diff options
Diffstat (limited to 'openssl/crypto/bn/bn_kron.c')
| -rw-r--r-- | openssl/crypto/bn/bn_kron.c | 246 |
1 files changed, 124 insertions, 122 deletions
diff --git a/openssl/crypto/bn/bn_kron.c b/openssl/crypto/bn/bn_kron.c index 740359b75..88d731ac7 100644 --- a/openssl/crypto/bn/bn_kron.c +++ b/openssl/crypto/bn/bn_kron.c @@ -7,7 +7,7 @@ * 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 @@ -61,124 +61,126 @@ /* Returns -2 for errors because both -1 and 0 are valid results. */ int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - int i; - int ret = -2; /* avoid 'uninitialized' warning */ - int err = 0; - BIGNUM *A, *B, *tmp; - /* In 'tab', only odd-indexed entries are relevant: - * For any odd BIGNUM n, - * tab[BN_lsw(n) & 7] - * is $(-1)^{(n^2-1)/8}$ (using TeX notation). - * Note that the sign of n does not matter. - */ - static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1}; - - bn_check_top(a); - bn_check_top(b); - - BN_CTX_start(ctx); - A = BN_CTX_get(ctx); - B = BN_CTX_get(ctx); - if (B == NULL) goto end; - - err = !BN_copy(A, a); - if (err) goto end; - err = !BN_copy(B, b); - if (err) goto end; - - /* - * Kronecker symbol, imlemented according to Henri Cohen, - * "A Course in Computational Algebraic Number Theory" - * (algorithm 1.4.10). - */ - - /* Cohen's step 1: */ - - if (BN_is_zero(B)) - { - ret = BN_abs_is_word(A, 1); - goto end; - } - - /* Cohen's step 2: */ - - if (!BN_is_odd(A) && !BN_is_odd(B)) - { - ret = 0; - goto end; - } - - /* now B is non-zero */ - i = 0; - while (!BN_is_bit_set(B, i)) - i++; - err = !BN_rshift(B, B, i); - if (err) goto end; - if (i & 1) - { - /* i is odd */ - /* (thus B was even, thus A must be odd!) */ - - /* set 'ret' to $(-1)^{(A^2-1)/8}$ */ - ret = tab[BN_lsw(A) & 7]; - } - else - { - /* i is even */ - ret = 1; - } - - if (B->neg) - { - B->neg = 0; - if (A->neg) - ret = -ret; - } - - /* now B is positive and odd, so what remains to be done is - * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */ - - while (1) - { - /* Cohen's step 3: */ - - /* B is positive and odd */ - - if (BN_is_zero(A)) - { - ret = BN_is_one(B) ? ret : 0; - goto end; - } - - /* now A is non-zero */ - i = 0; - while (!BN_is_bit_set(A, i)) - i++; - err = !BN_rshift(A, A, i); - if (err) goto end; - if (i & 1) - { - /* i is odd */ - /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ - ret = ret * tab[BN_lsw(B) & 7]; - } - - /* Cohen's step 4: */ - /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ - if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) - ret = -ret; - - /* (A, B) := (B mod |A|, |A|) */ - err = !BN_nnmod(B, B, A, ctx); - if (err) goto end; - tmp = A; A = B; B = tmp; - tmp->neg = 0; - } -end: - BN_CTX_end(ctx); - if (err) - return -2; - else - return ret; - } +{ + int i; + int ret = -2; /* avoid 'uninitialized' warning */ + int err = 0; + BIGNUM *A, *B, *tmp; + /*- + * In 'tab', only odd-indexed entries are relevant: + * For any odd BIGNUM n, + * tab[BN_lsw(n) & 7] + * is $(-1)^{(n^2-1)/8}$ (using TeX notation). + * Note that the sign of n does not matter. + */ + static const int tab[8] = { 0, 1, 0, -1, 0, -1, 0, 1 }; + + bn_check_top(a); + bn_check_top(b); + + BN_CTX_start(ctx); + A = BN_CTX_get(ctx); + B = BN_CTX_get(ctx); + if (B == NULL) + goto end; + + err = !BN_copy(A, a); + if (err) + goto end; + err = !BN_copy(B, b); + if (err) + goto end; + + /* + * Kronecker symbol, imlemented according to Henri Cohen, + * "A Course in Computational Algebraic Number Theory" + * (algorithm 1.4.10). + */ + + /* Cohen's step 1: */ + + if (BN_is_zero(B)) { + ret = BN_abs_is_word(A, 1); + goto end; + } + + /* Cohen's step 2: */ + + if (!BN_is_odd(A) && !BN_is_odd(B)) { + ret = 0; + goto end; + } + + /* now B is non-zero */ + i = 0; + while (!BN_is_bit_set(B, i)) + i++; + err = !BN_rshift(B, B, i); + if (err) + goto end; + if (i & 1) { + /* i is odd */ + /* (thus B was even, thus A must be odd!) */ + + /* set 'ret' to $(-1)^{(A^2-1)/8}$ */ + ret = tab[BN_lsw(A) & 7]; + } else { + /* i is even */ + ret = 1; + } + + if (B->neg) { + B->neg = 0; + if (A->neg) + ret = -ret; + } + + /* + * now B is positive and odd, so what remains to be done is to compute + * the Jacobi symbol (A/B) and multiply it by 'ret' + */ + + while (1) { + /* Cohen's step 3: */ + + /* B is positive and odd */ + + if (BN_is_zero(A)) { + ret = BN_is_one(B) ? ret : 0; + goto end; + } + + /* now A is non-zero */ + i = 0; + while (!BN_is_bit_set(A, i)) + i++; + err = !BN_rshift(A, A, i); + if (err) + goto end; + if (i & 1) { + /* i is odd */ + /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ + ret = ret * tab[BN_lsw(B) & 7]; + } + + /* Cohen's step 4: */ + /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ + if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) + ret = -ret; + + /* (A, B) := (B mod |A|, |A|) */ + err = !BN_nnmod(B, B, A, ctx); + if (err) + goto end; + tmp = A; + A = B; + B = tmp; + tmp->neg = 0; + } + end: + BN_CTX_end(ctx); + if (err) + return -2; + else + return ret; +} |