diff options
Diffstat (limited to 'openssl/crypto/bn/bn_gcd.c')
| -rw-r--r-- | openssl/crypto/bn/bn_gcd.c | 1117 |
1 files changed, 581 insertions, 536 deletions
diff --git a/openssl/crypto/bn/bn_gcd.c b/openssl/crypto/bn/bn_gcd.c index a808f5317..97c55ab72 100644 --- a/openssl/crypto/bn/bn_gcd.c +++ b/openssl/crypto/bn/bn_gcd.c @@ -5,21 +5,21 @@ * 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: @@ -34,10 +34,10 @@ * 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 + * 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 @@ -49,7 +49,7 @@ * 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 @@ -63,7 +63,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * 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 @@ -115,541 +115,586 @@ 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); - } +{ + 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); - } - +{ + 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); + 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. + 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); - } + 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); +} |