* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
+/* ====================================================================
+ * Copyright (c) 1998-2001 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"
static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
-int BN_gcd(BIGNUM *r, BIGNUM *in_a, BIGNUM *in_b, BN_CTX *ctx)
+int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
{
BIGNUM *a,*b,*t;
int ret=0;
if (BN_copy(a,in_a) == NULL) goto err;
if (BN_copy(b,in_b) == NULL) goto err;
+ a->neg = 0;
+ b->neg = 0;
if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; }
t=euclid(a,b);
bn_check_top(a);
bn_check_top(b);
- for (;;)
+ /* 0 <= b <= a */
+ while (!BN_is_zero(b))
{
- if (BN_is_zero(b))
- break;
+ /* 0 < b <= a */
if (BN_is_odd(a))
{
shifts++;
}
}
+ /* 0 <= b <= a */
}
+
if (shifts)
{
if (!BN_lshift(a,a,shifts)) goto err;
return(NULL);
}
+
/* solves ax == 1 (mod n) */
BIGNUM *BN_mod_inverse(BIGNUM *in,
const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
{
- BIGNUM *A,*B,*X,*Y,*M,*D,*R=NULL;
- BIGNUM *T,*ret=NULL;
+ BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
+ BIGNUM *ret=NULL;
int sign;
bn_check_top(a);
D = BN_CTX_get(ctx);
M = BN_CTX_get(ctx);
Y = BN_CTX_get(ctx);
- if (Y == NULL) goto err;
+ T = BN_CTX_get(ctx);
+ if (T == NULL) goto err;
if (in == NULL)
R=BN_new();
R=in;
if (R == NULL) goto err;
- BN_zero(X);
- BN_one(Y);
- if (BN_copy(A,a) == NULL) goto err;
- if (BN_copy(B,n) == NULL) goto err;
- sign=1;
+ 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|).
+ */
- while (!BN_is_zero(B))
+ if (BN_is_odd(n) && (BN_num_bits(n) <= 400))
{
- if (!BN_div(D,M,A,B,ctx)) goto err;
- T=A;
- A=B;
- B=M;
- /* T has a struct, M does not */
-
- if (!BN_mul(T,D,X,ctx)) goto err;
- if (!BN_add(T,T,Y)) goto err;
- M=Y;
- Y=X;
- X=T;
- sign= -sign;
+ /* Binary inversion algorithm; requires odd modulus.
+ * This is faster than the general algorithm if the modulus
+ * is sufficiently small. */
+ 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))
- { if (!BN_mod(R,Y,n,ctx)) goto err; }
+ {
+ /* Y*a == 1 (mod |n|) */
+ if (!Y->neg && BN_ucmp(Y,n) < 0)
+ {
+ if (!BN_copy(R,Y)) goto err;
+ }
+ else
+ {
+ if (!BN_nnmod(R,Y,n,ctx)) goto err;
+ }
+ }
else
{
BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
BN_CTX_end(ctx);
return(ret);
}
-
projects / openssl.git / blobdiff