--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ssl/libcrypto/src/crypto/bn/bn_gcd.c Fri Jun 04 16:20:51 2010 +0100
@@ -0,0 +1,653 @@
+/* crypto/bn/bn_gcd.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) 1998-2001 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 "cryptlib.h"
+#include "bn_lcl.h"
+
+static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
+
+EXPORT_C int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
+ {
+ BIGNUM *a,*b,*t;
+ int ret=0;
+
+ bn_check_top(in_a);
+ bn_check_top(in_b);
+
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+ if (a == NULL || b == NULL) goto err;
+
+ 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);
+ if (t == NULL) goto err;
+
+ if (BN_copy(r,t) == NULL) goto err;
+ ret=1;
+err:
+ BN_CTX_end(ctx);
+ bn_check_top(r);
+ return(ret);
+ }
+
+static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
+ {
+ BIGNUM *t;
+ int shifts=0;
+
+ bn_check_top(a);
+ bn_check_top(b);
+
+ /* 0 <= b <= a */
+ while (!BN_is_zero(b))
+ {
+ /* 0 < b <= a */
+
+ if (BN_is_odd(a))
+ {
+ if (BN_is_odd(b))
+ {
+ if (!BN_sub(a,a,b)) goto err;
+ if (!BN_rshift1(a,a)) goto err;
+ if (BN_cmp(a,b) < 0)
+ { t=a; a=b; b=t; }
+ }
+ else /* a odd - b even */
+ {
+ if (!BN_rshift1(b,b)) goto err;
+ if (BN_cmp(a,b) < 0)
+ { t=a; a=b; b=t; }
+ }
+ }
+ else /* a is even */
+ {
+ if (BN_is_odd(b))
+ {
+ if (!BN_rshift1(a,a)) goto err;
+ if (BN_cmp(a,b) < 0)
+ { t=a; a=b; b=t; }
+ }
+ else /* a even - b even */
+ {
+ if (!BN_rshift1(a,a)) goto err;
+ if (!BN_rshift1(b,b)) goto err;
+ 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);
+EXPORT_C BIGNUM *BN_mod_inverse(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
+ {
+ BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
+ BIGNUM *ret=NULL;
+ int sign;
+ 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
+ {
+ BNerr(BN_F_BN_MOD_INVERSE,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);
+ }
+
+
+/* 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);
+ 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))
+ {
+ /* 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))
+ {
+ 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;
+ /* ... 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;
+
+ 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
+ {
+ 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);
+ }