Initial import

1 files changed, 393 insertions, 0 deletions

diff --git a/openssl/crypto/bn/bn_sqrt.c b/openssl/crypto/bn/bn_sqrt.c
new file mode 100644
index 00000000..6beaf9e5
--- /dev/null
+++ b/openssl/crypto/bn/bn_sqrt.c
@@ -0,0 +1,393 @@
+/* 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).
+ *
+ */
+
+#include "cryptlib.h"
+#include "bn_lcl.h"
+
+
+BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) 
+/* Returns 'ret' such that
+ *      ret^2 == a (mod p),
+ * using the Tonelli/Shanks algorithm (cf. Henri Cohen, "A Course
+ * in Algebraic Computational Number Theory", algorithm 1.5.1).
+ * 'p' must be prime!
+ */
+	{
+	BIGNUM *ret = in;
+	int err = 1;
+	int r;
+	BIGNUM *A, *b, *q, *t, *x, *y;
+	int e, i, j;
+	
+	if (!BN_is_odd(p) || BN_abs_is_word(p, 1))
+		{
+		if (BN_abs_is_word(p, 2))
+			{
+			if (ret == NULL)
+				ret = BN_new();
+			if (ret == NULL)
+				goto end;
+			if (!BN_set_word(ret, BN_is_bit_set(a, 0)))
+				{
+				if (ret != in)
+					BN_free(ret);
+				return NULL;
+				}
+			bn_check_top(ret);
+			return ret;
+			}
+
+		BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
+		return(NULL);
+		}
+
+	if (BN_is_zero(a) || BN_is_one(a))
+		{
+		if (ret == NULL)
+			ret = BN_new();
+		if (ret == NULL)
+			goto end;
+		if (!BN_set_word(ret, BN_is_one(a)))
+			{
+			if (ret != in)
+				BN_free(ret);
+			return NULL;
+			}
+		bn_check_top(ret);
+		return ret;
+		}
+
+	BN_CTX_start(ctx);
+	A = BN_CTX_get(ctx);
+	b = BN_CTX_get(ctx);
+	q = BN_CTX_get(ctx);
+	t = BN_CTX_get(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	if (y == NULL) goto end;
+	
+	if (ret == NULL)
+		ret = BN_new();
+	if (ret == NULL) goto end;
+
+	/* A = a mod p */
+	if (!BN_nnmod(A, a, p, ctx)) goto end;
+
+	/* now write  |p| - 1  as  2^e*q  where  q  is odd */
+	e = 1;
+	while (!BN_is_bit_set(p, e))
+		e++;
+	/* we'll set  q  later (if needed) */
+
+	if (e == 1)
+		{
+		/* The easy case:  (|p|-1)/2  is odd, so 2 has an inverse
+		 * modulo  (|p|-1)/2,  and square roots can be computed
+		 * directly by modular exponentiation.
+		 * We have
+		 *     2 * (|p|+1)/4 == 1   (mod (|p|-1)/2),
+		 * so we can use exponent  (|p|+1)/4,  i.e.  (|p|-3)/4 + 1.
+		 */
+		if (!BN_rshift(q, p, 2)) goto end;
+		q->neg = 0;
+		if (!BN_add_word(q, 1)) goto end;
+		if (!BN_mod_exp(ret, A, q, p, ctx)) goto end;
+		err = 0;
+		goto vrfy;
+		}
+	
+	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.)
+		 */
+
+		/* t := 2*a */
+		if (!BN_mod_lshift1_quick(t, A, p)) goto end;
+
+		/* b := (2*a)^((|p|-5)/8) */
+		if (!BN_rshift(q, p, 3)) goto end;
+		q->neg = 0;
+		if (!BN_mod_exp(b, t, q, p, ctx)) goto end;
+
+		/* y := b^2 */
+		if (!BN_mod_sqr(y, b, p, ctx)) goto end;
+
+		/* t := (2*a)*b^2 - 1*/
+		if (!BN_mod_mul(t, t, y, p, ctx)) goto end;
+		if (!BN_sub_word(t, 1)) goto end;
+
+		/* x = a*b*t */
+		if (!BN_mod_mul(x, A, b, p, ctx)) goto end;
+		if (!BN_mod_mul(x, x, t, p, ctx)) goto end;
+
+		if (!BN_copy(ret, x)) goto end;
+		err = 0;
+		goto vrfy;
+		}
+	
+	/* e > 2, so we really have to use the Tonelli/Shanks algorithm.
+	 * First, find some  y  that is not a square. */
+	if (!BN_copy(q, p)) goto end; /* use 'q' as temp */
+	q->neg = 0;
+	i = 2;
+	do
+		{
+		/* For efficiency, try small numbers first;
+		 * if this fails, try random numbers.
+		 */
+		if (i < 22)
+			{
+			if (!BN_set_word(y, i)) goto end;
+			}
+		else
+			{
+			if (!BN_pseudo_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)) goto end;
+				}
+			/* now 0 <= y < |p| */
+			if (BN_is_zero(y))
+				if (!BN_set_word(y, i)) goto end;
+			}
+		
+		r = BN_kronecker(y, q, ctx); /* here 'q' is |p| */
+		if (r < -1) goto end;
+		if (r == 0)
+			{
+			/* m divides p */
+			BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
+			goto end;
+			}
+		}
+	while (r == 1 && ++i < 82);
+	
+	if (r != -1)
+		{
+		/* Many rounds and still no non-square -- this is more likely
+		 * a bug than just bad luck.
+		 * Even if  p  is not prime, we should have found some  y
+		 * such that r == -1.
+		 */
+		BNerr(BN_F_BN_MOD_SQRT, BN_R_TOO_MANY_ITERATIONS);
+		goto end;
+		}
+
+	/* Here's our actual 'q': */
+	if (!BN_rshift(q, q, e)) goto end;
+
+	/* Now that we have some non-square, we can find an element
+	 * of order  2^e  by computing its q'th power. */
+	if (!BN_mod_exp(y, y, q, p, ctx)) goto end;
+	if (BN_is_one(y))
+		{
+		BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
+		goto end;
+		}
+
+	/* Now we know that (if  p  is indeed prime) there is an integer
+	 * k,  0 <= k < 2^e,  such that
+	 *
+	 *      a^q * y^k == 1   (mod p).
+	 *
+	 * As  a^q  is a square and  y  is not,  k  must be even.
+	 * q+1  is even, too, so there is an element
+	 *
+	 *     X := a^((q+1)/2) * y^(k/2),
+	 *
+	 * and it satisfies
+	 *
+	 *     X^2 = a^q * a     * y^k
+	 *         = a,
+	 *
+	 * so it is the square root that we are looking for.
+	 */
+	
+	/* t := (q-1)/2  (note that  q  is odd) */
+	if (!BN_rshift1(t, q)) goto end;
+	
+	/* x := a^((q-1)/2) */
+	if (BN_is_zero(t)) /* special case: p = 2^e + 1 */
+		{
+		if (!BN_nnmod(t, A, p, ctx)) goto end;
+		if (BN_is_zero(t))
+			{
+			/* special case: a == 0  (mod p) */
+			BN_zero(ret);
+			err = 0;
+			goto end;
+			}
+		else
+			if (!BN_one(x)) goto end;
+		}
+	else
+		{
+		if (!BN_mod_exp(x, A, t, p, ctx)) goto end;
+		if (BN_is_zero(x))
+			{
+			/* special case: a == 0  (mod p) */
+			BN_zero(ret);
+			err = 0;
+			goto end;
+			}
+		}
+
+	/* b := a*x^2  (= a^q) */
+	if (!BN_mod_sqr(b, x, p, ctx)) goto end;
+	if (!BN_mod_mul(b, b, A, p, ctx)) goto end;
+	
+	/* x := a*x    (= a^((q+1)/2)) */
+	if (!BN_mod_mul(x, x, A, p, ctx)) goto end;
+
+	while (1)
+		{
+		/* Now  b  is  a^q * y^k  for some even  k  (0 <= k < 2^E
+		 * where  E  refers to the original value of  e,  which we
+		 * don't keep in a variable),  and  x  is  a^((q+1)/2) * y^(k/2).
+		 *
+		 * We have  a*b = x^2,
+		 *    y^2^(e-1) = -1,
+		 *    b^2^(e-1) = 1.
+		 */
+
+		if (BN_is_one(b))
+			{
+			if (!BN_copy(ret, x)) goto end;
+			err = 0;
+			goto vrfy;
+			}
+
+
+		/* find smallest  i  such that  b^(2^i) = 1 */
+		i = 1;
+		if (!BN_mod_sqr(t, b, p, ctx)) goto end;
+		while (!BN_is_one(t))
+			{
+			i++;
+			if (i == e)
+				{
+				BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
+				goto end;
+				}
+			if (!BN_mod_mul(t, t, t, p, ctx)) goto end;
+			}
+		
+
+		/* t := y^2^(e - i - 1) */
+		if (!BN_copy(t, y)) goto end;
+		for (j = e - i - 1; j > 0; j--)
+			{
+			if (!BN_mod_sqr(t, t, p, ctx)) goto end;
+			}
+		if (!BN_mod_mul(y, t, t, p, ctx)) goto end;
+		if (!BN_mod_mul(x, x, t, p, ctx)) goto end;
+		if (!BN_mod_mul(b, b, y, p, ctx)) goto end;
+		e = i;
+		}
+
+ vrfy:
+	if (!err)
+		{
+		/* verify the result -- the input might have been not a square
+		 * (test added in 0.9.8) */
+		
+		if (!BN_mod_sqr(x, ret, p, ctx))
+			err = 1;
+		
+		if (!err && 0 != BN_cmp(x, A))
+			{
+			BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
+			err = 1;
+			}
+		}
+
+ end:
+	if (err)
+		{
+		if (ret != NULL && ret != in)
+			{
+			BN_clear_free(ret);
+			}
+		ret = NULL;
+		}
+	BN_CTX_end(ctx);
+	bn_check_top(ret);
+	return ret;
+	}