--- /dev/null
+/* crypto/bn/bn_kron.c */
+/* ====================================================================
+ * Copyright (c) 1998-2000 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 "cryptlib.h"
+#include "bn_lcl.h"
+
+/* least significant word */
+#define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0])
+
+/* 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;
+ }
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