-/* crypto/bn/bn_sqrt.c */
/*
- * Written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> and Bodo
- * Moeller for the OpenSSL project.
- */
-/* ====================================================================
- * 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 OpenSSL license (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"
BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
}
BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
- return (NULL);
+ return NULL;
}
if (BN_is_zero(a) || BN_is_one(a)) {
}
if (e == 2) {
- /*-
- * |p| == 5 (mod 8)
- *
- * In this case 2 is always a non-square since
- * Legendre(2,p) = (-1)^((p^2-1)/8) for any odd prime.
- * So if a really is a square, then 2*a is a non-square.
- * Thus for
- * b := (2*a)^((|p|-5)/8),
- * i := (2*a)*b^2
- * we have
- * i^2 = (2*a)^((1 + (|p|-5)/4)*2)
- * = (2*a)^((p-1)/2)
- * = -1;
- * so if we set
- * x := a*b*(i-1),
- * then
- * x^2 = a^2 * b^2 * (i^2 - 2*i + 1)
- * = a^2 * b^2 * (-2*i)
- * = a*(-i)*(2*a*b^2)
- * = a*(-i)*i
- * = a.
- *
- * (This is due to A.O.L. Atkin,
- * <URL: http://listserv.nodak.edu/scripts/wa.exe?A2=ind9211&L=nmbrthry&O=T&P=562>,
- * November 1992.)
- */
+ /*-
+ * |p| == 5 (mod 8)
+ *
+ * In this case 2 is always a non-square since
+ * Legendre(2,p) = (-1)^((p^2-1)/8) for any odd prime.
+ * So if a really is a square, then 2*a is a non-square.
+ * Thus for
+ * b := (2*a)^((|p|-5)/8),
+ * i := (2*a)*b^2
+ * we have
+ * i^2 = (2*a)^((1 + (|p|-5)/4)*2)
+ * = (2*a)^((p-1)/2)
+ * = -1;
+ * so if we set
+ * x := a*b*(i-1),
+ * then
+ * x^2 = a^2 * b^2 * (i^2 - 2*i + 1)
+ * = a^2 * b^2 * (-2*i)
+ * = a*(-i)*(2*a*b^2)
+ * = a*(-i)*i
+ * = a.
+ *
+ * (This is due to A.O.L. Atkin,
+ * <URL: http://listserv.nodak.edu/scripts/wa.exe?A2=ind9211&L=nmbrthry&O=T&P=562>,
+ * November 1992.)
+ */
/* t := 2*a */
if (!BN_mod_lshift1_quick(t, A, p))
if (!BN_set_word(y, i))
goto end;
} else {
- if (!BN_pseudo_rand(y, BN_num_bits(p), 0, 0))
+ if (!BN_priv_rand(y, BN_num_bits(p), 0, 0))
goto end;
if (BN_ucmp(y, p) >= 0) {
if (!(p->neg ? BN_add : BN_sub) (y, y, p))
end:
if (err) {
- if (ret != NULL && ret != in) {
+ if (ret != in)
BN_clear_free(ret);
- }
ret = NULL;
}
BN_CTX_end(ctx);
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