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openssl/crypto/bn/bn_exp.c

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/* 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 <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
#define TABLE_SIZE 32
/* slow but works */
int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
{
BIGNUM *t;
int r=0;
bn_check_top(a);
bn_check_top(b);
bn_check_top(m);
BN_CTX_start(ctx);
if ((t = BN_CTX_get(ctx)) == NULL) goto err;
if (a == b)
{ if (!BN_sqr(t,a,ctx)) goto err; }
else
{ if (!BN_mul(t,a,b,ctx)) goto err; }
if (!BN_mod(ret,t,m,ctx)) goto err;
r=1;
err:
BN_CTX_end(ctx);
return(r);
}
/* this one works - simple but works */
int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx)
{
int i,bits,ret=0;
BIGNUM *v,*rr;
BN_CTX_start(ctx);
if ((r == a) || (r == p))
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);
BN_CTX_end(ctx);
return(ret);
}
int BN_mod_exp(BIGNUM *r, 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);
#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))
{
if (a->top == 1)
{
BN_ULONG A = a->d[0];
ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
}
else
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)
{
BN_one(r);
return(1);
}
BN_CTX_start(ctx);
if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
BN_RECP_CTX_init(&recp);
if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
BN_init(&(val[0]));
ts=1;
if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
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, 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;
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)
{
BN_one(rr);
return(1);
}
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 (BN_ucmp(a,m) >= 0)
{
if (!BN_mod(&(val[0]),a,m,ctx))
goto err;
aa= &(val[0]);
}
else
aa=a;
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). */
#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->d[0] & 1))
{
BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
return(0);
}
bits = BN_num_bits(p);
if (bits == 0)
{
BN_one(rr);
return(1);
}
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, BIGNUM *a, BIGNUM *p, 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)
{
BN_one(r);
return(1);
}
BN_CTX_start(ctx);
if ((d = BN_CTX_get(ctx)) == NULL) goto err;
BN_init(&(val[0]));
ts=1;
if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
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);
}
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