OpenSSL 0.9.7 stable 2002 05 08 merge

1 files changed, 309 insertions, 29 deletions

diff --git a/src/lib/libcrypto/bn/bn_gcd.c b/src/lib/libcrypto/bn/bn_gcd.c
index 398207196b..7649f63fd2 100644
--- a/src/lib/libcrypto/bn/bn_gcd.c
+++ b/src/lib/libcrypto/bn/bn_gcd.c
@@ -55,14 +55,66 @@
  * 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;
@@ -77,6 +129,8 @@ int BN_gcd(BIGNUM *r, BIGNUM *in_a, BIGNUM *in_b, BN_CTX *ctx)
 
         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);
@@ -97,10 +151,10 @@ static BIGNUM *euclid(BIGNUM *a, BIGNUM *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))
                         {
@@ -133,7 +187,9 @@ static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
                                 shifts++;
                                 }
                         }
+                /* 0 <= b <= a */
                 }
+
         if (shifts)
                 {
                 if (!BN_lshift(a,a,shifts)) goto err;
@@ -143,11 +199,13 @@ err:
         return(NULL);
         }
 
+
 /* solves ax == 1 (mod n) */
-BIGNUM *BN_mod_inverse(BIGNUM *in, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
+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);
@@ -160,7 +218,8 @@ BIGNUM *BN_mod_inverse(BIGNUM *in, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
         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();
@@ -168,34 +227,256 @@ BIGNUM *BN_mod_inverse(BIGNUM *in, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
                 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) <= (BN_BITS <= 32 ? 450 : 2048)))
                 {
-                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 (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))
-                { 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);
@@ -207,4 +488,3 @@ err:
         BN_CTX_end(ctx);
         return(ret);
         }
-