1 /* crypto/bn/bn_kron.c */
2 /* ====================================================================
3 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
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33 * "This product includes software developed by the OpenSSL Project
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48 * ====================================================================
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com). This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
59 /* least significant word */
60 #define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
62 /* Returns -2 for errors because both -1 and 0 are valid results. */
63 EXPORT_C int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
66 int ret = -2; /* avoid 'uninitialized' warning */
69 /* In 'tab', only odd-indexed entries are relevant:
70 * For any odd BIGNUM n,
72 * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
73 * Note that the sign of n does not matter.
75 static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1};
83 if (B == NULL) goto end;
91 * Kronecker symbol, imlemented according to Henri Cohen,
92 * "A Course in Computational Algebraic Number Theory"
100 ret = BN_abs_is_word(A, 1);
104 /* Cohen's step 2: */
106 if (!BN_is_odd(A) && !BN_is_odd(B))
112 /* now B is non-zero */
114 while (!BN_is_bit_set(B, i))
116 err = !BN_rshift(B, B, i);
121 /* (thus B was even, thus A must be odd!) */
123 /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
124 ret = tab[BN_lsw(A) & 7];
139 /* now B is positive and odd, so what remains to be done is
140 * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */
144 /* Cohen's step 3: */
146 /* B is positive and odd */
150 ret = BN_is_one(B) ? ret : 0;
154 /* now A is non-zero */
156 while (!BN_is_bit_set(A, i))
158 err = !BN_rshift(A, A, i);
163 /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */
164 ret = ret * tab[BN_lsw(B) & 7];
167 /* Cohen's step 4: */
168 /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */
169 if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2)
172 /* (A, B) := (B mod |A|, |A|) */
173 err = !BN_nnmod(B, B, A, ctx);
175 tmp = A; A = B; B = tmp;