summaryrefslogtreecommitdiff
path: root/openssl/crypto/bn/bn_gcd.c
diff options
context:
space:
mode:
Diffstat (limited to 'openssl/crypto/bn/bn_gcd.c')
-rw-r--r--openssl/crypto/bn/bn_gcd.c654
1 files changed, 0 insertions, 654 deletions
diff --git a/openssl/crypto/bn/bn_gcd.c b/openssl/crypto/bn/bn_gcd.c
deleted file mode 100644
index 4a352119..00000000
--- a/openssl/crypto/bn/bn_gcd.c
+++ /dev/null
@@ -1,654 +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);
- }
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-09 17:09:24 +0000