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[openssl.git] / crypto / bn / bn_gcd.c
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  * 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"
 
@@ -77,6 +131,8 @@ int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const 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);
@@ -86,6 +142,7 @@ int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
        ret=1;
 err:
        BN_CTX_end(ctx);
+       bn_check_top(r);
        return(ret);
        }
 
@@ -97,10 +154,10 @@ 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))
                        {
@@ -133,22 +190,348 @@ static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
                                shifts++;
                                }
                        }
+               /* 0 <= b <= a */
                }
+
        if (shifts)
                {
                if (!BN_lshift(a,a,shifts)) goto err;
                }
+       bn_check_top(a);
        return(a);
 err:
        return(NULL);
        }
 
+
 /* solves ax == 1 (mod n) */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+        const 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 *rv;
+       int noinv;
+       rv = int_bn_mod_inverse(in, a, n, ctx, &noinv);
+       if (noinv)
+               BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
+       return rv;
+       }
+
+BIGNUM *int_bn_mod_inverse(BIGNUM *in,
+       const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *pnoinv)
+       {
+       BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
+       BIGNUM *ret=NULL;
+       int sign;
+
+       if (pnoinv)
+               *pnoinv = 0;
+
+       if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))
+               {
+               return BN_mod_inverse_no_branch(in, a, n, ctx);
+               }
+
+       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 (in == NULL)
+               R=BN_new();
+       else
+               R=in;
+       if (R == 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(R,Y)) goto err;
+                       }
+               else
+                       {
+                       if (!BN_nnmod(R,Y,n,ctx)) goto err;
+                       }
+               }
+       else
+               {
+               if (pnoinv)
+                       *pnoinv = 1;
+               goto err;
+               }
+       ret=R;
+err:
+       if ((ret == NULL) && (in == NULL)) BN_free(R);
+       BN_CTX_end(ctx);
+       bn_check_top(ret);
+       return(ret);
+       }
+
+
+/* BN_mod_inverse_no_branch is a special version of BN_mod_inverse. 
+ * It does not contain branches that may leak sensitive information.
+ */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+       const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
+       {
+       BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
+       BIGNUM local_A, local_B;
+       BIGNUM *pA, *pB;
+       BIGNUM *ret=NULL;
        int sign;
 
        bn_check_top(a);
@@ -161,7 +544,8 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
        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();
@@ -169,43 +553,127 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
                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))
+               {
+               /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+                * BN_div_no_branch will be called eventually.
+                */
+               pB = &local_B;
+               BN_with_flags(pB, B, BN_FLG_CONSTTIME); 
+               if (!BN_nnmod(B, pB, 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_div(D,M,A,B,ctx)) goto err;
-               T=A;
+               BIGNUM *tmp;
+               
+               /*-
+                *      0 < B < A,
+                * (*) -sign*X*a  ==  B   (mod |n|),
+                *      sign*Y*a  ==  A   (mod |n|)
+                */
+
+               /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+                * BN_div_no_branch will be called eventually.
+                */
+               pA = &local_A;
+               BN_with_flags(pA, A, BN_FLG_CONSTTIME); 
+               
+               /* (D, M) := (A/B, A%B) ... */          
+               if (!BN_div(D,M,pA,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;
-               /* T has a struct, M does not */
+               /* ... 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.
+                */
+                       
+               if (!BN_mul(tmp,D,X,ctx)) goto err;
+               if (!BN_add(tmp,tmp,Y)) goto err;
 
-               if (!BN_mul(T,D,X,ctx)) goto err;
-               if (!BN_add(T,T,Y)) goto err;
-               M=Y;
+               M=Y; /* keep the BIGNUM object, the value does not matter */
                Y=X;
-               X=T;
-               sign= -sign;
+               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);
+               BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE);
                goto err;
                }
        ret=R;
 err:
        if ((ret == NULL) && (in == NULL)) BN_free(R);
        BN_CTX_end(ctx);
+       bn_check_top(ret);
        return(ret);
        }
-