Index: openssl/crypto/bn/bn_gcd.c |
diff --git a/openssl/crypto/bn/bn_gcd.c b/openssl/crypto/bn/bn_gcd.c |
deleted file mode 100644 |
index a808f53178fb830572a6d8c2edb4eabb5063c844..0000000000000000000000000000000000000000 |
--- a/openssl/crypto/bn/bn_gcd.c |
+++ /dev/null |
@@ -1,655 +0,0 @@ |
-/* 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); |
- |
-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); |
- |
-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); |
- } |