diff options
Diffstat (limited to 'crypto/openssl/crypto/bn/bn_gcd.c')
| -rw-r--r-- | crypto/openssl/crypto/bn/bn_gcd.c | 338 |
1 files changed, 309 insertions, 29 deletions
diff --git a/crypto/openssl/crypto/bn/bn_gcd.c b/crypto/openssl/crypto/bn/bn_gcd.c index e8cc6c5..7649f63 100644 --- a/crypto/openssl/crypto/bn/bn_gcd.c +++ b/crypto/openssl/crypto/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; - if (!BN_zero(X)) goto err; - if (!BN_one(Y)) goto err; - 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); } - |
