c86f2054f3
locally initialising their own. NB: I've removed the "BN_clear_free()" loops for the exit-paths in some of these functions, and that may be a major part of the performance improvements we're seeing. The "free" part can be removed because we're using BN_CTX. The "clear" part OTOH can be removed because BN_CTX destruction automatically performs this task, so performing it inside functions that may be called repeatedly is wasteful. This is currently safe within openssl due to the fact that BN_CTX objects are never created for longer than a single high-level operation. However, that is only because there's currently no mechanism in openssl for thread-local storage. Beyond that, this might be an issue for applications using the bignum API directly and caching their own BN_CTX objects. The solution is to introduce a flag to BN_CTX_start() that allows its variables to be automatically sanitised on release during BN_CTX_end(). This way any higher-level function (and perhaps the application) can specify this flag in its own BN_CTX_start()/BN_CTX_end() pair, and this will cause inner-loop functions specifying the flag to be ignored so that sanitisation is handled only once back out at the higher level. I will be implementing this in the near future.
747 lines
19 KiB
C
747 lines
19 KiB
C
/* 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) 1998-2000 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).
|
|
*
|
|
*/
|
|
|
|
|
|
#include "cryptlib.h"
|
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#include "bn_lcl.h"
|
|
|
|
#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;
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((r == a) || (r == p))
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|
rr = BN_CTX_get(ctx);
|
|
else
|
|
rr = r;
|
|
if ((v = BN_CTX_get(ctx)) == 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);
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|
BN_CTX_end(ctx);
|
|
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);
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|
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
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|
#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))
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|
{
|
|
# ifdef MONT_EXP_WORD
|
|
if (a->top == 1 && !a->neg)
|
|
{
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|
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
|
|
|
|
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,ts=0;
|
|
BIGNUM *aa;
|
|
BIGNUM val[TABLE_SIZE];
|
|
BN_RECP_CTX recp;
|
|
|
|
bits=BN_num_bits(p);
|
|
|
|
if (bits == 0)
|
|
{
|
|
ret = BN_one(r);
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((aa = BN_CTX_get(ctx)) == NULL) 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;
|
|
}
|
|
|
|
BN_init(&(val[0]));
|
|
ts=1;
|
|
|
|
if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
|
|
if (BN_is_zero(&(val[0])))
|
|
{
|
|
ret = BN_zero(r);
|
|
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++)
|
|
{
|
|
BN_init(&val[i]);
|
|
if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
|
|
goto err;
|
|
}
|
|
ts=i;
|
|
}
|
|
|
|
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);
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
BN_RECP_CTX_free(&recp);
|
|
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,ts=0;
|
|
BIGNUM *d,*r;
|
|
const BIGNUM *aa;
|
|
BIGNUM val[TABLE_SIZE];
|
|
BN_MONT_CTX *mont=NULL;
|
|
|
|
bn_check_top(a);
|
|
bn_check_top(p);
|
|
bn_check_top(m);
|
|
|
|
if (!(m->d[0] & 1))
|
|
{
|
|
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);
|
|
if (d == NULL || r == NULL) 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;
|
|
}
|
|
|
|
BN_init(&val[0]);
|
|
ts=1;
|
|
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))
|
|
{
|
|
ret = BN_zero(rr);
|
|
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++)
|
|
{
|
|
BN_init(&(val[i]));
|
|
if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
|
|
goto err;
|
|
}
|
|
ts=i;
|
|
}
|
|
|
|
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);
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
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))
|
|
|
|
bn_check_top(p);
|
|
bn_check_top(m);
|
|
|
|
if (m->top == 0 || !(m->d[0] & 1))
|
|
{
|
|
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)
|
|
{
|
|
ret = BN_one(rr);
|
|
return ret;
|
|
}
|
|
if (a == 0)
|
|
{
|
|
ret = BN_zero(rr);
|
|
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);
|
|
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,ts=0;
|
|
int start=1;
|
|
BIGNUM *d;
|
|
BIGNUM val[TABLE_SIZE];
|
|
|
|
bits=BN_num_bits(p);
|
|
|
|
if (bits == 0)
|
|
{
|
|
ret = BN_one(r);
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((d = BN_CTX_get(ctx)) == NULL) goto err;
|
|
|
|
BN_init(&(val[0]));
|
|
ts=1;
|
|
if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
|
|
if (BN_is_zero(&(val[0])))
|
|
{
|
|
ret = BN_zero(r);
|
|
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++)
|
|
{
|
|
BN_init(&(val[i]));
|
|
if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
|
|
goto err;
|
|
}
|
|
ts=i;
|
|
}
|
|
|
|
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);
|
|
for (i=0; i<ts; i++)
|
|
BN_clear_free(&(val[i]));
|
|
return(ret);
|
|
}
|
|
|