Delete bundled copy of OpenSSL and replace with README.

openssl/crypto/bn/bn_sqrt.c

Index: openssl/crypto/bn/bn_sqrt.c
diff --git a/openssl/crypto/bn/bn_sqrt.c b/openssl/crypto/bn/bn_sqrt.c
deleted file mode 100644
index 6beaf9e5e5ddfd6da6942c67b045049a7c979ddb..0000000000000000000000000000000000000000
--- a/openssl/crypto/bn/bn_sqrt.c
+++ /dev/null
@@ -1,393 +0,0 @@
-/* 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;
-	}