530 lines
15 KiB
C
530 lines
15 KiB
C
#include "bn.h"
|
|
|
|
#ifndef WITH_LIBCRYPTO
|
|
//FIXME Not checked on threadsafety yet; after checking please remove this line
|
|
/* 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 license 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 license
|
|
* [including the GNU Public License.]
|
|
*/
|
|
/* ====================================================================
|
|
* 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 "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);
|
|
}
|
|
|
|
|
|
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);
|
|
|
|
ret = BN_mod_exp_simple(r, a, p, m, ctx);
|
|
|
|
return (ret);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/* The old fallback, simple version :-) */
|
|
int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
|
|
BN_CTX *ctx)
|
|
{
|
|
int i, j = 0, bits, ret = 0, wstart = 0, wend = 0, window, wvalue = 0, 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. */
|
|
wstart = bits - 1; /* The top 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);
|
|
}
|
|
|
|
int
|
|
BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
|
|
{
|
|
/* like BN_mod, but returns non-negative remainder
|
|
* (i.e., 0 <= r < |d| always holds)
|
|
*/
|
|
|
|
if (!(BN_mod(r, m, d, ctx)))
|
|
return 0;
|
|
if (!r->neg)
|
|
return 1;
|
|
/* now -|d| < r < 0, so we have to set r : = r + |d| */
|
|
return (d->neg ? BN_sub : BN_add)(r, r, d);
|
|
}
|
|
|
|
/* solves ax == 1 (mod n) */
|
|
BIGNUM *
|
|
BN_mod_inverse(BIGNUM *ret, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *A, *B, *X, *Y, *M, *D, *T = NULL;
|
|
int sign;
|
|
|
|
bn_check_top(a);
|
|
bn_check_top(n);
|
|
|
|
BN_CTX_start(ctx);
|
|
A = BN_CTX_get(ctx);
|
|
B = BN_CTX_get(ctx);
|
|
X = BN_CTX_get(ctx);
|
|
D = BN_CTX_get(ctx);
|
|
M = BN_CTX_get(ctx);
|
|
Y = BN_CTX_get(ctx);
|
|
T = BN_CTX_get(ctx);
|
|
if (T == NULL) goto err;
|
|
|
|
if (ret == NULL) goto err;
|
|
|
|
BN_one(X);
|
|
BN_zero(Y);
|
|
if (BN_copy(B, a) == NULL) goto err;
|
|
if (BN_copy(A, n) == NULL) goto err;
|
|
A->neg = 0;
|
|
if (B->neg || (BN_ucmp(B, A) >= 0)) {
|
|
if (!BN_nnmod(B, B, A, ctx)) goto err;
|
|
}
|
|
sign = -1;
|
|
/* From B = a mod |n|, A = |n| it follows that
|
|
*
|
|
* 0 <= B < A,
|
|
* -sign*X*a == B (mod |n|),
|
|
* sign*Y*a == A (mod |n|).
|
|
*/
|
|
|
|
if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) {
|
|
/* Binary inversion algorithm; requires odd modulus.
|
|
* This is faster than the general algorithm if the modulus
|
|
* is sufficiently small (about 400 .. 500 bits on 32-bit
|
|
* sytems, but much more on 64-bit systems)
|
|
*/
|
|
int shift;
|
|
|
|
while (!BN_is_zero(B)) {
|
|
/*
|
|
* 0 < B < |n|,
|
|
* 0 < A <= |n|,
|
|
* (1) -sign*X*a == B (mod |n|),
|
|
* (2) sign*Y*a == A (mod |n|)
|
|
*/
|
|
|
|
/* Now divide B by the maximum possible power of two in the integers,
|
|
* and divide X by the same value mod |n|.
|
|
* When we're done, (1) still holds.
|
|
*/
|
|
shift = 0;
|
|
while (!BN_is_bit_set(B, shift)) /* note that 0 < B */ {
|
|
shift++;
|
|
|
|
if (BN_is_odd(X)) {
|
|
if (!BN_uadd(X, X, n)) goto err;
|
|
}
|
|
/* now X is even, so we can easily divide it by two */
|
|
if (!BN_rshift1(X, X)) goto err;
|
|
}
|
|
if (shift > 0) {
|
|
if (!BN_rshift(B, B, shift)) goto err;
|
|
}
|
|
|
|
|
|
/* Same for A and Y. Afterwards, (2) still holds. */
|
|
shift = 0;
|
|
while (!BN_is_bit_set(A, shift)) /* note that 0 < A */ {
|
|
shift++;
|
|
|
|
if (BN_is_odd(Y)) {
|
|
if (!BN_uadd(Y, Y, n)) goto err;
|
|
}
|
|
/* now Y is even */
|
|
if (!BN_rshift1(Y, Y)) goto err;
|
|
}
|
|
if (shift > 0) {
|
|
if (!BN_rshift(A, A, shift)) goto err;
|
|
}
|
|
|
|
/* We still have (1) and (2).
|
|
* Both A and B are odd.
|
|
* The following computations ensure that
|
|
*
|
|
* 0 <= B < |n|,
|
|
* 0 < A < |n|,
|
|
* (1) -sign*X*a == B (mod |n|),
|
|
* (2) sign*Y*a == A (mod |n|),
|
|
*
|
|
* and that either A or B is even in the next iteration.
|
|
*/
|
|
if (BN_ucmp(B, A) >= 0) {
|
|
/* -sign*(X + Y)*a == B - A (mod |n|) */
|
|
if (!BN_uadd(X, X, Y)) goto err;
|
|
/* NB: we could use BN_mod_add_quick(X, X, Y, n), but that
|
|
* actually makes the algorithm slower
|
|
*/
|
|
if (!BN_usub(B, B, A)) goto err;
|
|
} else {
|
|
/* sign*(X + Y)*a == A - B (mod |n|) */
|
|
if (!BN_uadd(Y, Y, X)) goto err;
|
|
/* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */
|
|
if (!BN_usub(A, A, B)) goto err;
|
|
}
|
|
}
|
|
} else {
|
|
/* general inversion algorithm */
|
|
|
|
while (!BN_is_zero(B)) {
|
|
BIGNUM *tmp;
|
|
|
|
/*
|
|
* 0 < B < A,
|
|
* (*) -sign*X*a == B (mod |n|),
|
|
* sign*Y*a == A (mod |n|)
|
|
*/
|
|
|
|
/* (D, M) : = (A/B, A%B) ... */
|
|
if (BN_num_bits(A) == BN_num_bits(B)) {
|
|
if (!BN_one(D)) goto err;
|
|
if (!BN_sub(M, A, B)) goto err;
|
|
} else if (BN_num_bits(A) == BN_num_bits(B) + 1) {
|
|
/* A/B is 1, 2, or 3 */
|
|
if (!BN_lshift1(T, B)) goto err;
|
|
if (BN_ucmp(A, T) < 0) {
|
|
/* A < 2*B, so D = 1 */
|
|
if (!BN_one(D)) goto err;
|
|
if (!BN_sub(M, A, B)) goto err;
|
|
} else {
|
|
/* A >= 2*B, so D = 2 or D = 3 */
|
|
if (!BN_sub(M, A, T)) goto err;
|
|
if (!BN_add(D, T, B)) goto err;
|
|
/* use D ( := 3 * B) as temp */
|
|
if (BN_ucmp(A, D) < 0) {
|
|
/* A < 3*B, so D = 2 */
|
|
if (!BN_set_word(D, 2)) goto err;
|
|
/* M ( = A - 2*B) already has the correct value */
|
|
} else {
|
|
/* only D = 3 remains */
|
|
if (!BN_set_word(D, 3)) goto err;
|
|
/* currently M = A - 2 * B,
|
|
* but we need M = A - 3 * B
|
|
*/
|
|
if (!BN_sub(M, M, B)) goto err;
|
|
}
|
|
}
|
|
} else {
|
|
if (!BN_div(D, M, A, B, ctx)) goto err;
|
|
}
|
|
|
|
/* Now
|
|
* A = D*B + M;
|
|
* thus we have
|
|
* (**) sign*Y*a == D*B + M (mod |n|).
|
|
*/
|
|
|
|
tmp = A; /* keep the BIGNUM object, the value does not matter */
|
|
|
|
/* (A, B) : = (B, A mod B) ... */
|
|
A = B;
|
|
B = M;
|
|
/* ... so we have 0 <= B < A again */
|
|
|
|
/* Since the former M is now B and the former B is now A,
|
|
* (**) translates into
|
|
* sign*Y*a == D*A + B (mod |n|),
|
|
* i.e.
|
|
* sign*Y*a - D*A == B (mod |n|).
|
|
* Similarly, (*) translates into
|
|
* -sign*X*a == A (mod |n|).
|
|
*
|
|
* Thus,
|
|
* sign*Y*a + D*sign*X*a == B (mod |n|),
|
|
* i.e.
|
|
* sign*(Y + D*X)*a == B (mod |n|).
|
|
*
|
|
* So if we set (X, Y, sign) : = (Y + D*X, X, -sign), we arrive back at
|
|
* -sign*X*a == B (mod |n|),
|
|
* sign*Y*a == A (mod |n|).
|
|
* Note that X and Y stay non-negative all the time.
|
|
*/
|
|
|
|
/* most of the time D is very small, so we can optimize tmp : = D*X+Y */
|
|
if (BN_is_one(D)) {
|
|
if (!BN_add(tmp, X, Y)) goto err;
|
|
} else {
|
|
if (BN_is_word(D, 2)) {
|
|
if (!BN_lshift1(tmp, X)) goto err;
|
|
} else if (BN_is_word(D, 4)) {
|
|
if (!BN_lshift(tmp, X, 2)) goto err;
|
|
} else if (D->top == 1) {
|
|
if (!BN_copy(tmp, X)) goto err;
|
|
if (!BN_mul_word(tmp, D->d[0])) goto err;
|
|
} else {
|
|
if (!BN_mul(tmp, D, X, ctx)) goto err;
|
|
}
|
|
if (!BN_add(tmp, tmp, Y)) goto err;
|
|
}
|
|
|
|
M = Y; /* keep the BIGNUM object, the value does not matter */
|
|
Y = X;
|
|
X = tmp;
|
|
sign = -sign;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* The while loop (Euclid's algorithm) ends when
|
|
* A == gcd(a, n);
|
|
* we have
|
|
* sign*Y*a == A (mod |n|),
|
|
* where Y is non-negative.
|
|
*/
|
|
|
|
if (sign < 0) {
|
|
if (!BN_sub(Y, n, Y)) goto err;
|
|
}
|
|
/* Now Y*a == A (mod |n|). */
|
|
|
|
|
|
if (BN_is_one(A)) {
|
|
/* Y*a == 1 (mod |n|) */
|
|
if (!Y->neg && BN_ucmp(Y, n) < 0) {
|
|
if (!BN_copy(ret, Y)) goto err;
|
|
} else {
|
|
if (!BN_nnmod(ret, Y, n, ctx)) goto err;
|
|
}
|
|
} else {
|
|
goto err;
|
|
}
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return (ret);
|
|
}
|
|
|
|
#endif
|