-/* 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).
+/*
+ * Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.
*
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
*/
-#include "cryptlib.h"
+#include "internal/cryptlib.h"
#include "bn_lcl.h"
/* least significant word */
/* 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, implemented 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;
+}
projects / openssl.git / blobdiff