/* crypto/bn/bn_exp.c */
/* 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) 1998-2005 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).
*
*/
#include "cryptlib.h"
#include "bn_lcl.h"
#include <stdlib.h>
#ifdef _WIN32
# include <malloc.h>
# ifndef alloca
# define alloca _alloca
# endif
#elif defined(__GNUC__)
# ifndef alloca
# define alloca(s) __builtin_alloca((s))
# endif
#endif
/* maximum precomputation table size for *variable* sliding windows */
#define TABLE_SIZE 32
/* this one works - simple but works */
int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
int i,bits,ret=0;
BIGNUM *v,*rr;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
{
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
BN_CTX_start(ctx);
if ((r == a) || (r == p))
rr = BN_CTX_get(ctx);
else
rr = r;
v = BN_CTX_get(ctx);
if (rr == NULL || v == NULL) goto err;
if (BN_copy(v,a) == NULL) goto err;
bits=BN_num_bits(p);
if (BN_is_odd(p))
{ if (BN_copy(rr,a) == NULL) goto err; }
else { if (!BN_one(rr)) goto err; }
for (i=1; i<bits; i++)
{
if (!BN_sqr(v,v,ctx)) goto err;
if (BN_is_bit_set(p,i))
{
if (!BN_mul(rr,rr,v,ctx)) goto err;
}
}
ret=1;
err:
if (r != rr) BN_copy(r,rr);
BN_CTX_end(ctx);
bn_check_top(r);
return(ret);
}
int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
BN_CTX *ctx)
{
int ret;
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
/* For even modulus m = 2^k*m_odd, it might make sense to compute
* a^p mod m_odd and a^p mod 2^k separately (with Montgomery
* exponentiation for the odd part), using appropriate exponent
* reductions, and combine the results using the CRT.
*
* For now, we use Montgomery only if the modulus is odd; otherwise,
* exponentiation using the reciprocal-based quick remaindering
* algorithm is used.
*
* (Timing obtained with expspeed.c [computations a^p mod m
* where a, p, m are of the same length: 256, 512, 1024, 2048,
* 4096, 8192 bits], compared to the running time of the
* standard algorithm:
*
* BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
* 55 .. 77 % [UltraSparc processor, but
* debug-solaris-sparcv8-gcc conf.]
*
* BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
* 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
*
* On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
* at 2048 and more bits, but at 512 and 1024 bits, it was
* slower even than the standard algorithm!
*
* "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
* should be obtained when the new Montgomery reduction code
* has been integrated into OpenSSL.)
*/
#define MONT_MUL_MOD
#define MONT_EXP_WORD
#define RECP_MUL_MOD
#ifdef MONT_MUL_MOD
/* I have finally been able to take out this pre-condition of
* the top bit being set. It was caused by an error in BN_div
* with negatives. There was also another problem when for a^b%m
* a >= m. eay 07-May-97 */
/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
if (BN_is_odd(m))
{
# ifdef MONT_EXP_WORD
if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
{
BN_ULONG A = a->d[0];
ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
}
else
# endif
ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
}
else
#endif
#ifdef RECP_MUL_MOD
{ ret=BN_mod_exp_recp(r,a,p,m,ctx); }
#else
{ ret=BN_mod_exp_simple(r,a,p,m,ctx); }
#endif
bn_check_top(r);
return(ret);
}
int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx)
{
int i,j,bits,ret=0,wstart,wend,window,wvalue;
int start=1;
BIGNUM *aa;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
BN_RECP_CTX recp;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
{
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
bits=BN_num_bits(p);
if (bits == 0)
{
ret = BN_one(r);
return ret;
}
BN_CTX_start(ctx);
aa = BN_CTX_get(ctx);
val[0] = BN_CTX_get(ctx);
if(!aa || !val[0]) goto err;
BN_RECP_CTX_init(&recp);
if (m->neg)
{
/* ignore sign of 'm' */
if (!BN_copy(aa, m)) goto err;
aa->neg = 0;
if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
}
else
{
if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
}
if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
if (BN_is_zero(val[0]))
{
BN_zero(r);
ret = 1;
goto err;
}
window = BN_window_bits_for_exponent_size(bits);
if (window > 1)
{
if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
goto err; /* 2 */
j=1<<(window-1);
for (i=1; i<j; i++)
{
if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
!BN_mod_mul_reciprocal(val[i],val[i-1],
aa,&recp,ctx))
goto err;
}
}
start=1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
wvalue=0; /* The 'value' of the window */
wstart=bits-1; /* The top bit of the window */
wend=0; /* The bottom bit of the window */
if (!BN_one(r)) goto err;
for (;;)
{
if (BN_is_bit_set(p,wstart) == 0)
{
if (!start)
if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
goto err;
if (wstart == 0) break;
wstart--;
continue;
}
/* We now have wstart on a 'set' bit, we now need to work out
* how bit a window to do. To do this we need to scan
* forward until the last set bit before the end of the
* window */
j=wstart;
wvalue=1;
wend=0;
for (i=1; i<window; i++)
{
if (wstart-i < 0) break;
if (BN_is_bit_set(p,wstart-i))
{
wvalue<<=(i-wend);
wvalue|=1;
wend=i;
}
}
/* wend is the size of the current window */
j=wend+1;
/* add the 'bytes above' */
if (!start)
for (i=0; i<j; i++)
{
if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
goto err;
/* move the 'window' down further */
wstart-=wend+1;
wvalue=0;
start=0;
if (wstart < 0) break;
}
ret=1;
err:
BN_CTX_end(ctx);
BN_RECP_CTX_free(&recp);
bn_check_top(r);
return(ret);
}
int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
int i,j,bits,ret=0,wstart,wend,window,wvalue;
int start=1;
BIGNUM *d,*r;
const BIGNUM *aa;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
BN_MONT_CTX *mont=NULL;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
{
return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
}
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m))
{
BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
return(0);
}
bits=BN_num_bits(p);
if (bits == 0)
{
ret = BN_one(rr);
return ret;
}
BN_CTX_start(ctx);
d = BN_CTX_get(ctx);
r = BN_CTX_get(ctx);
val[0] = BN_CTX_get(ctx);
if (!d || !r || !val[0]) goto err;
/* If this is not done, things will break in the montgomery
* part */
if (in_mont != NULL)
mont=in_mont;
else
{
if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
}
if (a->neg || BN_ucmp(a,m) >= 0)
{
if (!BN_nnmod(val[0],a,m,ctx))
goto err;
aa= val[0];
}
else
aa=a;
if (BN_is_zero(aa))
{
BN_zero(rr);
ret = 1;
goto err;
}
if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
window = BN_window_bits_for_exponent_size(bits);
if (window > 1)
{
if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
j=1<<(window-1);
for (i=1; i<j; i++)
{
if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
!BN_mod_mul_montgomery(val[i],val[i-1],
d,mont,ctx))
goto err;
}
}
start=1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
wvalue=0; /* The 'value' of the window */
wstart=bits-1; /* The top bit of the window */
wend=0; /* The bottom bit of the window */
if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
for (;;)
{
if (BN_is_bit_set(p,wstart) == 0)
{
if (!start)
{
if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
goto err;
}
if (wstart == 0) break;
wstart--;
continue;
}
/* We now have wstart on a 'set' bit, we now need to work out
* how bit a window to do. To do this we need to scan
* forward until the last set bit before the end of the
* window */
j=wstart;
wvalue=1;
wend=0;
for (i=1; i<window; i++)
{
if (wstart-i < 0) break;
if (BN_is_bit_set(p,wstart-i))
{
wvalue<<=(i-wend);
wvalue|=1;
wend=i;
}
}
/* wend is the size of the current window */
j=wend+1;
/* add the 'bytes above' */
if (!start)
for (i=0; i<j; i++)
{
if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
goto err;
/* move the 'window' down further */
wstart-=wend+1;
wvalue=0;
start=0;
if (wstart < 0) break;
}
if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
ret=1;
err:
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
BN_CTX_end(ctx);
bn_check_top(rr);
return(ret);
}
/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
* so that accessing any of these table values shows the same access pattern as far
* as cache lines are concerned. The following functions are used to transfer a BIGNUM
* from/to that table. */
static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
{
size_t i, j;
if (top > b->top)
top = b->top; /* this works because 'buf' is explicitly zeroed */
for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
{
buf[j] = ((unsigned char*)b->d)[i];
}
return 1;
}
static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
{
size_t i, j;
if (bn_wexpand(b, top) == NULL)
return 0;
for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
{
((unsigned char*)b->d)[i] = buf[j];
}
b->top = top;
bn_correct_top(b);
return 1;
}
/* Given a pointer value, compute the next address that is a cache line multiple. */
#define MOD_EXP_CTIME_ALIGN(x_) \
((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
/* This variant of BN_mod_exp_mont() uses fixed windows and the special
* precomputation memory layout to limit data-dependency to a minimum
* to protect secret exponents (cf. the hyper-threading timing attacks
* pointed out by Colin Percival,
* http://www.daemonology.net/hyperthreading-considered-harmful/)
*/
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 i,bits,ret=0,window,wvalue;
int top;
BN_MONT_CTX *mont=NULL;
int numPowers;
unsigned char *powerbufFree=NULL;
int powerbufLen = 0;
unsigned char *powerbuf=NULL;
BIGNUM tmp, am;
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
top = m->top;
if (!(m->d[0] & 1))
{
BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
return(0);
}
bits=BN_num_bits(p);
if (bits == 0)
{
ret = BN_one(rr);
return ret;
}
BN_CTX_start(ctx);
/* Allocate a montgomery context if it was not supplied by the caller.
* If this is not done, things will break in the montgomery part.
*/
if (in_mont != NULL)
mont=in_mont;
else
{
if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
}
/* Get the window size to use with size of p. */
window = BN_window_bits_for_ctime_exponent_size(bits);
#if defined(OPENSSL_BN_ASM_MONT5)
if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
#endif
/* Allocate a buffer large enough to hold all of the pre-computed
* powers of am, am itself and tmp.
*/
numPowers = 1 << window;
powerbufLen = sizeof(m->d[0])*(top*numPowers +
((2*top)>numPowers?(2*top):numPowers));
#ifdef alloca
if (powerbufLen < 3072)
powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
else
#endif
if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
goto err;
powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
memset(powerbuf, 0, powerbufLen);
#ifdef alloca
if (powerbufLen < 3072)
powerbufFree = NULL;
#endif
/* lay down tmp and am right after powers table */
tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
am.d = tmp.d + top;
tmp.top = am.top = 0;
tmp.dmax = am.dmax = top;
tmp.neg = am.neg = 0;
tmp.flags = am.flags = BN_FLG_STATIC_DATA;
/* prepare a^0 in Montgomery domain */
#if 1
if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
#else
tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
for (i=1;i<top;i++)
tmp.d[i] = (~m->d[i])&BN_MASK2;
tmp.top = top;
#endif
/* prepare a^1 in Montgomery domain */
if (a->neg || BN_ucmp(a,m) >= 0)
{
if (!BN_mod(&am,a,m,ctx)) goto err;
if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
}
else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
#if defined(OPENSSL_BN_ASM_MONT5)
/* This optimization uses ideas from http://eprint.iacr.org/2011/239,
* specifically optimization of cache-timing attack countermeasures
* and pre-computation optimization. */
/* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
* 512-bit RSA is hardly relevant, we omit it to spare size... */
if (window==5 && top>1)
{
void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
const void *table,const BN_ULONG *np,
const BN_ULONG *n0,int num,int power);
void bn_scatter5(const BN_ULONG *inp,size_t num,
void *table,size_t power);
void bn_gather5(BN_ULONG *out,size_t num,
void *table,size_t power);
BN_ULONG *np=mont->N.d, *n0=mont->n0;
/* BN_to_montgomery can contaminate words above .top
* [in BN_DEBUG[_DEBUG] build]... */
for (i=am.top; i<top; i++) am.d[i]=0;
for (i=tmp.top; i<top; i++) tmp.d[i]=0;
bn_scatter5(tmp.d,top,powerbuf,0);
bn_scatter5(am.d,am.top,powerbuf,1);
bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
bn_scatter5(tmp.d,top,powerbuf,2);
#if 0
for (i=3; i<32; i++)
{
/* Calculate a^i = a^(i-1) * a */
bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
bn_scatter5(tmp.d,top,powerbuf,i);
}
#else
/* same as above, but uses squaring for 1/2 of operations */
for (i=4; i<32; i*=2)
{
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_scatter5(tmp.d,top,powerbuf,i);
}
for (i=3; i<8; i+=2)
{
int j;
bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
bn_scatter5(tmp.d,top,powerbuf,i);
for (j=2*i; j<32; j*=2)
{
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_scatter5(tmp.d,top,powerbuf,j);
}
}
for (; i<16; i+=2)
{
bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
bn_scatter5(tmp.d,top,powerbuf,i);
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_scatter5(tmp.d,top,powerbuf,2*i);
}
for (; i<32; i+=2)
{
bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
bn_scatter5(tmp.d,top,powerbuf,i);
}
#endif
bits--;
for (wvalue=0, i=bits%5; i>=0; i--,bits--)
wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
bn_gather5(tmp.d,top,powerbuf,wvalue);
/* Scan the exponent one window at a time starting from the most
* significant bits.
*/
while (bits >= 0)
{
for (wvalue=0, i=0; i<5; i++,bits--)
wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
}
tmp.top=top;
bn_correct_top(&tmp);
}
else
#endif
{
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
/* If the window size is greater than 1, then calculate
* val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
* (even powers could instead be computed as (a^(i/2))^2
* to use the slight performance advantage of sqr over mul).
*/
if (window > 1)
{
if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
for (i=3; i<numPowers; i++)
{
/* Calculate a^i = a^(i-1) * a */
if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
goto err;
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
}
}
bits--;
for (wvalue=0, i=bits%window; i>=0; i--,bits--)
wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
/* Scan the exponent one window at a time starting from the most
* significant bits.
*/
while (bits >= 0)
{
wvalue=0; /* The 'value' of the window */
/* Scan the window, squaring the result as we go */
for (i=0; i<window; i++,bits--)
{
if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
}
/* Fetch the appropriate pre-computed value from the pre-buf */
if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
/* Multiply the result into the intermediate result */
if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
}
}
/* Convert the final result from montgomery to standard format */
if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
ret=1;
err:
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
if (powerbuf!=NULL)
{
OPENSSL_cleanse(powerbuf,powerbufLen);
if (powerbufFree) OPENSSL_free(powerbufFree);
}
BN_CTX_end(ctx);
return(ret);
}
int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
BN_MONT_CTX *mont = NULL;
int b, bits, ret=0;
int r_is_one;
BN_ULONG w, next_w;
BIGNUM *d, *r, *t;
BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
(BN_mul_word(r, (w)) && \
(/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
(BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
/* BN_MOD_MUL_WORD is only used with 'w' large,
* so the BN_ucmp test is probably more overhead
* than always using BN_mod (which uses BN_copy if
* a similar test returns true). */
/* We can use BN_mod and do not need BN_nnmod because our
* accumulator is never negative (the result of BN_mod does
* not depend on the sign of the modulus).
*/
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
{
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m))
{
BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
return(0);
}
if (m->top == 1)
a %= m->d[0]; /* make sure that 'a' is reduced */
bits = BN_num_bits(p);
if (bits == 0)
{
/* x**0 mod 1 is still zero. */
if (BN_is_one(m))
{
ret = 1;
BN_zero(rr);
}
else
ret = BN_one(rr);
return ret;
}
if (a == 0)
{
BN_zero(rr);
ret = 1;
return ret;
}
BN_CTX_start(ctx);
d = BN_CTX_get(ctx);
r = BN_CTX_get(ctx);
t = BN_CTX_get(ctx);
if (d == NULL || r == NULL || t == NULL) goto err;
if (in_mont != NULL)
mont=in_mont;
else
{
if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
}
r_is_one = 1; /* except for Montgomery factor */
/* bits-1 >= 0 */
/* The result is accumulated in the product r*w. */
w = a; /* bit 'bits-1' of 'p' is always set */
for (b = bits-2; b >= 0; b--)
{
/* First, square r*w. */
next_w = w*w;
if ((next_w/w) != w) /* overflow */
{
if (r_is_one)
{
if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
r_is_one = 0;
}
else
{
if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
}
next_w = 1;
}
w = next_w;
if (!r_is_one)
{
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
}
/* Second, multiply r*w by 'a' if exponent bit is set. */
if (BN_is_bit_set(p, b))
{
next_w = w*a;
if ((next_w/a) != w) /* overflow */
{
if (r_is_one)
{
if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
r_is_one = 0;
}
else
{
if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
}
next_w = a;
}
w = next_w;
}
}
/* Finally, set r:=r*w. */
if (w != 1)
{
if (r_is_one)
{
if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
r_is_one = 0;
}
else
{
if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
}
}
if (r_is_one) /* can happen only if a == 1*/
{
if (!BN_one(rr)) goto err;
}
else
{
if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
}
ret = 1;
err:
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
BN_CTX_end(ctx);
bn_check_top(rr);
return(ret);
}
/* The old fallback, simple version :-) */
int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx)
{
int i,j,bits,ret=0,wstart,wend,window,wvalue;
int start=1;
BIGNUM *d;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
{
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return -1;
}
bits=BN_num_bits(p);
if (bits == 0)
{
ret = BN_one(r);
return ret;
}
BN_CTX_start(ctx);
d = BN_CTX_get(ctx);
val[0] = BN_CTX_get(ctx);
if(!d || !val[0]) goto err;
if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
if (BN_is_zero(val[0]))
{
BN_zero(r);
ret = 1;
goto err;
}
window = BN_window_bits_for_exponent_size(bits);
if (window > 1)
{
if (!BN_mod_mul(d,val[0],val[0],m,ctx))
goto err; /* 2 */
j=1<<(window-1);
for (i=1; i<j; i++)
{
if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
!BN_mod_mul(val[i],val[i-1],d,m,ctx))
goto err;
}
}
start=1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
wvalue=0; /* The 'value' of the window */
wstart=bits-1; /* The top bit of the window */
wend=0; /* The bottom bit of the window */
if (!BN_one(r)) goto err;
for (;;)
{
if (BN_is_bit_set(p,wstart) == 0)
{
if (!start)
if (!BN_mod_mul(r,r,r,m,ctx))
goto err;
if (wstart == 0) break;
wstart--;
continue;
}
/* We now have wstart on a 'set' bit, we now need to work out
* how bit a window to do. To do this we need to scan
* forward until the last set bit before the end of the
* window */
j=wstart;
wvalue=1;
wend=0;
for (i=1; i<window; i++)
{
if (wstart-i < 0) break;
if (BN_is_bit_set(p,wstart-i))
{
wvalue<<=(i-wend);
wvalue|=1;
wend=i;
}
}
/* wend is the size of the current window */
j=wend+1;
/* add the 'bytes above' */
if (!start)
for (i=0; i<j; i++)
{
if (!BN_mod_mul(r,r,r,m,ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
goto err;
/* move the 'window' down further */
wstart-=wend+1;
wvalue=0;
start=0;
if (wstart < 0) break;
}
ret=1;
err:
BN_CTX_end(ctx);
bn_check_top(r);
return(ret);
}