3 /* crypto/bn/bn_kron.c */
4 /* ====================================================================
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50 * ====================================================================
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
61 /* least significant word */
62 #define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
64 /* Returns -2 for errors because both -1 and 0 are valid results. */
65 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
71 /* In 'tab', only odd-indexed entries are relevant:
72 * For any odd BIGNUM n,
74 * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
75 * Note that the sign of n does not matter.
77 static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1};
82 if (B == NULL) goto end;
90 * Kronecker symbol, imlemented according to Henri Cohen,
91 * "A Course in Computational Algebraic Number Theory"
99 ret = BN_abs_is_word(A, 1);
103 /* Cohen's step 2: */
105 if (!BN_is_odd(A) && !BN_is_odd(B))
111 /* now B is non-zero */
113 while (!BN_is_bit_set(B, i))
115 err = !BN_rshift(B, B, i);
120 /* (thus B was even, thus A must be odd!) */
122 /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
123 ret = tab[BN_lsw(A) & 7];
138 /* now B is positive and odd, so what remains to be done is
139 * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */
143 /* Cohen's step 3: */
145 /* B is positive and odd */
149 ret = BN_is_one(B) ? ret : 0;
153 /* now A is non-zero */
155 while (!BN_is_bit_set(A, i))
157 err = !BN_rshift(A, A, i);
162 /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */
163 ret = ret * tab[BN_lsw(B) & 7];
166 /* Cohen's step 4: */
167 /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */
168 if (BN_lsw(A) & BN_lsw(B) & 2)
171 /* (A, B) := (B mod |A|, |A|) */
172 err = !BN_nnmod(B, B, A, ctx);
174 tmp = A; A = B; B = tmp;