - (a)->top; \
BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
for (; ind != 0; ind--) \
*(++ftl) = 0x0; \
}
#else
#define bn_clear_top2max(a)
#endif
#ifdef BN_LLONG
#define mul_add(r,a,w,c) { \
BN_ULLONG t; \
t=(BN_ULLONG)w * (a) + (r) + (c); \
(r)= Lw(t); \
(c)= Hw(t); \
}
#define mul(r,a,w,c) { \
BN_ULLONG t; \
t=(BN_ULLONG)w * (a) + (c); \
(r)= Lw(t); \
(c)= Hw(t); \
}
#define sqr(r0,r1,a) { \
BN_ULLONG t; \
t=(BN_ULLONG)(a)*(a); \
(r0)=Lw(t); \
(r1)=Hw(t); \
}
#elif defined(BN_UMULT_LOHI)
#define mul_add(r,a,w,c) { \
BN_ULONG high,low,ret,tmp=(a); \
ret = (r); \
BN_UMULT_LOHI(low,high,w,tmp); \
ret += (c); \
(c) = (ret<(c))?1:0; \
(c) += high; \
ret += low; \
(c) += (ret<low)?1:0; \
(r) = ret; \
}
#define mul(r,a,w,c) { \
BN_ULONG high,low,ret,ta=(a); \
BN_UMULT_LOHI(low,high,w,ta); \
ret = low + (c); \
(c) = high; \
(c) += (ret<low)?1:0; \
(r) = ret; \
}
#define sqr(r0,r1,a) { \
BN_ULONG tmp=(a); \
BN_UMULT_LOHI(r0,r1,tmp,tmp); \
}
#elif defined(BN_UMULT_HIGH)
#define mul_add(r,a,w,c) { \
BN_ULONG high,low,ret,tmp=(a); \
ret = (r); \
high= BN_UMULT_HIGH(w,tmp); \
ret += (c); \
low = (w) * tmp; \
(c) = (ret<(c))?1:0; \
(c) += high; \
ret += low; \
(c) += (ret<low)?1:0; \
(r) = ret; \
}
#define mul(r,a,w,c) { \
BN_ULONG high,low,ret,ta=(a); \
low = (w) * ta; \
high= BN_UMULT_HIGH(w,ta); \
ret = low + (c); \
(c) = high; \
(c) += (ret<low)?1:0; \
(r) = ret; \
}
#define sqr(r0,r1,a) { \
BN_ULONG tmp=(a); \
(r0) = tmp * tmp; \
(r1) = BN_UMULT_HIGH(tmp,tmp); \
}
#else
/*************************************************************
* No long long type
*/
#define LBITS(a) ((a)&BN_MASK2l)
#define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
#define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
#define mul64(l,h,bl,bh) \
{ \
BN_ULONG m,m1,lt,ht; \
\
lt=l; \
ht=h; \
m =(bh)*(lt); \
lt=(bl)*(lt); \
m1=(bl)*(ht); \
ht =(bh)*(ht); \
m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
ht+=HBITS(m); \
m1=L2HBITS(m); \
lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
(l)=lt; \
(h)=ht; \
}
#define sqr64(lo,ho,in) \
{ \
BN_ULONG l,h,m; \
\
h=(in); \
l=LBITS(h); \
h=HBITS(h); \
m =(l)*(h); \
l*=l; \
h*=h; \
h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
m =(m&BN_MASK2l)<<(BN_BITS4+1); \
l=(l+m)&BN_MASK2; if (l < m) h++; \
(lo)=l; \
(ho)=h; \
}
#define mul_add(r,a,bl,bh,c) { \
BN_ULONG l,h; \
\
h= (a); \
l=LBITS(h); \
h=HBITS(h); \
mul64(l,h,(bl),(bh)); \
\
/* non-multiply part */ \
l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
(c)=(r); \
l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
(c)=h&BN_MASK2; \
(r)=l; \
}
#define mul(r,a,bl,bh,c) { \
BN_ULONG l,h; \
\
h= (a); \
l=LBITS(h); \
h=HBITS(h); \
mul64(l,h,(bl),(bh)); \
\
/* non-multiply part */ \
l+=(c); if ((l&BN_MASK2) < (c)) h++; \
(c)=h&BN_MASK2; \
(r)=l&BN_MASK2; \
}
#endif /* !BN_LLONG */
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl);
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
int dna, int dnb, BN_ULONG *t);
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
int n, int tna, int tnb, BN_ULONG *t);
void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
BN_ULONG *t);
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
BN_ULONG *t);
BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl);
BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl);
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np, const BN_ULONG *n0, int num);
#define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
BIGNUM *bn_expand2(BIGNUM *a, int words);
BIGNUM *bn_expand(BIGNUM *a, int bits);
BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
/* 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>
#ifdef BN_DEBUG_RAND
#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*)); \
arc4random_buf(&_tmp_char, 1); \
memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
(_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
} \
} while(0)
#else
#define bn_pollute(a)
#endif
#define bn_check_top(a) \
do { \
const BIGNUM *_bnum2 = (a); \
if (_bnum2 != NULL) { \
assert((_bnum2->top == 0) || \
(_bnum2->d[_bnum2->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); \
} while(0)
#else /* !BN_DEBUG */
#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; \
} \
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);
int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
int bn_rand_interval(BIGNUM *rnd, const BIGNUM *lower_inc, const BIGNUM *upper_exc);
/* Explicitly const time / non-const time versions for internal use */
int BN_mod_exp_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx);
int BN_mod_exp_nonct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx);
int BN_mod_exp_mont_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
int BN_mod_exp_mont_nonct(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
int BN_div_nonct(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
BN_CTX *ctx);
int BN_div_ct(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
BN_CTX *ctx);
#define BN_mod_ct(rem,m,d,ctx) BN_div_ct(NULL,(rem),(m),(d),(ctx))
#define BN_mod_nonct(rem,m,d,ctx) BN_div_nonct(NULL,(rem),(m),(d),(ctx))
BIGNUM *BN_mod_inverse_ct(BIGNUM *ret, const BIGNUM *a, const BIGNUM *n,
BN_CTX *ctx);
BIGNUM *BN_mod_inverse_nonct(BIGNUM *ret, const BIGNUM *a, const BIGNUM *n,
BN_CTX *ctx);
int BN_gcd_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_gcd_nonct(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_swap_ct(BN_ULONG swap, BIGNUM *a, BIGNUM *b, size_t nwords);
__END_HIDDEN_DECLS
#endif