Synchronised line endinge with release branch

3 files changed, 3224 insertions, 3224 deletions

diff --git a/openssl/crypto/ec/ec2_smpl.c b/openssl/crypto/ec/ec2_smpl.c
index 1725dd128..af94458ca 100644
--- a/openssl/crypto/ec/ec2_smpl.c
+++ b/openssl/crypto/ec/ec2_smpl.c
@@ -1,1042 +1,1042 @@
-/* crypto/ec/ec2_smpl.c */

-/* ====================================================================

- * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.

- *

- * The Elliptic Curve Public-Key Crypto Library (ECC Code) included

- * herein is developed by SUN MICROSYSTEMS, INC., and is contributed

- * to the OpenSSL project.

- *

- * The ECC Code is licensed pursuant to the OpenSSL open source

- * license provided below.

- *

- * The software is originally written by Sheueling Chang Shantz and

- * Douglas Stebila of Sun Microsystems Laboratories.

- *

- */

-/* ====================================================================

- * Copyright (c) 1998-2005 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 <openssl/err.h>

-

-#include "ec_lcl.h"

-

-

-const EC_METHOD *EC_GF2m_simple_method(void)

-	{

-	static const EC_METHOD ret = {

-		NID_X9_62_characteristic_two_field,

-		ec_GF2m_simple_group_init,

-		ec_GF2m_simple_group_finish,

-		ec_GF2m_simple_group_clear_finish,

-		ec_GF2m_simple_group_copy,

-		ec_GF2m_simple_group_set_curve,

-		ec_GF2m_simple_group_get_curve,

-		ec_GF2m_simple_group_get_degree,

-		ec_GF2m_simple_group_check_discriminant,

-		ec_GF2m_simple_point_init,

-		ec_GF2m_simple_point_finish,

-		ec_GF2m_simple_point_clear_finish,

-		ec_GF2m_simple_point_copy,

-		ec_GF2m_simple_point_set_to_infinity,

-		0 /* set_Jprojective_coordinates_GFp */,

-		0 /* get_Jprojective_coordinates_GFp */,

-		ec_GF2m_simple_point_set_affine_coordinates,

-		ec_GF2m_simple_point_get_affine_coordinates,

-		ec_GF2m_simple_set_compressed_coordinates,

-		ec_GF2m_simple_point2oct,

-		ec_GF2m_simple_oct2point,

-		ec_GF2m_simple_add,

-		ec_GF2m_simple_dbl,

-		ec_GF2m_simple_invert,

-		ec_GF2m_simple_is_at_infinity,

-		ec_GF2m_simple_is_on_curve,

-		ec_GF2m_simple_cmp,

-		ec_GF2m_simple_make_affine,

-		ec_GF2m_simple_points_make_affine,

-

-		/* the following three method functions are defined in ec2_mult.c */

-		ec_GF2m_simple_mul,

-		ec_GF2m_precompute_mult,

-		ec_GF2m_have_precompute_mult,

-

-		ec_GF2m_simple_field_mul,

-		ec_GF2m_simple_field_sqr,

-		ec_GF2m_simple_field_div,

-		0 /* field_encode */,

-		0 /* field_decode */,

-		0 /* field_set_to_one */ };

-

-	return &ret;

-	}

-

-

-/* Initialize a GF(2^m)-based EC_GROUP structure.

- * Note that all other members are handled by EC_GROUP_new.

- */

-int ec_GF2m_simple_group_init(EC_GROUP *group)

-	{

-	BN_init(&group->field);

-	BN_init(&group->a);

-	BN_init(&group->b);

-	return 1;

-	}

-

-

-/* Free a GF(2^m)-based EC_GROUP structure.

- * Note that all other members are handled by EC_GROUP_free.

- */

-void ec_GF2m_simple_group_finish(EC_GROUP *group)

-	{

-	BN_free(&group->field);

-	BN_free(&group->a);

-	BN_free(&group->b);

-	}

-

-

-/* Clear and free a GF(2^m)-based EC_GROUP structure.

- * Note that all other members are handled by EC_GROUP_clear_free.

- */

-void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)

-	{

-	BN_clear_free(&group->field);

-	BN_clear_free(&group->a);

-	BN_clear_free(&group->b);

-	group->poly[0] = 0;

-	group->poly[1] = 0;

-	group->poly[2] = 0;

-	group->poly[3] = 0;

-	group->poly[4] = 0;

-	group->poly[5] = -1;

-	}

-

-

-/* Copy a GF(2^m)-based EC_GROUP structure.

- * Note that all other members are handled by EC_GROUP_copy.

- */

-int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)

-	{

-	int i;

-	if (!BN_copy(&dest->field, &src->field)) return 0;

-	if (!BN_copy(&dest->a, &src->a)) return 0;

-	if (!BN_copy(&dest->b, &src->b)) return 0;

-	dest->poly[0] = src->poly[0];

-	dest->poly[1] = src->poly[1];

-	dest->poly[2] = src->poly[2];

-	dest->poly[3] = src->poly[3];

-	dest->poly[4] = src->poly[4];

-	dest->poly[5] = src->poly[5];

-	if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;

-	if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;

-	for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;

-	for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;

-	return 1;

-	}

-

-

-/* Set the curve parameters of an EC_GROUP structure. */

-int ec_GF2m_simple_group_set_curve(EC_GROUP *group,

-	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)

-	{

-	int ret = 0, i;

-

-	/* group->field */

-	if (!BN_copy(&group->field, p)) goto err;

-	i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;

-	if ((i != 5) && (i != 3))

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);

-		goto err;

-		}

-

-	/* group->a */

-	if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;

-	if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;

-	for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;

-	

-	/* group->b */

-	if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;

-	if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;

-	for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;

-		

-	ret = 1;

-  err:

-	return ret;

-	}

-

-

-/* Get the curve parameters of an EC_GROUP structure.

- * If p, a, or b are NULL then there values will not be set but the method will return with success.

- */

-int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)

-	{

-	int ret = 0;

-	

-	if (p != NULL)

-		{

-		if (!BN_copy(p, &group->field)) return 0;

-		}

-

-	if (a != NULL)

-		{

-		if (!BN_copy(a, &group->a)) goto err;

-		}

-

-	if (b != NULL)

-		{

-		if (!BN_copy(b, &group->b)) goto err;

-		}

-	

-	ret = 1;

-	

-  err:

-	return ret;

-	}

-

-

-/* Gets the degree of the field.  For a curve over GF(2^m) this is the value m. */

-int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)

-	{

-	return BN_num_bits(&group->field)-1;

-	}

-

-

-/* Checks the discriminant of the curve.

- * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 

- */

-int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)

-	{

-	int ret = 0;

-	BIGNUM *b;

-	BN_CTX *new_ctx = NULL;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);

-			goto err;

-			}

-		}

-	BN_CTX_start(ctx);

-	b = BN_CTX_get(ctx);

-	if (b == NULL) goto err;

-

-	if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;

-	

-	/* check the discriminant:

-	 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 

-	 */

-	if (BN_is_zero(b)) goto err;

-

-	ret = 1;

-

-err:

-	if (ctx != NULL)

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Initializes an EC_POINT. */

-int ec_GF2m_simple_point_init(EC_POINT *point)

-	{

-	BN_init(&point->X);

-	BN_init(&point->Y);

-	BN_init(&point->Z);

-	return 1;

-	}

-

-

-/* Frees an EC_POINT. */

-void ec_GF2m_simple_point_finish(EC_POINT *point)

-	{

-	BN_free(&point->X);

-	BN_free(&point->Y);

-	BN_free(&point->Z);

-	}

-

-

-/* Clears and frees an EC_POINT. */

-void ec_GF2m_simple_point_clear_finish(EC_POINT *point)

-	{

-	BN_clear_free(&point->X);

-	BN_clear_free(&point->Y);

-	BN_clear_free(&point->Z);

-	point->Z_is_one = 0;

-	}

-

-

-/* Copy the contents of one EC_POINT into another.  Assumes dest is initialized. */

-int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)

-	{

-	if (!BN_copy(&dest->X, &src->X)) return 0;

-	if (!BN_copy(&dest->Y, &src->Y)) return 0;

-	if (!BN_copy(&dest->Z, &src->Z)) return 0;

-	dest->Z_is_one = src->Z_is_one;

-

-	return 1;

-	}

-

-

-/* Set an EC_POINT to the point at infinity.  

- * A point at infinity is represented by having Z=0.

- */

-int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)

-	{

-	point->Z_is_one = 0;

-	BN_zero(&point->Z);

-	return 1;

-	}

-

-

-/* Set the coordinates of an EC_POINT using affine coordinates. 

- * Note that the simple implementation only uses affine coordinates.

- */

-int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,

-	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)

-	{

-	int ret = 0;	

-	if (x == NULL || y == NULL)

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);

-		return 0;

-		}

-

-	if (!BN_copy(&point->X, x)) goto err;

-	BN_set_negative(&point->X, 0);

-	if (!BN_copy(&point->Y, y)) goto err;

-	BN_set_negative(&point->Y, 0);

-	if (!BN_copy(&point->Z, BN_value_one())) goto err;

-	BN_set_negative(&point->Z, 0);

-	point->Z_is_one = 1;

-	ret = 1;

-

-  err:

-	return ret;

-	}

-

-

-/* Gets the affine coordinates of an EC_POINT. 

- * Note that the simple implementation only uses affine coordinates.

- */

-int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,

-	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)

-	{

-	int ret = 0;

-

-	if (EC_POINT_is_at_infinity(group, point))

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);

-		return 0;

-		}

-

-	if (BN_cmp(&point->Z, BN_value_one())) 

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);

-		return 0;

-		}

-	if (x != NULL)

-		{

-		if (!BN_copy(x, &point->X)) goto err;

-		BN_set_negative(x, 0);

-		}

-	if (y != NULL)

-		{

-		if (!BN_copy(y, &point->Y)) goto err;

-		BN_set_negative(y, 0);

-		}

-	ret = 1;

-		

- err:

-	return ret;

-	}

-

-

-/* Calculates and sets the affine coordinates of an EC_POINT from the given

- * compressed coordinates.  Uses algorithm 2.3.4 of SEC 1. 

- * Note that the simple implementation only uses affine coordinates.

- *

- * The method is from the following publication:

- * 

- *     Harper, Menezes, Vanstone:

- *     "Public-Key Cryptosystems with Very Small Key Lengths",

- *     EUROCRYPT '92, Springer-Verlag LNCS 658,

- *     published February 1993

- *

- * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe

- * the same method, but claim no priority date earlier than July 29, 1994

- * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).

- */

-int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,

-	const BIGNUM *x_, int y_bit, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *tmp, *x, *y, *z;

-	int ret = 0, z0;

-

-	/* clear error queue */

-	ERR_clear_error();

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	y_bit = (y_bit != 0) ? 1 : 0;

-

-	BN_CTX_start(ctx);

-	tmp = BN_CTX_get(ctx);

-	x = BN_CTX_get(ctx);

-	y = BN_CTX_get(ctx);

-	z = BN_CTX_get(ctx);

-	if (z == NULL) goto err;

-

-	if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;

-	if (BN_is_zero(x))

-		{

-		if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;

-		}

-	else

-		{

-		if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;

-		if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;

-		if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;

-		if (!BN_GF2m_add(tmp, x, tmp)) goto err;

-		if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))

-			{

-			unsigned long err = ERR_peek_last_error();

-			

-			if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)

-				{

-				ERR_clear_error();

-				ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);

-				}

-			else

-				ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);

-			goto err;

-			}

-		z0 = (BN_is_odd(z)) ? 1 : 0;

-		if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;

-		if (z0 != y_bit)

-			{

-			if (!BN_GF2m_add(y, y, x)) goto err;

-			}

-		}

-

-	if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;

-

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Converts an EC_POINT to an octet string.  

- * If buf is NULL, the encoded length will be returned.

- * If the length len of buf is smaller than required an error will be returned.

- */

-size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,

-	unsigned char *buf, size_t len, BN_CTX *ctx)

-	{

-	size_t ret;

-	BN_CTX *new_ctx = NULL;

-	int used_ctx = 0;

-	BIGNUM *x, *y, *yxi;

-	size_t field_len, i, skip;

-

-	if ((form != POINT_CONVERSION_COMPRESSED)

-		&& (form != POINT_CONVERSION_UNCOMPRESSED)

-		&& (form != POINT_CONVERSION_HYBRID))

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);

-		goto err;

-		}

-

-	if (EC_POINT_is_at_infinity(group, point))

-		{

-		/* encodes to a single 0 octet */

-		if (buf != NULL)

-			{

-			if (len < 1)

-				{

-				ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);

-				return 0;

-				}

-			buf[0] = 0;

-			}

-		return 1;

-		}

-

-

-	/* ret := required output buffer length */

-	field_len = (EC_GROUP_get_degree(group) + 7) / 8;

-	ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;

-

-	/* if 'buf' is NULL, just return required length */

-	if (buf != NULL)

-		{

-		if (len < ret)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);

-			goto err;

-			}

-

-		if (ctx == NULL)

-			{

-			ctx = new_ctx = BN_CTX_new();

-			if (ctx == NULL)

-				return 0;

-			}

-

-		BN_CTX_start(ctx);

-		used_ctx = 1;

-		x = BN_CTX_get(ctx);

-		y = BN_CTX_get(ctx);

-		yxi = BN_CTX_get(ctx);

-		if (yxi == NULL) goto err;

-

-		if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;

-

-		buf[0] = form;

-		if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))

-			{

-			if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;

-			if (BN_is_odd(yxi)) buf[0]++;

-			}

-

-		i = 1;

-		

-		skip = field_len - BN_num_bytes(x);

-		if (skip > field_len)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-			goto err;

-			}

-		while (skip > 0)

-			{

-			buf[i++] = 0;

-			skip--;

-			}

-		skip = BN_bn2bin(x, buf + i);

-		i += skip;

-		if (i != 1 + field_len)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-			goto err;

-			}

-

-		if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)

-			{

-			skip = field_len - BN_num_bytes(y);

-			if (skip > field_len)

-				{

-				ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-				goto err;

-				}

-			while (skip > 0)

-				{

-				buf[i++] = 0;

-				skip--;

-				}

-			skip = BN_bn2bin(y, buf + i);

-			i += skip;

-			}

-

-		if (i != ret)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-			goto err;

-			}

-		}

-	

-	if (used_ctx)

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-

- err:

-	if (used_ctx)

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return 0;

-	}

-

-

-/* Converts an octet string representation to an EC_POINT. 

- * Note that the simple implementation only uses affine coordinates.

- */

-int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,

-	const unsigned char *buf, size_t len, BN_CTX *ctx)

-	{

-	point_conversion_form_t form;

-	int y_bit;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *x, *y, *yxi;

-	size_t field_len, enc_len;

-	int ret = 0;

-

-	if (len == 0)

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);

-		return 0;

-		}

-	form = buf[0];

-	y_bit = form & 1;

-	form = form & ~1U;

-	if ((form != 0)	&& (form != POINT_CONVERSION_COMPRESSED)

-		&& (form != POINT_CONVERSION_UNCOMPRESSED)

-		&& (form != POINT_CONVERSION_HYBRID))

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		return 0;

-		}

-	if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		return 0;

-		}

-

-	if (form == 0)

-		{

-		if (len != 1)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-			return 0;

-			}

-

-		return EC_POINT_set_to_infinity(group, point);

-		}

-	

-	field_len = (EC_GROUP_get_degree(group) + 7) / 8;

-	enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;

-

-	if (len != enc_len)

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		return 0;

-		}

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	x = BN_CTX_get(ctx);

-	y = BN_CTX_get(ctx);

-	yxi = BN_CTX_get(ctx);

-	if (yxi == NULL) goto err;

-

-	if (!BN_bin2bn(buf + 1, field_len, x)) goto err;

-	if (BN_ucmp(x, &group->field) >= 0)

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		goto err;

-		}

-

-	if (form == POINT_CONVERSION_COMPRESSED)

-		{

-		if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;

-		}

-	else

-		{

-		if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;

-		if (BN_ucmp(y, &group->field) >= 0)

-			{

-			ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-			goto err;

-			}

-		if (form == POINT_CONVERSION_HYBRID)

-			{

-			if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;

-			if (y_bit != BN_is_odd(yxi))

-				{

-				ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-				goto err;

-				}

-			}

-

-		if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;

-		}

-	

-	if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */

-		{

-		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);

-		goto err;

-		}

-

-	ret = 1;

-	

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Computes a + b and stores the result in r.  r could be a or b, a could be b.

- * Uses algorithm A.10.2 of IEEE P1363.

- */

-int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;

-	int ret = 0;

-	

-	if (EC_POINT_is_at_infinity(group, a))

-		{

-		if (!EC_POINT_copy(r, b)) return 0;

-		return 1;

-		}

-

-	if (EC_POINT_is_at_infinity(group, b))

-		{

-		if (!EC_POINT_copy(r, a)) return 0;

-		return 1;

-		}

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	x0 = BN_CTX_get(ctx);

-	y0 = BN_CTX_get(ctx);

-	x1 = BN_CTX_get(ctx);

-	y1 = BN_CTX_get(ctx);

-	x2 = BN_CTX_get(ctx);

-	y2 = BN_CTX_get(ctx);

-	s = BN_CTX_get(ctx);

-	t = BN_CTX_get(ctx);

-	if (t == NULL) goto err;

-

-	if (a->Z_is_one) 

-		{

-		if (!BN_copy(x0, &a->X)) goto err;

-		if (!BN_copy(y0, &a->Y)) goto err;

-		}

-	else

-		{

-		if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;

-		}

-	if (b->Z_is_one) 

-		{

-		if (!BN_copy(x1, &b->X)) goto err;

-		if (!BN_copy(y1, &b->Y)) goto err;

-		}

-	else

-		{

-		if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;

-		}

-

-

-	if (BN_GF2m_cmp(x0, x1))

-		{

-		if (!BN_GF2m_add(t, x0, x1)) goto err;

-		if (!BN_GF2m_add(s, y0, y1)) goto err;

-		if (!group->meth->field_div(group, s, s, t, ctx)) goto err;

-		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;

-		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;

-		if (!BN_GF2m_add(x2, x2, s)) goto err;

-		if (!BN_GF2m_add(x2, x2, t)) goto err;

-		}

-	else

-		{

-		if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))

-			{

-			if (!EC_POINT_set_to_infinity(group, r)) goto err;

-			ret = 1;

-			goto err;

-			}

-		if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;

-		if (!BN_GF2m_add(s, s, x1)) goto err;

-		

-		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;

-		if (!BN_GF2m_add(x2, x2, s)) goto err;

-		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;

-		}

-

-	if (!BN_GF2m_add(y2, x1, x2)) goto err;

-	if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;

-	if (!BN_GF2m_add(y2, y2, x2)) goto err;

-	if (!BN_GF2m_add(y2, y2, y1)) goto err;

-

-	if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;

-

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Computes 2 * a and stores the result in r.  r could be a.

- * Uses algorithm A.10.2 of IEEE P1363.

- */

-int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)

-	{

-	return ec_GF2m_simple_add(group, r, a, a, ctx);

-	}

-

-

-int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)

-	{

-	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))

-		/* point is its own inverse */

-		return 1;

-	

-	if (!EC_POINT_make_affine(group, point, ctx)) return 0;

-	return BN_GF2m_add(&point->Y, &point->X, &point->Y);

-	}

-

-

-/* Indicates whether the given point is the point at infinity. */

-int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)

-	{

-	return BN_is_zero(&point->Z);

-	}

-

-

-/* Determines whether the given EC_POINT is an actual point on the curve defined

- * in the EC_GROUP.  A point is valid if it satisfies the Weierstrass equation:

- *      y^2 + x*y = x^3 + a*x^2 + b.

- */

-int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)

-	{

-	int ret = -1;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *lh, *y2;

-	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);

-	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);

-

-	if (EC_POINT_is_at_infinity(group, point))

-		return 1;

-

-	field_mul = group->meth->field_mul;

-	field_sqr = group->meth->field_sqr;	

-

-	/* only support affine coordinates */

-	if (!point->Z_is_one) goto err;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return -1;

-		}

-

-	BN_CTX_start(ctx);

-	y2 = BN_CTX_get(ctx);

-	lh = BN_CTX_get(ctx);

-	if (lh == NULL) goto err;

-

-	/* We have a curve defined by a Weierstrass equation

-	 *      y^2 + x*y = x^3 + a*x^2 + b.

-	 *  <=> x^3 + a*x^2 + x*y + b + y^2 = 0

-	 *  <=> ((x + a) * x + y ) * x + b + y^2 = 0

-	 */

-	if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;

-	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;

-	if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;

-	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;

-	if (!BN_GF2m_add(lh, lh, &group->b)) goto err;

-	if (!field_sqr(group, y2, &point->Y, ctx)) goto err;

-	if (!BN_GF2m_add(lh, lh, y2)) goto err;

-	ret = BN_is_zero(lh);

- err:

-	if (ctx) BN_CTX_end(ctx);

-	if (new_ctx) BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Indicates whether two points are equal.

- * Return values:

- *  -1   error

- *   0   equal (in affine coordinates)

- *   1   not equal

- */

-int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)

-	{

-	BIGNUM *aX, *aY, *bX, *bY;

-	BN_CTX *new_ctx = NULL;

-	int ret = -1;

-

-	if (EC_POINT_is_at_infinity(group, a))

-		{

-		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;

-		}

-

-	if (EC_POINT_is_at_infinity(group, b))

-		return 1;

-	

-	if (a->Z_is_one && b->Z_is_one)

-		{

-		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;

-		}

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return -1;

-		}

-

-	BN_CTX_start(ctx);

-	aX = BN_CTX_get(ctx);

-	aY = BN_CTX_get(ctx);

-	bX = BN_CTX_get(ctx);

-	bY = BN_CTX_get(ctx);

-	if (bY == NULL) goto err;

-

-	if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;

-	if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;

-	ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;

-

-  err:	

-	if (ctx) BN_CTX_end(ctx);

-	if (new_ctx) BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Forces the given EC_POINT to internally use affine coordinates. */

-int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *x, *y;

-	int ret = 0;

-

-	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))

-		return 1;

-	

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	x = BN_CTX_get(ctx);

-	y = BN_CTX_get(ctx);

-	if (y == NULL) goto err;

-	

-	if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;

-	if (!BN_copy(&point->X, x)) goto err;

-	if (!BN_copy(&point->Y, y)) goto err;

-	if (!BN_one(&point->Z)) goto err;

-	

-	ret = 1;		

-

-  err:

-	if (ctx) BN_CTX_end(ctx);

-	if (new_ctx) BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-/* Forces each of the EC_POINTs in the given array to use affine coordinates. */

-int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)

-	{

-	size_t i;

-

-	for (i = 0; i < num; i++)

-		{

-		if (!group->meth->make_affine(group, points[i], ctx)) return 0;

-		}

-

-	return 1;

-	}

-

-

-/* Wrapper to simple binary polynomial field multiplication implementation. */

-int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)

-	{

-	return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);

-	}

-

-

-/* Wrapper to simple binary polynomial field squaring implementation. */

-int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)

-	{

-	return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);

-	}

-

-

-/* Wrapper to simple binary polynomial field division implementation. */

-int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)

-	{

-	return BN_GF2m_mod_div(r, a, b, &group->field, ctx);

-	}

+/* crypto/ec/ec2_smpl.c */
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
+ * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
+ * to the OpenSSL project.
+ *
+ * The ECC Code is licensed pursuant to the OpenSSL open source
+ * license provided below.
+ *
+ * The software is originally written by Sheueling Chang Shantz and
+ * Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2005 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 <openssl/err.h>
+
+#include "ec_lcl.h"
+
+
+const EC_METHOD *EC_GF2m_simple_method(void)
+	{
+	static const EC_METHOD ret = {
+		NID_X9_62_characteristic_two_field,
+		ec_GF2m_simple_group_init,
+		ec_GF2m_simple_group_finish,
+		ec_GF2m_simple_group_clear_finish,
+		ec_GF2m_simple_group_copy,
+		ec_GF2m_simple_group_set_curve,
+		ec_GF2m_simple_group_get_curve,
+		ec_GF2m_simple_group_get_degree,
+		ec_GF2m_simple_group_check_discriminant,
+		ec_GF2m_simple_point_init,
+		ec_GF2m_simple_point_finish,
+		ec_GF2m_simple_point_clear_finish,
+		ec_GF2m_simple_point_copy,
+		ec_GF2m_simple_point_set_to_infinity,
+		0 /* set_Jprojective_coordinates_GFp */,
+		0 /* get_Jprojective_coordinates_GFp */,
+		ec_GF2m_simple_point_set_affine_coordinates,
+		ec_GF2m_simple_point_get_affine_coordinates,
+		ec_GF2m_simple_set_compressed_coordinates,
+		ec_GF2m_simple_point2oct,
+		ec_GF2m_simple_oct2point,
+		ec_GF2m_simple_add,
+		ec_GF2m_simple_dbl,
+		ec_GF2m_simple_invert,
+		ec_GF2m_simple_is_at_infinity,
+		ec_GF2m_simple_is_on_curve,
+		ec_GF2m_simple_cmp,
+		ec_GF2m_simple_make_affine,
+		ec_GF2m_simple_points_make_affine,
+
+		/* the following three method functions are defined in ec2_mult.c */
+		ec_GF2m_simple_mul,
+		ec_GF2m_precompute_mult,
+		ec_GF2m_have_precompute_mult,
+
+		ec_GF2m_simple_field_mul,
+		ec_GF2m_simple_field_sqr,
+		ec_GF2m_simple_field_div,
+		0 /* field_encode */,
+		0 /* field_decode */,
+		0 /* field_set_to_one */ };
+
+	return &ret;
+	}
+
+
+/* Initialize a GF(2^m)-based EC_GROUP structure.
+ * Note that all other members are handled by EC_GROUP_new.
+ */
+int ec_GF2m_simple_group_init(EC_GROUP *group)
+	{
+	BN_init(&group->field);
+	BN_init(&group->a);
+	BN_init(&group->b);
+	return 1;
+	}
+
+
+/* Free a GF(2^m)-based EC_GROUP structure.
+ * Note that all other members are handled by EC_GROUP_free.
+ */
+void ec_GF2m_simple_group_finish(EC_GROUP *group)
+	{
+	BN_free(&group->field);
+	BN_free(&group->a);
+	BN_free(&group->b);
+	}
+
+
+/* Clear and free a GF(2^m)-based EC_GROUP structure.
+ * Note that all other members are handled by EC_GROUP_clear_free.
+ */
+void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
+	{
+	BN_clear_free(&group->field);
+	BN_clear_free(&group->a);
+	BN_clear_free(&group->b);
+	group->poly[0] = 0;
+	group->poly[1] = 0;
+	group->poly[2] = 0;
+	group->poly[3] = 0;
+	group->poly[4] = 0;
+	group->poly[5] = -1;
+	}
+
+
+/* Copy a GF(2^m)-based EC_GROUP structure.
+ * Note that all other members are handled by EC_GROUP_copy.
+ */
+int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+	{
+	int i;
+	if (!BN_copy(&dest->field, &src->field)) return 0;
+	if (!BN_copy(&dest->a, &src->a)) return 0;
+	if (!BN_copy(&dest->b, &src->b)) return 0;
+	dest->poly[0] = src->poly[0];
+	dest->poly[1] = src->poly[1];
+	dest->poly[2] = src->poly[2];
+	dest->poly[3] = src->poly[3];
+	dest->poly[4] = src->poly[4];
+	dest->poly[5] = src->poly[5];
+	if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
+	if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
+	for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
+	for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
+	return 1;
+	}
+
+
+/* Set the curve parameters of an EC_GROUP structure. */
+int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
+	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	int ret = 0, i;
+
+	/* group->field */
+	if (!BN_copy(&group->field, p)) goto err;
+	i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
+	if ((i != 5) && (i != 3))
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
+		goto err;
+		}
+
+	/* group->a */
+	if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
+	if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
+	for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
+	
+	/* group->b */
+	if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
+	if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
+	for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
+		
+	ret = 1;
+  err:
+	return ret;
+	}
+
+
+/* Get the curve parameters of an EC_GROUP structure.
+ * If p, a, or b are NULL then there values will not be set but the method will return with success.
+ */
+int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
+	{
+	int ret = 0;
+	
+	if (p != NULL)
+		{
+		if (!BN_copy(p, &group->field)) return 0;
+		}
+
+	if (a != NULL)
+		{
+		if (!BN_copy(a, &group->a)) goto err;
+		}
+
+	if (b != NULL)
+		{
+		if (!BN_copy(b, &group->b)) goto err;
+		}
+	
+	ret = 1;
+	
+  err:
+	return ret;
+	}
+
+
+/* Gets the degree of the field.  For a curve over GF(2^m) this is the value m. */
+int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
+	{
+	return BN_num_bits(&group->field)-1;
+	}
+
+
+/* Checks the discriminant of the curve.
+ * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 
+ */
+int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
+	{
+	int ret = 0;
+	BIGNUM *b;
+	BN_CTX *new_ctx = NULL;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
+			goto err;
+			}
+		}
+	BN_CTX_start(ctx);
+	b = BN_CTX_get(ctx);
+	if (b == NULL) goto err;
+
+	if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
+	
+	/* check the discriminant:
+	 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 
+	 */
+	if (BN_is_zero(b)) goto err;
+
+	ret = 1;
+
+err:
+	if (ctx != NULL)
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Initializes an EC_POINT. */
+int ec_GF2m_simple_point_init(EC_POINT *point)
+	{
+	BN_init(&point->X);
+	BN_init(&point->Y);
+	BN_init(&point->Z);
+	return 1;
+	}
+
+
+/* Frees an EC_POINT. */
+void ec_GF2m_simple_point_finish(EC_POINT *point)
+	{
+	BN_free(&point->X);
+	BN_free(&point->Y);
+	BN_free(&point->Z);
+	}
+
+
+/* Clears and frees an EC_POINT. */
+void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
+	{
+	BN_clear_free(&point->X);
+	BN_clear_free(&point->Y);
+	BN_clear_free(&point->Z);
+	point->Z_is_one = 0;
+	}
+
+
+/* Copy the contents of one EC_POINT into another.  Assumes dest is initialized. */
+int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
+	{
+	if (!BN_copy(&dest->X, &src->X)) return 0;
+	if (!BN_copy(&dest->Y, &src->Y)) return 0;
+	if (!BN_copy(&dest->Z, &src->Z)) return 0;
+	dest->Z_is_one = src->Z_is_one;
+
+	return 1;
+	}
+
+
+/* Set an EC_POINT to the point at infinity.  
+ * A point at infinity is represented by having Z=0.
+ */
+int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
+	{
+	point->Z_is_one = 0;
+	BN_zero(&point->Z);
+	return 1;
+	}
+
+
+/* Set the coordinates of an EC_POINT using affine coordinates. 
+ * Note that the simple implementation only uses affine coordinates.
+ */
+int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
+	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+	{
+	int ret = 0;	
+	if (x == NULL || y == NULL)
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
+		return 0;
+		}
+
+	if (!BN_copy(&point->X, x)) goto err;
+	BN_set_negative(&point->X, 0);
+	if (!BN_copy(&point->Y, y)) goto err;
+	BN_set_negative(&point->Y, 0);
+	if (!BN_copy(&point->Z, BN_value_one())) goto err;
+	BN_set_negative(&point->Z, 0);
+	point->Z_is_one = 1;
+	ret = 1;
+
+  err:
+	return ret;
+	}
+
+
+/* Gets the affine coordinates of an EC_POINT. 
+ * Note that the simple implementation only uses affine coordinates.
+ */
+int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
+	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
+	{
+	int ret = 0;
+
+	if (EC_POINT_is_at_infinity(group, point))
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
+		return 0;
+		}
+
+	if (BN_cmp(&point->Z, BN_value_one())) 
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+		return 0;
+		}
+	if (x != NULL)
+		{
+		if (!BN_copy(x, &point->X)) goto err;
+		BN_set_negative(x, 0);
+		}
+	if (y != NULL)
+		{
+		if (!BN_copy(y, &point->Y)) goto err;
+		BN_set_negative(y, 0);
+		}
+	ret = 1;
+		
+ err:
+	return ret;
+	}
+
+
+/* Calculates and sets the affine coordinates of an EC_POINT from the given
+ * compressed coordinates.  Uses algorithm 2.3.4 of SEC 1. 
+ * Note that the simple implementation only uses affine coordinates.
+ *
+ * The method is from the following publication:
+ * 
+ *     Harper, Menezes, Vanstone:
+ *     "Public-Key Cryptosystems with Very Small Key Lengths",
+ *     EUROCRYPT '92, Springer-Verlag LNCS 658,
+ *     published February 1993
+ *
+ * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
+ * the same method, but claim no priority date earlier than July 29, 1994
+ * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
+ */
+int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
+	const BIGNUM *x_, int y_bit, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *tmp, *x, *y, *z;
+	int ret = 0, z0;
+
+	/* clear error queue */
+	ERR_clear_error();
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	y_bit = (y_bit != 0) ? 1 : 0;
+
+	BN_CTX_start(ctx);
+	tmp = BN_CTX_get(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	z = BN_CTX_get(ctx);
+	if (z == NULL) goto err;
+
+	if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
+	if (BN_is_zero(x))
+		{
+		if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
+		}
+	else
+		{
+		if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
+		if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
+		if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
+		if (!BN_GF2m_add(tmp, x, tmp)) goto err;
+		if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
+			{
+			unsigned long err = ERR_peek_last_error();
+			
+			if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
+				{
+				ERR_clear_error();
+				ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+				}
+			else
+				ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
+			goto err;
+			}
+		z0 = (BN_is_odd(z)) ? 1 : 0;
+		if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
+		if (z0 != y_bit)
+			{
+			if (!BN_GF2m_add(y, y, x)) goto err;
+			}
+		}
+
+	if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Converts an EC_POINT to an octet string.  
+ * If buf is NULL, the encoded length will be returned.
+ * If the length len of buf is smaller than required an error will be returned.
+ */
+size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
+	unsigned char *buf, size_t len, BN_CTX *ctx)
+	{
+	size_t ret;
+	BN_CTX *new_ctx = NULL;
+	int used_ctx = 0;
+	BIGNUM *x, *y, *yxi;
+	size_t field_len, i, skip;
+
+	if ((form != POINT_CONVERSION_COMPRESSED)
+		&& (form != POINT_CONVERSION_UNCOMPRESSED)
+		&& (form != POINT_CONVERSION_HYBRID))
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
+		goto err;
+		}
+
+	if (EC_POINT_is_at_infinity(group, point))
+		{
+		/* encodes to a single 0 octet */
+		if (buf != NULL)
+			{
+			if (len < 1)
+				{
+				ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
+				return 0;
+				}
+			buf[0] = 0;
+			}
+		return 1;
+		}
+
+
+	/* ret := required output buffer length */
+	field_len = (EC_GROUP_get_degree(group) + 7) / 8;
+	ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
+
+	/* if 'buf' is NULL, just return required length */
+	if (buf != NULL)
+		{
+		if (len < ret)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
+			goto err;
+			}
+
+		if (ctx == NULL)
+			{
+			ctx = new_ctx = BN_CTX_new();
+			if (ctx == NULL)
+				return 0;
+			}
+
+		BN_CTX_start(ctx);
+		used_ctx = 1;
+		x = BN_CTX_get(ctx);
+		y = BN_CTX_get(ctx);
+		yxi = BN_CTX_get(ctx);
+		if (yxi == NULL) goto err;
+
+		if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
+
+		buf[0] = form;
+		if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
+			{
+			if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
+			if (BN_is_odd(yxi)) buf[0]++;
+			}
+
+		i = 1;
+		
+		skip = field_len - BN_num_bytes(x);
+		if (skip > field_len)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+			goto err;
+			}
+		while (skip > 0)
+			{
+			buf[i++] = 0;
+			skip--;
+			}
+		skip = BN_bn2bin(x, buf + i);
+		i += skip;
+		if (i != 1 + field_len)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+			goto err;
+			}
+
+		if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
+			{
+			skip = field_len - BN_num_bytes(y);
+			if (skip > field_len)
+				{
+				ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+				goto err;
+				}
+			while (skip > 0)
+				{
+				buf[i++] = 0;
+				skip--;
+				}
+			skip = BN_bn2bin(y, buf + i);
+			i += skip;
+			}
+
+		if (i != ret)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+			goto err;
+			}
+		}
+	
+	if (used_ctx)
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+
+ err:
+	if (used_ctx)
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return 0;
+	}
+
+
+/* Converts an octet string representation to an EC_POINT. 
+ * Note that the simple implementation only uses affine coordinates.
+ */
+int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
+	const unsigned char *buf, size_t len, BN_CTX *ctx)
+	{
+	point_conversion_form_t form;
+	int y_bit;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *x, *y, *yxi;
+	size_t field_len, enc_len;
+	int ret = 0;
+
+	if (len == 0)
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
+		return 0;
+		}
+	form = buf[0];
+	y_bit = form & 1;
+	form = form & ~1U;
+	if ((form != 0)	&& (form != POINT_CONVERSION_COMPRESSED)
+		&& (form != POINT_CONVERSION_UNCOMPRESSED)
+		&& (form != POINT_CONVERSION_HYBRID))
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		return 0;
+		}
+	if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		return 0;
+		}
+
+	if (form == 0)
+		{
+		if (len != 1)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+			return 0;
+			}
+
+		return EC_POINT_set_to_infinity(group, point);
+		}
+	
+	field_len = (EC_GROUP_get_degree(group) + 7) / 8;
+	enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
+
+	if (len != enc_len)
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		return 0;
+		}
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	yxi = BN_CTX_get(ctx);
+	if (yxi == NULL) goto err;
+
+	if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
+	if (BN_ucmp(x, &group->field) >= 0)
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		goto err;
+		}
+
+	if (form == POINT_CONVERSION_COMPRESSED)
+		{
+		if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
+		}
+	else
+		{
+		if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
+		if (BN_ucmp(y, &group->field) >= 0)
+			{
+			ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+			goto err;
+			}
+		if (form == POINT_CONVERSION_HYBRID)
+			{
+			if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
+			if (y_bit != BN_is_odd(yxi))
+				{
+				ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+				goto err;
+				}
+			}
+
+		if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
+		}
+	
+	if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
+		{
+		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
+		goto err;
+		}
+
+	ret = 1;
+	
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Computes a + b and stores the result in r.  r could be a or b, a could be b.
+ * Uses algorithm A.10.2 of IEEE P1363.
+ */
+int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
+	int ret = 0;
+	
+	if (EC_POINT_is_at_infinity(group, a))
+		{
+		if (!EC_POINT_copy(r, b)) return 0;
+		return 1;
+		}
+
+	if (EC_POINT_is_at_infinity(group, b))
+		{
+		if (!EC_POINT_copy(r, a)) return 0;
+		return 1;
+		}
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	x0 = BN_CTX_get(ctx);
+	y0 = BN_CTX_get(ctx);
+	x1 = BN_CTX_get(ctx);
+	y1 = BN_CTX_get(ctx);
+	x2 = BN_CTX_get(ctx);
+	y2 = BN_CTX_get(ctx);
+	s = BN_CTX_get(ctx);
+	t = BN_CTX_get(ctx);
+	if (t == NULL) goto err;
+
+	if (a->Z_is_one) 
+		{
+		if (!BN_copy(x0, &a->X)) goto err;
+		if (!BN_copy(y0, &a->Y)) goto err;
+		}
+	else
+		{
+		if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
+		}
+	if (b->Z_is_one) 
+		{
+		if (!BN_copy(x1, &b->X)) goto err;
+		if (!BN_copy(y1, &b->Y)) goto err;
+		}
+	else
+		{
+		if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
+		}
+
+
+	if (BN_GF2m_cmp(x0, x1))
+		{
+		if (!BN_GF2m_add(t, x0, x1)) goto err;
+		if (!BN_GF2m_add(s, y0, y1)) goto err;
+		if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
+		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
+		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
+		if (!BN_GF2m_add(x2, x2, s)) goto err;
+		if (!BN_GF2m_add(x2, x2, t)) goto err;
+		}
+	else
+		{
+		if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
+			{
+			if (!EC_POINT_set_to_infinity(group, r)) goto err;
+			ret = 1;
+			goto err;
+			}
+		if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
+		if (!BN_GF2m_add(s, s, x1)) goto err;
+		
+		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
+		if (!BN_GF2m_add(x2, x2, s)) goto err;
+		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
+		}
+
+	if (!BN_GF2m_add(y2, x1, x2)) goto err;
+	if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
+	if (!BN_GF2m_add(y2, y2, x2)) goto err;
+	if (!BN_GF2m_add(y2, y2, y1)) goto err;
+
+	if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Computes 2 * a and stores the result in r.  r could be a.
+ * Uses algorithm A.10.2 of IEEE P1363.
+ */
+int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
+	{
+	return ec_GF2m_simple_add(group, r, a, a, ctx);
+	}
+
+
+int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+	{
+	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
+		/* point is its own inverse */
+		return 1;
+	
+	if (!EC_POINT_make_affine(group, point, ctx)) return 0;
+	return BN_GF2m_add(&point->Y, &point->X, &point->Y);
+	}
+
+
+/* Indicates whether the given point is the point at infinity. */
+int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
+	{
+	return BN_is_zero(&point->Z);
+	}
+
+
+/* Determines whether the given EC_POINT is an actual point on the curve defined
+ * in the EC_GROUP.  A point is valid if it satisfies the Weierstrass equation:
+ *      y^2 + x*y = x^3 + a*x^2 + b.
+ */
+int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
+	{
+	int ret = -1;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *lh, *y2;
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+
+	if (EC_POINT_is_at_infinity(group, point))
+		return 1;
+
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;	
+
+	/* only support affine coordinates */
+	if (!point->Z_is_one) goto err;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return -1;
+		}
+
+	BN_CTX_start(ctx);
+	y2 = BN_CTX_get(ctx);
+	lh = BN_CTX_get(ctx);
+	if (lh == NULL) goto err;
+
+	/* We have a curve defined by a Weierstrass equation
+	 *      y^2 + x*y = x^3 + a*x^2 + b.
+	 *  <=> x^3 + a*x^2 + x*y + b + y^2 = 0
+	 *  <=> ((x + a) * x + y ) * x + b + y^2 = 0
+	 */
+	if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
+	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
+	if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
+	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
+	if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
+	if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
+	if (!BN_GF2m_add(lh, lh, y2)) goto err;
+	ret = BN_is_zero(lh);
+ err:
+	if (ctx) BN_CTX_end(ctx);
+	if (new_ctx) BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Indicates whether two points are equal.
+ * Return values:
+ *  -1   error
+ *   0   equal (in affine coordinates)
+ *   1   not equal
+ */
+int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+	{
+	BIGNUM *aX, *aY, *bX, *bY;
+	BN_CTX *new_ctx = NULL;
+	int ret = -1;
+
+	if (EC_POINT_is_at_infinity(group, a))
+		{
+		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
+		}
+
+	if (EC_POINT_is_at_infinity(group, b))
+		return 1;
+	
+	if (a->Z_is_one && b->Z_is_one)
+		{
+		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
+		}
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return -1;
+		}
+
+	BN_CTX_start(ctx);
+	aX = BN_CTX_get(ctx);
+	aY = BN_CTX_get(ctx);
+	bX = BN_CTX_get(ctx);
+	bY = BN_CTX_get(ctx);
+	if (bY == NULL) goto err;
+
+	if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
+	if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
+	ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
+
+  err:	
+	if (ctx) BN_CTX_end(ctx);
+	if (new_ctx) BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Forces the given EC_POINT to internally use affine coordinates. */
+int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *x, *y;
+	int ret = 0;
+
+	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
+		return 1;
+	
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	if (y == NULL) goto err;
+	
+	if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
+	if (!BN_copy(&point->X, x)) goto err;
+	if (!BN_copy(&point->Y, y)) goto err;
+	if (!BN_one(&point->Z)) goto err;
+	
+	ret = 1;		
+
+  err:
+	if (ctx) BN_CTX_end(ctx);
+	if (new_ctx) BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+/* Forces each of the EC_POINTs in the given array to use affine coordinates. */
+int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
+	{
+	size_t i;
+
+	for (i = 0; i < num; i++)
+		{
+		if (!group->meth->make_affine(group, points[i], ctx)) return 0;
+		}
+
+	return 1;
+	}
+
+
+/* Wrapper to simple binary polynomial field multiplication implementation. */
+int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
+	}
+
+
+/* Wrapper to simple binary polynomial field squaring implementation. */
+int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
+	{
+	return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
+	}
+
+
+/* Wrapper to simple binary polynomial field division implementation. */
+int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
+	}
diff --git a/openssl/crypto/ec/ec_key.c b/openssl/crypto/ec/ec_key.c
index 0458d340b..522802c07 100644
--- a/openssl/crypto/ec/ec_key.c
+++ b/openssl/crypto/ec/ec_key.c
@@ -1,463 +1,463 @@
-/* crypto/ec/ec_key.c */

-/*

- * Written by Nils Larsch for the OpenSSL project.

- */

-/* ====================================================================

- * Copyright (c) 1998-2005 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 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.

- * Portions originally developed by SUN MICROSYSTEMS, INC., and 

- * contributed to the OpenSSL project.

- */

-

-#include <string.h>

-#include "ec_lcl.h"

-#include <openssl/err.h>

-#include <string.h>

-

-EC_KEY *EC_KEY_new(void)

-	{

-	EC_KEY *ret;

-

-	ret=(EC_KEY *)OPENSSL_malloc(sizeof(EC_KEY));

-	if (ret == NULL)

-		{

-		ECerr(EC_F_EC_KEY_NEW, ERR_R_MALLOC_FAILURE);

-		return(NULL);

-		}

-

-	ret->version = 1;	

-	ret->group   = NULL;

-	ret->pub_key = NULL;

-	ret->priv_key= NULL;

-	ret->enc_flag= 0; 

-	ret->conv_form = POINT_CONVERSION_UNCOMPRESSED;

-	ret->references= 1;

-	ret->method_data = NULL;

-	return(ret);

-	}

-

-EC_KEY *EC_KEY_new_by_curve_name(int nid)

-	{

-	EC_KEY *ret = EC_KEY_new();

-	if (ret == NULL)

-		return NULL;

-	ret->group = EC_GROUP_new_by_curve_name(nid);

-	if (ret->group == NULL)

-		{

-		EC_KEY_free(ret);

-		return NULL;

-		}

-	return ret;

-	}

-

-void EC_KEY_free(EC_KEY *r)

-	{

-	int i;

-

-	if (r == NULL) return;

-

-	i=CRYPTO_add(&r->references,-1,CRYPTO_LOCK_EC);

-#ifdef REF_PRINT

-	REF_PRINT("EC_KEY",r);

-#endif

-	if (i > 0) return;

-#ifdef REF_CHECK

-	if (i < 0)

-		{

-		fprintf(stderr,"EC_KEY_free, bad reference count\n");

-		abort();

-		}

-#endif

-

-	if (r->group    != NULL) 

-		EC_GROUP_free(r->group);

-	if (r->pub_key  != NULL)

-		EC_POINT_free(r->pub_key);

-	if (r->priv_key != NULL)

-		BN_clear_free(r->priv_key);

-

-	EC_EX_DATA_free_all_data(&r->method_data);

-

-	OPENSSL_cleanse((void *)r, sizeof(EC_KEY));

-

-	OPENSSL_free(r);

-	}

-

-EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src)

-	{

-	EC_EXTRA_DATA *d;

-

-	if (dest == NULL || src == NULL)

-		{

-		ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER);

-		return NULL;

-		}

-	/* copy the parameters */

-	if (src->group)

-		{

-		const EC_METHOD *meth = EC_GROUP_method_of(src->group);

-		/* clear the old group */

-		if (dest->group)

-			EC_GROUP_free(dest->group);

-		dest->group = EC_GROUP_new(meth);

-		if (dest->group == NULL)

-			return NULL;

-		if (!EC_GROUP_copy(dest->group, src->group))

-			return NULL;

-		}

-	/*  copy the public key */

-	if (src->pub_key && src->group)

-		{

-		if (dest->pub_key)

-			EC_POINT_free(dest->pub_key);

-		dest->pub_key = EC_POINT_new(src->group);

-		if (dest->pub_key == NULL)

-			return NULL;

-		if (!EC_POINT_copy(dest->pub_key, src->pub_key))

-			return NULL;

-		}

-	/* copy the private key */

-	if (src->priv_key)

-		{

-		if (dest->priv_key == NULL)

-			{

-			dest->priv_key = BN_new();

-			if (dest->priv_key == NULL)

-				return NULL;

-			}

-		if (!BN_copy(dest->priv_key, src->priv_key))

-			return NULL;

-		}

-	/* copy method/extra data */

-	EC_EX_DATA_free_all_data(&dest->method_data);

-

-	for (d = src->method_data; d != NULL; d = d->next)

-		{

-		void *t = d->dup_func(d->data);

-		

-		if (t == NULL)

-			return 0;

-		if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, d->free_func, d->clear_free_func))

-			return 0;

-		}

-

-	/* copy the rest */

-	dest->enc_flag  = src->enc_flag;

-	dest->conv_form = src->conv_form;

-	dest->version   = src->version;

-

-	return dest;

-	}

-

-EC_KEY *EC_KEY_dup(const EC_KEY *ec_key)

-	{

-	EC_KEY *ret = EC_KEY_new();

-	if (ret == NULL)

-		return NULL;

-	if (EC_KEY_copy(ret, ec_key) == NULL)

-		{

-		EC_KEY_free(ret);

-		return NULL;

-		}

-	return ret;

-	}

-

-int EC_KEY_up_ref(EC_KEY *r)

-	{

-	int i = CRYPTO_add(&r->references, 1, CRYPTO_LOCK_EC);

-#ifdef REF_PRINT

-	REF_PRINT("EC_KEY",r);

-#endif

-#ifdef REF_CHECK

-	if (i < 2)

-		{

-		fprintf(stderr, "EC_KEY_up, bad reference count\n");

-		abort();

-		}

-#endif

-	return ((i > 1) ? 1 : 0);

-	}

-

-int EC_KEY_generate_key(EC_KEY *eckey)

-	{	

-	int	ok = 0;

-	BN_CTX	*ctx = NULL;

-	BIGNUM	*priv_key = NULL, *order = NULL;

-	EC_POINT *pub_key = NULL;

-

-	if (!eckey || !eckey->group)

-		{

-		ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER);

-		return 0;

-		}

-

-	if ((order = BN_new()) == NULL) goto err;

-	if ((ctx = BN_CTX_new()) == NULL) goto err;

-

-	if (eckey->priv_key == NULL)

-		{

-		priv_key = BN_new();

-		if (priv_key == NULL)

-			goto err;

-		}

-	else

-		priv_key = eckey->priv_key;

-

-	if (!EC_GROUP_get_order(eckey->group, order, ctx))

-		goto err;

-

-	do

-		if (!BN_rand_range(priv_key, order))

-			goto err;

-	while (BN_is_zero(priv_key));

-

-	if (eckey->pub_key == NULL)

-		{

-		pub_key = EC_POINT_new(eckey->group);

-		if (pub_key == NULL)

-			goto err;

-		}

-	else

-		pub_key = eckey->pub_key;

-

-	if (!EC_POINT_mul(eckey->group, pub_key, priv_key, NULL, NULL, ctx))

-		goto err;

-

-	eckey->priv_key = priv_key;

-	eckey->pub_key  = pub_key;

-

-	ok=1;

-

-err:	

-	if (order)

-		BN_free(order);

-	if (pub_key  != NULL && eckey->pub_key  == NULL)

-		EC_POINT_free(pub_key);

-	if (priv_key != NULL && eckey->priv_key == NULL)

-		BN_free(priv_key);

-	if (ctx != NULL)

-		BN_CTX_free(ctx);

-	return(ok);

-	}

-

-int EC_KEY_check_key(const EC_KEY *eckey)

-	{

-	int	ok   = 0;

-	BN_CTX	*ctx = NULL;

-	const BIGNUM	*order  = NULL;

-	EC_POINT *point = NULL;

-

-	if (!eckey || !eckey->group || !eckey->pub_key)

-		{

-		ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER);

-		return 0;

-		}

-

-	if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key))

-		{

-		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_AT_INFINITY);

-		goto err;

-		}

-

-	if ((ctx = BN_CTX_new()) == NULL)

-		goto err;

-	if ((point = EC_POINT_new(eckey->group)) == NULL)

-		goto err;

-

-	/* testing whether the pub_key is on the elliptic curve */

-	if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx))

-		{

-		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE);

-		goto err;

-		}

-	/* testing whether pub_key * order is the point at infinity */

-	order = &eckey->group->order;

-	if (BN_is_zero(order))

-		{

-		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_GROUP_ORDER);

-		goto err;

-		}

-	if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx))

-		{

-		ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);

-		goto err;

-		}

-	if (!EC_POINT_is_at_infinity(eckey->group, point))

-		{

-		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER);

-		goto err;

-		}

-	/* in case the priv_key is present : 

-	 * check if generator * priv_key == pub_key 

-	 */

-	if (eckey->priv_key)

-		{

-		if (BN_cmp(eckey->priv_key, order) >= 0)

-			{

-			ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER);

-			goto err;

-			}

-		if (!EC_POINT_mul(eckey->group, point, eckey->priv_key,

-			NULL, NULL, ctx))

-			{

-			ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);

-			goto err;

-			}

-		if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, 

-			ctx) != 0)

-			{

-			ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY);

-			goto err;

-			}

-		}

-	ok = 1;

-err:

-	if (ctx   != NULL)

-		BN_CTX_free(ctx);

-	if (point != NULL)

-		EC_POINT_free(point);

-	return(ok);

-	}

-

-const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key)

-	{

-	return key->group;

-	}

-

-int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group)

-	{

-	if (key->group != NULL)

-		EC_GROUP_free(key->group);

-	key->group = EC_GROUP_dup(group);

-	return (key->group == NULL) ? 0 : 1;

-	}

-

-const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key)

-	{

-	return key->priv_key;

-	}

-

-int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *priv_key)

-	{

-	if (key->priv_key)

-		BN_clear_free(key->priv_key);

-	key->priv_key = BN_dup(priv_key);

-	return (key->priv_key == NULL) ? 0 : 1;

-	}

-

-const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key)

-	{

-	return key->pub_key;

-	}

-

-int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub_key)

-	{

-	if (key->pub_key != NULL)

-		EC_POINT_free(key->pub_key);

-	key->pub_key = EC_POINT_dup(pub_key, key->group);

-	return (key->pub_key == NULL) ? 0 : 1;

-	}

-

-unsigned int EC_KEY_get_enc_flags(const EC_KEY *key)

-	{

-	return key->enc_flag;

-	}

-

-void EC_KEY_set_enc_flags(EC_KEY *key, unsigned int flags)

-	{

-	key->enc_flag = flags;

-	}

-

-point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key)

-	{

-	return key->conv_form;

-	}

-

-void EC_KEY_set_conv_form(EC_KEY *key, point_conversion_form_t cform)

-	{

-	key->conv_form = cform;

-	if (key->group != NULL)

-		EC_GROUP_set_point_conversion_form(key->group, cform);

-	}

-

-void *EC_KEY_get_key_method_data(EC_KEY *key,

-	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *))

-	{

-	return EC_EX_DATA_get_data(key->method_data, dup_func, free_func, clear_free_func);

-	}

-

-void EC_KEY_insert_key_method_data(EC_KEY *key, void *data,

-	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *))

-	{

-	EC_EXTRA_DATA *ex_data;

-	CRYPTO_w_lock(CRYPTO_LOCK_EC);

-	ex_data = EC_EX_DATA_get_data(key->method_data, dup_func, free_func, clear_free_func);

-	if (ex_data == NULL)

-		EC_EX_DATA_set_data(&key->method_data, data, dup_func, free_func, clear_free_func);

-	CRYPTO_w_unlock(CRYPTO_LOCK_EC);

-	}

-

-void EC_KEY_set_asn1_flag(EC_KEY *key, int flag)

-	{

-	if (key->group != NULL)

-		EC_GROUP_set_asn1_flag(key->group, flag);

-	}

-

-int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx)

-	{

-	if (key->group == NULL)

-		return 0;

-	return EC_GROUP_precompute_mult(key->group, ctx);

-	}

+/* crypto/ec/ec_key.c */
+/*
+ * Written by Nils Larsch for the OpenSSL project.
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2005 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 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ * Portions originally developed by SUN MICROSYSTEMS, INC., and 
+ * contributed to the OpenSSL project.
+ */
+
+#include <string.h>
+#include "ec_lcl.h"
+#include <openssl/err.h>
+#include <string.h>
+
+EC_KEY *EC_KEY_new(void)
+	{
+	EC_KEY *ret;
+
+	ret=(EC_KEY *)OPENSSL_malloc(sizeof(EC_KEY));
+	if (ret == NULL)
+		{
+		ECerr(EC_F_EC_KEY_NEW, ERR_R_MALLOC_FAILURE);
+		return(NULL);
+		}
+
+	ret->version = 1;	
+	ret->group   = NULL;
+	ret->pub_key = NULL;
+	ret->priv_key= NULL;
+	ret->enc_flag= 0; 
+	ret->conv_form = POINT_CONVERSION_UNCOMPRESSED;
+	ret->references= 1;
+	ret->method_data = NULL;
+	return(ret);
+	}
+
+EC_KEY *EC_KEY_new_by_curve_name(int nid)
+	{
+	EC_KEY *ret = EC_KEY_new();
+	if (ret == NULL)
+		return NULL;
+	ret->group = EC_GROUP_new_by_curve_name(nid);
+	if (ret->group == NULL)
+		{
+		EC_KEY_free(ret);
+		return NULL;
+		}
+	return ret;
+	}
+
+void EC_KEY_free(EC_KEY *r)
+	{
+	int i;
+
+	if (r == NULL) return;
+
+	i=CRYPTO_add(&r->references,-1,CRYPTO_LOCK_EC);
+#ifdef REF_PRINT
+	REF_PRINT("EC_KEY",r);
+#endif
+	if (i > 0) return;
+#ifdef REF_CHECK
+	if (i < 0)
+		{
+		fprintf(stderr,"EC_KEY_free, bad reference count\n");
+		abort();
+		}
+#endif
+
+	if (r->group    != NULL) 
+		EC_GROUP_free(r->group);
+	if (r->pub_key  != NULL)
+		EC_POINT_free(r->pub_key);
+	if (r->priv_key != NULL)
+		BN_clear_free(r->priv_key);
+
+	EC_EX_DATA_free_all_data(&r->method_data);
+
+	OPENSSL_cleanse((void *)r, sizeof(EC_KEY));
+
+	OPENSSL_free(r);
+	}
+
+EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src)
+	{
+	EC_EXTRA_DATA *d;
+
+	if (dest == NULL || src == NULL)
+		{
+		ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER);
+		return NULL;
+		}
+	/* copy the parameters */
+	if (src->group)
+		{
+		const EC_METHOD *meth = EC_GROUP_method_of(src->group);
+		/* clear the old group */
+		if (dest->group)
+			EC_GROUP_free(dest->group);
+		dest->group = EC_GROUP_new(meth);
+		if (dest->group == NULL)
+			return NULL;
+		if (!EC_GROUP_copy(dest->group, src->group))
+			return NULL;
+		}
+	/*  copy the public key */
+	if (src->pub_key && src->group)
+		{
+		if (dest->pub_key)
+			EC_POINT_free(dest->pub_key);
+		dest->pub_key = EC_POINT_new(src->group);
+		if (dest->pub_key == NULL)
+			return NULL;
+		if (!EC_POINT_copy(dest->pub_key, src->pub_key))
+			return NULL;
+		}
+	/* copy the private key */
+	if (src->priv_key)
+		{
+		if (dest->priv_key == NULL)
+			{
+			dest->priv_key = BN_new();
+			if (dest->priv_key == NULL)
+				return NULL;
+			}
+		if (!BN_copy(dest->priv_key, src->priv_key))
+			return NULL;
+		}
+	/* copy method/extra data */
+	EC_EX_DATA_free_all_data(&dest->method_data);
+
+	for (d = src->method_data; d != NULL; d = d->next)
+		{
+		void *t = d->dup_func(d->data);
+		
+		if (t == NULL)
+			return 0;
+		if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, d->free_func, d->clear_free_func))
+			return 0;
+		}
+
+	/* copy the rest */
+	dest->enc_flag  = src->enc_flag;
+	dest->conv_form = src->conv_form;
+	dest->version   = src->version;
+
+	return dest;
+	}
+
+EC_KEY *EC_KEY_dup(const EC_KEY *ec_key)
+	{
+	EC_KEY *ret = EC_KEY_new();
+	if (ret == NULL)
+		return NULL;
+	if (EC_KEY_copy(ret, ec_key) == NULL)
+		{
+		EC_KEY_free(ret);
+		return NULL;
+		}
+	return ret;
+	}
+
+int EC_KEY_up_ref(EC_KEY *r)
+	{
+	int i = CRYPTO_add(&r->references, 1, CRYPTO_LOCK_EC);
+#ifdef REF_PRINT
+	REF_PRINT("EC_KEY",r);
+#endif
+#ifdef REF_CHECK
+	if (i < 2)
+		{
+		fprintf(stderr, "EC_KEY_up, bad reference count\n");
+		abort();
+		}
+#endif
+	return ((i > 1) ? 1 : 0);
+	}
+
+int EC_KEY_generate_key(EC_KEY *eckey)
+	{	
+	int	ok = 0;
+	BN_CTX	*ctx = NULL;
+	BIGNUM	*priv_key = NULL, *order = NULL;
+	EC_POINT *pub_key = NULL;
+
+	if (!eckey || !eckey->group)
+		{
+		ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER);
+		return 0;
+		}
+
+	if ((order = BN_new()) == NULL) goto err;
+	if ((ctx = BN_CTX_new()) == NULL) goto err;
+
+	if (eckey->priv_key == NULL)
+		{
+		priv_key = BN_new();
+		if (priv_key == NULL)
+			goto err;
+		}
+	else
+		priv_key = eckey->priv_key;
+
+	if (!EC_GROUP_get_order(eckey->group, order, ctx))
+		goto err;
+
+	do
+		if (!BN_rand_range(priv_key, order))
+			goto err;
+	while (BN_is_zero(priv_key));
+
+	if (eckey->pub_key == NULL)
+		{
+		pub_key = EC_POINT_new(eckey->group);
+		if (pub_key == NULL)
+			goto err;
+		}
+	else
+		pub_key = eckey->pub_key;
+
+	if (!EC_POINT_mul(eckey->group, pub_key, priv_key, NULL, NULL, ctx))
+		goto err;
+
+	eckey->priv_key = priv_key;
+	eckey->pub_key  = pub_key;
+
+	ok=1;
+
+err:	
+	if (order)
+		BN_free(order);
+	if (pub_key  != NULL && eckey->pub_key  == NULL)
+		EC_POINT_free(pub_key);
+	if (priv_key != NULL && eckey->priv_key == NULL)
+		BN_free(priv_key);
+	if (ctx != NULL)
+		BN_CTX_free(ctx);
+	return(ok);
+	}
+
+int EC_KEY_check_key(const EC_KEY *eckey)
+	{
+	int	ok   = 0;
+	BN_CTX	*ctx = NULL;
+	const BIGNUM	*order  = NULL;
+	EC_POINT *point = NULL;
+
+	if (!eckey || !eckey->group || !eckey->pub_key)
+		{
+		ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER);
+		return 0;
+		}
+
+	if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key))
+		{
+		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_AT_INFINITY);
+		goto err;
+		}
+
+	if ((ctx = BN_CTX_new()) == NULL)
+		goto err;
+	if ((point = EC_POINT_new(eckey->group)) == NULL)
+		goto err;
+
+	/* testing whether the pub_key is on the elliptic curve */
+	if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx))
+		{
+		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE);
+		goto err;
+		}
+	/* testing whether pub_key * order is the point at infinity */
+	order = &eckey->group->order;
+	if (BN_is_zero(order))
+		{
+		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_GROUP_ORDER);
+		goto err;
+		}
+	if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx))
+		{
+		ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);
+		goto err;
+		}
+	if (!EC_POINT_is_at_infinity(eckey->group, point))
+		{
+		ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER);
+		goto err;
+		}
+	/* in case the priv_key is present : 
+	 * check if generator * priv_key == pub_key 
+	 */
+	if (eckey->priv_key)
+		{
+		if (BN_cmp(eckey->priv_key, order) >= 0)
+			{
+			ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER);
+			goto err;
+			}
+		if (!EC_POINT_mul(eckey->group, point, eckey->priv_key,
+			NULL, NULL, ctx))
+			{
+			ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);
+			goto err;
+			}
+		if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, 
+			ctx) != 0)
+			{
+			ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY);
+			goto err;
+			}
+		}
+	ok = 1;
+err:
+	if (ctx   != NULL)
+		BN_CTX_free(ctx);
+	if (point != NULL)
+		EC_POINT_free(point);
+	return(ok);
+	}
+
+const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key)
+	{
+	return key->group;
+	}
+
+int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group)
+	{
+	if (key->group != NULL)
+		EC_GROUP_free(key->group);
+	key->group = EC_GROUP_dup(group);
+	return (key->group == NULL) ? 0 : 1;
+	}
+
+const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key)
+	{
+	return key->priv_key;
+	}
+
+int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *priv_key)
+	{
+	if (key->priv_key)
+		BN_clear_free(key->priv_key);
+	key->priv_key = BN_dup(priv_key);
+	return (key->priv_key == NULL) ? 0 : 1;
+	}
+
+const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key)
+	{
+	return key->pub_key;
+	}
+
+int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub_key)
+	{
+	if (key->pub_key != NULL)
+		EC_POINT_free(key->pub_key);
+	key->pub_key = EC_POINT_dup(pub_key, key->group);
+	return (key->pub_key == NULL) ? 0 : 1;
+	}
+
+unsigned int EC_KEY_get_enc_flags(const EC_KEY *key)
+	{
+	return key->enc_flag;
+	}
+
+void EC_KEY_set_enc_flags(EC_KEY *key, unsigned int flags)
+	{
+	key->enc_flag = flags;
+	}
+
+point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key)
+	{
+	return key->conv_form;
+	}
+
+void EC_KEY_set_conv_form(EC_KEY *key, point_conversion_form_t cform)
+	{
+	key->conv_form = cform;
+	if (key->group != NULL)
+		EC_GROUP_set_point_conversion_form(key->group, cform);
+	}
+
+void *EC_KEY_get_key_method_data(EC_KEY *key,
+	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *))
+	{
+	return EC_EX_DATA_get_data(key->method_data, dup_func, free_func, clear_free_func);
+	}
+
+void EC_KEY_insert_key_method_data(EC_KEY *key, void *data,
+	void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *))
+	{
+	EC_EXTRA_DATA *ex_data;
+	CRYPTO_w_lock(CRYPTO_LOCK_EC);
+	ex_data = EC_EX_DATA_get_data(key->method_data, dup_func, free_func, clear_free_func);
+	if (ex_data == NULL)
+		EC_EX_DATA_set_data(&key->method_data, data, dup_func, free_func, clear_free_func);
+	CRYPTO_w_unlock(CRYPTO_LOCK_EC);
+	}
+
+void EC_KEY_set_asn1_flag(EC_KEY *key, int flag)
+	{
+	if (key->group != NULL)
+		EC_GROUP_set_asn1_flag(key->group, flag);
+	}
+
+int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx)
+	{
+	if (key->group == NULL)
+		return 0;
+	return EC_GROUP_precompute_mult(key->group, ctx);
+	}
diff --git a/openssl/crypto/ec/ecp_smpl.c b/openssl/crypto/ec/ecp_smpl.c
index 766f5fc51..66a92e2a9 100644
--- a/openssl/crypto/ec/ecp_smpl.c
+++ b/openssl/crypto/ec/ecp_smpl.c
@@ -1,1719 +1,1719 @@
-/* crypto/ec/ecp_smpl.c */

-/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>

- * for the OpenSSL project. 

- * Includes code written by Bodo Moeller for the OpenSSL project.

-*/

-/* ====================================================================

- * Copyright (c) 1998-2002 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 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.

- * Portions of this software developed by SUN MICROSYSTEMS, INC.,

- * and contributed to the OpenSSL project.

- */

-

-#include <openssl/err.h>

-#include <openssl/symhacks.h>

-

-#include "ec_lcl.h"

-

-const EC_METHOD *EC_GFp_simple_method(void)

-	{

-	static const EC_METHOD ret = {

-		NID_X9_62_prime_field,

-		ec_GFp_simple_group_init,

-		ec_GFp_simple_group_finish,

-		ec_GFp_simple_group_clear_finish,

-		ec_GFp_simple_group_copy,

-		ec_GFp_simple_group_set_curve,

-		ec_GFp_simple_group_get_curve,

-		ec_GFp_simple_group_get_degree,

-		ec_GFp_simple_group_check_discriminant,

-		ec_GFp_simple_point_init,

-		ec_GFp_simple_point_finish,

-		ec_GFp_simple_point_clear_finish,

-		ec_GFp_simple_point_copy,

-		ec_GFp_simple_point_set_to_infinity,

-		ec_GFp_simple_set_Jprojective_coordinates_GFp,

-		ec_GFp_simple_get_Jprojective_coordinates_GFp,

-		ec_GFp_simple_point_set_affine_coordinates,

-		ec_GFp_simple_point_get_affine_coordinates,

-		ec_GFp_simple_set_compressed_coordinates,

-		ec_GFp_simple_point2oct,

-		ec_GFp_simple_oct2point,

-		ec_GFp_simple_add,

-		ec_GFp_simple_dbl,

-		ec_GFp_simple_invert,

-		ec_GFp_simple_is_at_infinity,

-		ec_GFp_simple_is_on_curve,

-		ec_GFp_simple_cmp,

-		ec_GFp_simple_make_affine,

-		ec_GFp_simple_points_make_affine,

-		0 /* mul */,

-		0 /* precompute_mult */,

-		0 /* have_precompute_mult */,	

-		ec_GFp_simple_field_mul,

-		ec_GFp_simple_field_sqr,

-		0 /* field_div */,

-		0 /* field_encode */,

-		0 /* field_decode */,

-		0 /* field_set_to_one */ };

-

-	return &ret;

-	}

-

-

-/* Most method functions in this file are designed to work with

- * non-trivial representations of field elements if necessary

- * (see ecp_mont.c): while standard modular addition and subtraction

- * are used, the field_mul and field_sqr methods will be used for

- * multiplication, and field_encode and field_decode (if defined)

- * will be used for converting between representations.

-

- * Functions ec_GFp_simple_points_make_affine() and

- * ec_GFp_simple_point_get_affine_coordinates() specifically assume

- * that if a non-trivial representation is used, it is a Montgomery

- * representation (i.e. 'encoding' means multiplying by some factor R).

- */

-

-

-int ec_GFp_simple_group_init(EC_GROUP *group)

-	{

-	BN_init(&group->field);

-	BN_init(&group->a);

-	BN_init(&group->b);

-	group->a_is_minus3 = 0;

-	return 1;

-	}

-

-

-void ec_GFp_simple_group_finish(EC_GROUP *group)

-	{

-	BN_free(&group->field);

-	BN_free(&group->a);

-	BN_free(&group->b);

-	}

-

-

-void ec_GFp_simple_group_clear_finish(EC_GROUP *group)

-	{

-	BN_clear_free(&group->field);

-	BN_clear_free(&group->a);

-	BN_clear_free(&group->b);

-	}

-

-

-int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)

-	{

-	if (!BN_copy(&dest->field, &src->field)) return 0;

-	if (!BN_copy(&dest->a, &src->a)) return 0;

-	if (!BN_copy(&dest->b, &src->b)) return 0;

-

-	dest->a_is_minus3 = src->a_is_minus3;

-

-	return 1;

-	}

-

-

-int ec_GFp_simple_group_set_curve(EC_GROUP *group,

-	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)

-	{

-	int ret = 0;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *tmp_a;

-	

-	/* p must be a prime > 3 */

-	if (BN_num_bits(p) <= 2 || !BN_is_odd(p))

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);

-		return 0;

-		}

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	tmp_a = BN_CTX_get(ctx);

-	if (tmp_a == NULL) goto err;

-

-	/* group->field */

-	if (!BN_copy(&group->field, p)) goto err;

-	BN_set_negative(&group->field, 0);

-

-	/* group->a */

-	if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;

-	if (group->meth->field_encode)

-		{ if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }	

-	else

-		if (!BN_copy(&group->a, tmp_a)) goto err;

-	

-	/* group->b */

-	if (!BN_nnmod(&group->b, b, p, ctx)) goto err;

-	if (group->meth->field_encode)

-		if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;

-	

-	/* group->a_is_minus3 */

-	if (!BN_add_word(tmp_a, 3)) goto err;

-	group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));

-

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)

-	{

-	int ret = 0;

-	BN_CTX *new_ctx = NULL;

-	

-	if (p != NULL)

-		{

-		if (!BN_copy(p, &group->field)) return 0;

-		}

-

-	if (a != NULL || b != NULL)

-		{

-		if (group->meth->field_decode)

-			{

-			if (ctx == NULL)

-				{

-				ctx = new_ctx = BN_CTX_new();

-				if (ctx == NULL)

-					return 0;

-				}

-			if (a != NULL)

-				{

-				if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;

-				}

-			if (b != NULL)

-				{

-				if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;

-				}

-			}

-		else

-			{

-			if (a != NULL)

-				{

-				if (!BN_copy(a, &group->a)) goto err;

-				}

-			if (b != NULL)

-				{

-				if (!BN_copy(b, &group->b)) goto err;

-				}

-			}

-		}

-	

-	ret = 1;

-	

- err:

-	if (new_ctx)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_group_get_degree(const EC_GROUP *group)

-	{

-	return BN_num_bits(&group->field);

-	}

-

-

-int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)

-	{

-	int ret = 0;

-	BIGNUM *a,*b,*order,*tmp_1,*tmp_2;

-	const BIGNUM *p = &group->field;

-	BN_CTX *new_ctx = NULL;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);

-			goto err;

-			}

-		}

-	BN_CTX_start(ctx);

-	a = BN_CTX_get(ctx);

-	b = BN_CTX_get(ctx);

-	tmp_1 = BN_CTX_get(ctx);

-	tmp_2 = BN_CTX_get(ctx);

-	order = BN_CTX_get(ctx);

-	if (order == NULL) goto err;

-

-	if (group->meth->field_decode)

-		{

-		if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;

-		if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;

-		}

-	else

-		{

-		if (!BN_copy(a, &group->a)) goto err;

-		if (!BN_copy(b, &group->b)) goto err;

-		}

-	

-	/* check the discriminant:

-	 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) 

-         * 0 =< a, b < p */

-	if (BN_is_zero(a))

-		{

-		if (BN_is_zero(b)) goto err;

-		}

-	else if (!BN_is_zero(b))

-		{

-		if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;

-		if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;

-		if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;

-		/* tmp_1 = 4*a^3 */

-

-		if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;

-		if (!BN_mul_word(tmp_2, 27)) goto err;

-		/* tmp_2 = 27*b^2 */

-

-		if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;

-		if (BN_is_zero(a)) goto err;

-		}

-	ret = 1;

-

-err:

-	if (ctx != NULL)

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_point_init(EC_POINT *point)

-	{

-	BN_init(&point->X);

-	BN_init(&point->Y);

-	BN_init(&point->Z);

-	point->Z_is_one = 0;

-

-	return 1;

-	}

-

-

-void ec_GFp_simple_point_finish(EC_POINT *point)

-	{

-	BN_free(&point->X);

-	BN_free(&point->Y);

-	BN_free(&point->Z);

-	}

-

-

-void ec_GFp_simple_point_clear_finish(EC_POINT *point)

-	{

-	BN_clear_free(&point->X);

-	BN_clear_free(&point->Y);

-	BN_clear_free(&point->Z);

-	point->Z_is_one = 0;

-	}

-

-

-int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)

-	{

-	if (!BN_copy(&dest->X, &src->X)) return 0;

-	if (!BN_copy(&dest->Y, &src->Y)) return 0;

-	if (!BN_copy(&dest->Z, &src->Z)) return 0;

-	dest->Z_is_one = src->Z_is_one;

-

-	return 1;

-	}

-

-

-int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)

-	{

-	point->Z_is_one = 0;

-	BN_zero(&point->Z);

-	return 1;

-	}

-

-

-int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,

-	const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	int ret = 0;

-	

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	if (x != NULL)

-		{

-		if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;

-		if (group->meth->field_encode)

-			{

-			if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;

-			}

-		}

-	

-	if (y != NULL)

-		{

-		if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;

-		if (group->meth->field_encode)

-			{

-			if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;

-			}

-		}

-	

-	if (z != NULL)

-		{

-		int Z_is_one;

-

-		if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;

-		Z_is_one = BN_is_one(&point->Z);

-		if (group->meth->field_encode)

-			{

-			if (Z_is_one && (group->meth->field_set_to_one != 0))

-				{

-				if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;

-				}

-			else

-				{

-				if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;

-				}

-			}

-		point->Z_is_one = Z_is_one;

-		}

-	

-	ret = 1;

-	

- err:

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,

-	BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	int ret = 0;

-	

-	if (group->meth->field_decode != 0)

-		{

-		if (ctx == NULL)

-			{

-			ctx = new_ctx = BN_CTX_new();

-			if (ctx == NULL)

-				return 0;

-			}

-

-		if (x != NULL)

-			{

-			if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;

-			}

-		if (y != NULL)

-			{

-			if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;

-			}

-		if (z != NULL)

-			{

-			if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;

-			}

-		}

-	else	

-		{

-		if (x != NULL)

-			{

-			if (!BN_copy(x, &point->X)) goto err;

-			}

-		if (y != NULL)

-			{

-			if (!BN_copy(y, &point->Y)) goto err;

-			}

-		if (z != NULL)

-			{

-			if (!BN_copy(z, &point->Z)) goto err;

-			}

-		}

-	

-	ret = 1;

-

- err:

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,

-	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)

-	{

-	if (x == NULL || y == NULL)

-		{

-		/* unlike for projective coordinates, we do not tolerate this */

-		ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);

-		return 0;

-		}

-

-	return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);

-	}

-

-

-int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,

-	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *Z, *Z_1, *Z_2, *Z_3;

-	const BIGNUM *Z_;

-	int ret = 0;

-

-	if (EC_POINT_is_at_infinity(group, point))

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);

-		return 0;

-		}

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	Z = BN_CTX_get(ctx);

-	Z_1 = BN_CTX_get(ctx);

-	Z_2 = BN_CTX_get(ctx);

-	Z_3 = BN_CTX_get(ctx);

-	if (Z_3 == NULL) goto err;

-

-	/* transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3) */

-	

-	if (group->meth->field_decode)

-		{

-		if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;

-		Z_ = Z;

-		}

-	else

-		{

-		Z_ = &point->Z;

-		}

-	

-	if (BN_is_one(Z_))

-		{

-		if (group->meth->field_decode)

-			{

-			if (x != NULL)

-				{

-				if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;

-				}

-			if (y != NULL)

-				{

-				if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;

-				}

-			}

-		else

-			{

-			if (x != NULL)

-				{

-				if (!BN_copy(x, &point->X)) goto err;

-				}

-			if (y != NULL)

-				{

-				if (!BN_copy(y, &point->Y)) goto err;

-				}

-			}

-		}

-	else

-		{

-		if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);

-			goto err;

-			}

-		

-		if (group->meth->field_encode == 0)

-			{

-			/* field_sqr works on standard representation */

-			if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;

-			}

-		else

-			{

-			if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;

-			}

-	

-		if (x != NULL)

-			{

-			/* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */

-			if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;

-			}

-

-		if (y != NULL)

-			{

-			if (group->meth->field_encode == 0)

-				{

-				/* field_mul works on standard representation */

-				if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;

-				}

-			else

-				{

-				if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;

-				}

-

-			/* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */

-			if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;

-			}

-		}

-

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,

-	const BIGNUM *x_, int y_bit, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *tmp1, *tmp2, *x, *y;

-	int ret = 0;

-

-	/* clear error queue*/

-	ERR_clear_error();

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	y_bit = (y_bit != 0);

-

-	BN_CTX_start(ctx);

-	tmp1 = BN_CTX_get(ctx);

-	tmp2 = BN_CTX_get(ctx);

-	x = BN_CTX_get(ctx);

-	y = BN_CTX_get(ctx);

-	if (y == NULL) goto err;

-

-	/* Recover y.  We have a Weierstrass equation

-	 *     y^2 = x^3 + a*x + b,

-	 * so  y  is one of the square roots of  x^3 + a*x + b.

-	 */

-

-	/* tmp1 := x^3 */

-	if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;

-	if (group->meth->field_decode == 0)

-		{

-		/* field_{sqr,mul} work on standard representation */

-		if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;

-		if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;

-		}

-	else

-		{

-		if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;

-		if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;

-		}

-	

-	/* tmp1 := tmp1 + a*x */

-	if (group->a_is_minus3)

-		{

-		if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;

-		if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;

-		if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;

-		}

-	else

-		{

-		if (group->meth->field_decode)

-			{

-			if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;

-			if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;

-			}

-		else

-			{

-			/* field_mul works on standard representation */

-			if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;

-			}

-		

-		if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;

-		}

-	

-	/* tmp1 := tmp1 + b */

-	if (group->meth->field_decode)

-		{

-		if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;

-		if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;

-		}

-	else

-		{

-		if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;

-		}

-	

-	if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))

-		{

-		unsigned long err = ERR_peek_last_error();

-		

-		if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)

-			{

-			ERR_clear_error();

-			ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);

-			}

-		else

-			ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);

-		goto err;

-		}

-

-	if (y_bit != BN_is_odd(y))

-		{

-		if (BN_is_zero(y))

-			{

-			int kron;

-

-			kron = BN_kronecker(x, &group->field, ctx);

-			if (kron == -2) goto err;

-

-			if (kron == 1)

-				ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);

-			else

-				/* BN_mod_sqrt() should have cought this error (not a square) */

-				ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);

-			goto err;

-			}

-		if (!BN_usub(y, &group->field, y)) goto err;

-		}

-	if (y_bit != BN_is_odd(y))

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);

-		goto err;

-		}

-

-	if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;

-

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,

-	unsigned char *buf, size_t len, BN_CTX *ctx)

-	{

-	size_t ret;

-	BN_CTX *new_ctx = NULL;

-	int used_ctx = 0;

-	BIGNUM *x, *y;

-	size_t field_len, i, skip;

-

-	if ((form != POINT_CONVERSION_COMPRESSED)

-		&& (form != POINT_CONVERSION_UNCOMPRESSED)

-		&& (form != POINT_CONVERSION_HYBRID))

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);

-		goto err;

-		}

-

-	if (EC_POINT_is_at_infinity(group, point))

-		{

-		/* encodes to a single 0 octet */

-		if (buf != NULL)

-			{

-			if (len < 1)

-				{

-				ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);

-				return 0;

-				}

-			buf[0] = 0;

-			}

-		return 1;

-		}

-

-

-	/* ret := required output buffer length */

-	field_len = BN_num_bytes(&group->field);

-	ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;

-

-	/* if 'buf' is NULL, just return required length */

-	if (buf != NULL)

-		{

-		if (len < ret)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);

-			goto err;

-			}

-

-		if (ctx == NULL)

-			{

-			ctx = new_ctx = BN_CTX_new();

-			if (ctx == NULL)

-				return 0;

-			}

-

-		BN_CTX_start(ctx);

-		used_ctx = 1;

-		x = BN_CTX_get(ctx);

-		y = BN_CTX_get(ctx);

-		if (y == NULL) goto err;

-

-		if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;

-

-		if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))

-			buf[0] = form + 1;

-		else

-			buf[0] = form;

-	

-		i = 1;

-		

-		skip = field_len - BN_num_bytes(x);

-		if (skip > field_len)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-			goto err;

-			}

-		while (skip > 0)

-			{

-			buf[i++] = 0;

-			skip--;

-			}

-		skip = BN_bn2bin(x, buf + i);

-		i += skip;

-		if (i != 1 + field_len)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-			goto err;

-			}

-

-		if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)

-			{

-			skip = field_len - BN_num_bytes(y);

-			if (skip > field_len)

-				{

-				ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-				goto err;

-				}

-			while (skip > 0)

-				{

-				buf[i++] = 0;

-				skip--;

-				}

-			skip = BN_bn2bin(y, buf + i);

-			i += skip;

-			}

-

-		if (i != ret)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);

-			goto err;

-			}

-		}

-	

-	if (used_ctx)

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-

- err:

-	if (used_ctx)

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return 0;

-	}

-

-

-int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,

-	const unsigned char *buf, size_t len, BN_CTX *ctx)

-	{

-	point_conversion_form_t form;

-	int y_bit;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *x, *y;

-	size_t field_len, enc_len;

-	int ret = 0;

-

-	if (len == 0)

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);

-		return 0;

-		}

-	form = buf[0];

-	y_bit = form & 1;

-	form = form & ~1U;

-	if ((form != 0)	&& (form != POINT_CONVERSION_COMPRESSED)

-		&& (form != POINT_CONVERSION_UNCOMPRESSED)

-		&& (form != POINT_CONVERSION_HYBRID))

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		return 0;

-		}

-	if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		return 0;

-		}

-

-	if (form == 0)

-		{

-		if (len != 1)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-			return 0;

-			}

-

-		return EC_POINT_set_to_infinity(group, point);

-		}

-	

-	field_len = BN_num_bytes(&group->field);

-	enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;

-

-	if (len != enc_len)

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		return 0;

-		}

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	x = BN_CTX_get(ctx);

-	y = BN_CTX_get(ctx);

-	if (y == NULL) goto err;

-

-	if (!BN_bin2bn(buf + 1, field_len, x)) goto err;

-	if (BN_ucmp(x, &group->field) >= 0)

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-		goto err;

-		}

-

-	if (form == POINT_CONVERSION_COMPRESSED)

-		{

-		if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;

-		}

-	else

-		{

-		if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;

-		if (BN_ucmp(y, &group->field) >= 0)

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-			goto err;

-			}

-		if (form == POINT_CONVERSION_HYBRID)

-			{

-			if (y_bit != BN_is_odd(y))

-				{

-				ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);

-				goto err;

-				}

-			}

-

-		if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;

-		}

-	

-	if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);

-		goto err;

-		}

-

-	ret = 1;

-	

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)

-	{

-	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);

-	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);

-	const BIGNUM *p;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;

-	int ret = 0;

-	

-	if (a == b)

-		return EC_POINT_dbl(group, r, a, ctx);

-	if (EC_POINT_is_at_infinity(group, a))

-		return EC_POINT_copy(r, b);

-	if (EC_POINT_is_at_infinity(group, b))

-		return EC_POINT_copy(r, a);

-	

-	field_mul = group->meth->field_mul;

-	field_sqr = group->meth->field_sqr;

-	p = &group->field;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	n0 = BN_CTX_get(ctx);

-	n1 = BN_CTX_get(ctx);

-	n2 = BN_CTX_get(ctx);

-	n3 = BN_CTX_get(ctx);

-	n4 = BN_CTX_get(ctx);

-	n5 = BN_CTX_get(ctx);

-	n6 = BN_CTX_get(ctx);

-	if (n6 == NULL) goto end;

-

-	/* Note that in this function we must not read components of 'a' or 'b'

-	 * once we have written the corresponding components of 'r'.

-	 * ('r' might be one of 'a' or 'b'.)

-	 */

-

-	/* n1, n2 */

-	if (b->Z_is_one)

-		{

-		if (!BN_copy(n1, &a->X)) goto end;

-		if (!BN_copy(n2, &a->Y)) goto end;

-		/* n1 = X_a */

-		/* n2 = Y_a */

-		}

-	else

-		{

-		if (!field_sqr(group, n0, &b->Z, ctx)) goto end;

-		if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;

-		/* n1 = X_a * Z_b^2 */

-

-		if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;

-		if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;

-		/* n2 = Y_a * Z_b^3 */

-		}

-

-	/* n3, n4 */

-	if (a->Z_is_one)

-		{

-		if (!BN_copy(n3, &b->X)) goto end;

-		if (!BN_copy(n4, &b->Y)) goto end;

-		/* n3 = X_b */

-		/* n4 = Y_b */

-		}

-	else

-		{

-		if (!field_sqr(group, n0, &a->Z, ctx)) goto end;

-		if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;

-		/* n3 = X_b * Z_a^2 */

-

-		if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;

-		if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;

-		/* n4 = Y_b * Z_a^3 */

-		}

-

-	/* n5, n6 */

-	if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;

-	if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;

-	/* n5 = n1 - n3 */

-	/* n6 = n2 - n4 */

-

-	if (BN_is_zero(n5))

-		{

-		if (BN_is_zero(n6))

-			{

-			/* a is the same point as b */

-			BN_CTX_end(ctx);

-			ret = EC_POINT_dbl(group, r, a, ctx);

-			ctx = NULL;

-			goto end;

-			}

-		else

-			{

-			/* a is the inverse of b */

-			BN_zero(&r->Z);

-			r->Z_is_one = 0;

-			ret = 1;

-			goto end;

-			}

-		}

-

-	/* 'n7', 'n8' */

-	if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;

-	if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;

-	/* 'n7' = n1 + n3 */

-	/* 'n8' = n2 + n4 */

-

-	/* Z_r */

-	if (a->Z_is_one && b->Z_is_one)

-		{

-		if (!BN_copy(&r->Z, n5)) goto end;

-		}

-	else

-		{

-		if (a->Z_is_one)

-			{ if (!BN_copy(n0, &b->Z)) goto end; }

-		else if (b->Z_is_one)

-			{ if (!BN_copy(n0, &a->Z)) goto end; }

-		else

-			{ if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }

-		if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;

-		}

-	r->Z_is_one = 0;

-	/* Z_r = Z_a * Z_b * n5 */

-

-	/* X_r */

-	if (!field_sqr(group, n0, n6, ctx)) goto end;

-	if (!field_sqr(group, n4, n5, ctx)) goto end;

-	if (!field_mul(group, n3, n1, n4, ctx)) goto end;

-	if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;

-	/* X_r = n6^2 - n5^2 * 'n7' */

-	

-	/* 'n9' */

-	if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;

-	if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;

-	/* n9 = n5^2 * 'n7' - 2 * X_r */

-

-	/* Y_r */

-	if (!field_mul(group, n0, n0, n6, ctx)) goto end;

-	if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */

-	if (!field_mul(group, n1, n2, n5, ctx)) goto end;

-	if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;

-	if (BN_is_odd(n0))

-		if (!BN_add(n0, n0, p)) goto end;

-	/* now  0 <= n0 < 2*p,  and n0 is even */

-	if (!BN_rshift1(&r->Y, n0)) goto end;

-	/* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */

-

-	ret = 1;

-

- end:

-	if (ctx) /* otherwise we already called BN_CTX_end */

-		BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)

-	{

-	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);

-	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);

-	const BIGNUM *p;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *n0, *n1, *n2, *n3;

-	int ret = 0;

-	

-	if (EC_POINT_is_at_infinity(group, a))

-		{

-		BN_zero(&r->Z);

-		r->Z_is_one = 0;

-		return 1;

-		}

-

-	field_mul = group->meth->field_mul;

-	field_sqr = group->meth->field_sqr;

-	p = &group->field;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	n0 = BN_CTX_get(ctx);

-	n1 = BN_CTX_get(ctx);

-	n2 = BN_CTX_get(ctx);

-	n3 = BN_CTX_get(ctx);

-	if (n3 == NULL) goto err;

-

-	/* Note that in this function we must not read components of 'a'

-	 * once we have written the corresponding components of 'r'.

-	 * ('r' might the same as 'a'.)

-	 */

-

-	/* n1 */

-	if (a->Z_is_one)

-		{

-		if (!field_sqr(group, n0, &a->X, ctx)) goto err;

-		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;

-		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;

-		if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;

-		/* n1 = 3 * X_a^2 + a_curve */

-		}

-	else if (group->a_is_minus3)

-		{

-		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;

-		if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;

-		if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;

-		if (!field_mul(group, n1, n0, n2, ctx)) goto err;

-		if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;

-		if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;

-		/* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)

-		 *    = 3 * X_a^2 - 3 * Z_a^4 */

-		}

-	else

-		{

-		if (!field_sqr(group, n0, &a->X, ctx)) goto err;

-		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;

-		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;

-		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;

-		if (!field_sqr(group, n1, n1, ctx)) goto err;

-		if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;

-		if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;

-		/* n1 = 3 * X_a^2 + a_curve * Z_a^4 */

-		}

-

-	/* Z_r */

-	if (a->Z_is_one)

-		{

-		if (!BN_copy(n0, &a->Y)) goto err;

-		}

-	else

-		{

-		if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;

-		}

-	if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;

-	r->Z_is_one = 0;

-	/* Z_r = 2 * Y_a * Z_a */

-

-	/* n2 */

-	if (!field_sqr(group, n3, &a->Y, ctx)) goto err;

-	if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;

-	if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;

-	/* n2 = 4 * X_a * Y_a^2 */

-

-	/* X_r */

-	if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;

-	if (!field_sqr(group, &r->X, n1, ctx)) goto err;

-	if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;

-	/* X_r = n1^2 - 2 * n2 */

-	

-	/* n3 */

-	if (!field_sqr(group, n0, n3, ctx)) goto err;

-	if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;

-	/* n3 = 8 * Y_a^4 */

-	

-	/* Y_r */

-	if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;

-	if (!field_mul(group, n0, n1, n0, ctx)) goto err;

-	if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;

-	/* Y_r = n1 * (n2 - X_r) - n3 */

-

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)

-	{

-	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))

-		/* point is its own inverse */

-		return 1;

-	

-	return BN_usub(&point->Y, &group->field, &point->Y);

-	}

-

-

-int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)

-	{

-	return BN_is_zero(&point->Z);

-	}

-

-

-int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)

-	{

-	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);

-	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);

-	const BIGNUM *p;

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *rh, *tmp, *Z4, *Z6;

-	int ret = -1;

-

-	if (EC_POINT_is_at_infinity(group, point))

-		return 1;

-	

-	field_mul = group->meth->field_mul;

-	field_sqr = group->meth->field_sqr;

-	p = &group->field;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return -1;

-		}

-

-	BN_CTX_start(ctx);

-	rh = BN_CTX_get(ctx);

-	tmp = BN_CTX_get(ctx);

-	Z4 = BN_CTX_get(ctx);

-	Z6 = BN_CTX_get(ctx);

-	if (Z6 == NULL) goto err;

-

-	/* We have a curve defined by a Weierstrass equation

-	 *      y^2 = x^3 + a*x + b.

-	 * The point to consider is given in Jacobian projective coordinates

-	 * where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).

-	 * Substituting this and multiplying by  Z^6  transforms the above equation into

-	 *      Y^2 = X^3 + a*X*Z^4 + b*Z^6.

-	 * To test this, we add up the right-hand side in 'rh'.

-	 */

-

-	/* rh := X^2 */

-	if (!field_sqr(group, rh, &point->X, ctx)) goto err;

-

-	if (!point->Z_is_one)

-		{

-		if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;

-		if (!field_sqr(group, Z4, tmp, ctx)) goto err;

-		if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;

-

-		/* rh := (rh + a*Z^4)*X */

-		if (group->a_is_minus3)

-			{

-			if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;

-			if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;

-			if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;

-			if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;

-			}

-		else

-			{

-			if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;

-			if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;

-			if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;

-			}

-

-		/* rh := rh + b*Z^6 */

-		if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;

-		if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;

-		}

-	else

-		{

-		/* point->Z_is_one */

-

-		/* rh := (rh + a)*X */

-		if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;

-		if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;

-		/* rh := rh + b */

-		if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;

-		}

-

-	/* 'lh' := Y^2 */

-	if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;

-

-	ret = (0 == BN_ucmp(tmp, rh));

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)

-	{

-	/* return values:

-	 *  -1   error

-	 *   0   equal (in affine coordinates)

-	 *   1   not equal

-	 */

-

-	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);

-	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *tmp1, *tmp2, *Za23, *Zb23;

-	const BIGNUM *tmp1_, *tmp2_;

-	int ret = -1;

-	

-	if (EC_POINT_is_at_infinity(group, a))

-		{

-		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;

-		}

-

-	if (EC_POINT_is_at_infinity(group, b))

-		return 1;

-	

-	if (a->Z_is_one && b->Z_is_one)

-		{

-		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;

-		}

-

-	field_mul = group->meth->field_mul;

-	field_sqr = group->meth->field_sqr;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return -1;

-		}

-

-	BN_CTX_start(ctx);

-	tmp1 = BN_CTX_get(ctx);

-	tmp2 = BN_CTX_get(ctx);

-	Za23 = BN_CTX_get(ctx);

-	Zb23 = BN_CTX_get(ctx);

-	if (Zb23 == NULL) goto end;

-

-	/* We have to decide whether

-	 *     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),

-	 * or equivalently, whether

-	 *     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).

-	 */

-

-	if (!b->Z_is_one)

-		{

-		if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;

-		if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;

-		tmp1_ = tmp1;

-		}

-	else

-		tmp1_ = &a->X;

-	if (!a->Z_is_one)

-		{

-		if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;

-		if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;

-		tmp2_ = tmp2;

-		}

-	else

-		tmp2_ = &b->X;

-	

-	/* compare  X_a*Z_b^2  with  X_b*Z_a^2 */

-	if (BN_cmp(tmp1_, tmp2_) != 0)

-		{

-		ret = 1; /* points differ */

-		goto end;

-		}

-

-

-	if (!b->Z_is_one)

-		{

-		if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;

-		if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;

-		/* tmp1_ = tmp1 */

-		}

-	else

-		tmp1_ = &a->Y;

-	if (!a->Z_is_one)

-		{

-		if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;

-		if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;

-		/* tmp2_ = tmp2 */

-		}

-	else

-		tmp2_ = &b->Y;

-

-	/* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */

-	if (BN_cmp(tmp1_, tmp2_) != 0)

-		{

-		ret = 1; /* points differ */

-		goto end;

-		}

-

-	/* points are equal */

-	ret = 0;

-

- end:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *x, *y;

-	int ret = 0;

-

-	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))

-		return 1;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	x = BN_CTX_get(ctx);

-	y = BN_CTX_get(ctx);

-	if (y == NULL) goto err;

-

-	if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;

-	if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;

-	if (!point->Z_is_one)

-		{

-		ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);

-		goto err;

-		}

-	

-	ret = 1;

-

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	return ret;

-	}

-

-

-int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)

-	{

-	BN_CTX *new_ctx = NULL;

-	BIGNUM *tmp0, *tmp1;

-	size_t pow2 = 0;

-	BIGNUM **heap = NULL;

-	size_t i;

-	int ret = 0;

-

-	if (num == 0)

-		return 1;

-

-	if (ctx == NULL)

-		{

-		ctx = new_ctx = BN_CTX_new();

-		if (ctx == NULL)

-			return 0;

-		}

-

-	BN_CTX_start(ctx);

-	tmp0 = BN_CTX_get(ctx);

-	tmp1 = BN_CTX_get(ctx);

-	if (tmp0  == NULL || tmp1 == NULL) goto err;

-

-	/* Before converting the individual points, compute inverses of all Z values.

-	 * Modular inversion is rather slow, but luckily we can do with a single

-	 * explicit inversion, plus about 3 multiplications per input value.

-	 */

-

-	pow2 = 1;

-	while (num > pow2)

-		pow2 <<= 1;

-	/* Now pow2 is the smallest power of 2 satifsying pow2 >= num.

-	 * We need twice that. */

-	pow2 <<= 1;

-

-	heap = OPENSSL_malloc(pow2 * sizeof heap[0]);

-	if (heap == NULL) goto err;

-	

-	/* The array is used as a binary tree, exactly as in heapsort:

-	 *

-	 *                               heap[1]

-	 *                 heap[2]                     heap[3]

-	 *          heap[4]       heap[5]       heap[6]       heap[7]

-	 *   heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]

-	 *

-	 * We put the Z's in the last line;

-	 * then we set each other node to the product of its two child-nodes (where

-	 * empty or 0 entries are treated as ones);

-	 * then we invert heap[1];

-	 * then we invert each other node by replacing it by the product of its

-	 * parent (after inversion) and its sibling (before inversion).

-	 */

-	heap[0] = NULL;

-	for (i = pow2/2 - 1; i > 0; i--)

-		heap[i] = NULL;

-	for (i = 0; i < num; i++)

-		heap[pow2/2 + i] = &points[i]->Z;

-	for (i = pow2/2 + num; i < pow2; i++)

-		heap[i] = NULL;

-	

-	/* set each node to the product of its children */

-	for (i = pow2/2 - 1; i > 0; i--)

-		{

-		heap[i] = BN_new();

-		if (heap[i] == NULL) goto err;

-		

-		if (heap[2*i] != NULL)

-			{

-			if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))

-				{

-				if (!BN_copy(heap[i], heap[2*i])) goto err;

-				}

-			else

-				{

-				if (BN_is_zero(heap[2*i]))

-					{

-					if (!BN_copy(heap[i], heap[2*i + 1])) goto err;

-					}

-				else

-					{

-					if (!group->meth->field_mul(group, heap[i],

-						heap[2*i], heap[2*i + 1], ctx)) goto err;

-					}

-				}

-			}

-		}

-

-	/* invert heap[1] */

-	if (!BN_is_zero(heap[1]))

-		{

-		if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))

-			{

-			ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);

-			goto err;

-			}

-		}

-	if (group->meth->field_encode != 0)

-		{

-		/* in the Montgomery case, we just turned  R*H  (representing H)

-		 * into  1/(R*H),  but we need  R*(1/H)  (representing 1/H);

-		 * i.e. we have need to multiply by the Montgomery factor twice */

-		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;

-		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;

-		}

-

-	/* set other heap[i]'s to their inverses */

-	for (i = 2; i < pow2/2 + num; i += 2)

-		{

-		/* i is even */

-		if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))

-			{

-			if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;

-			if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;

-			if (!BN_copy(heap[i], tmp0)) goto err;

-			if (!BN_copy(heap[i + 1], tmp1)) goto err;

-			}

-		else

-			{

-			if (!BN_copy(heap[i], heap[i/2])) goto err;

-			}

-		}

-

-	/* we have replaced all non-zero Z's by their inverses, now fix up all the points */

-	for (i = 0; i < num; i++)

-		{

-		EC_POINT *p = points[i];

-		

-		if (!BN_is_zero(&p->Z))

-			{

-			/* turn  (X, Y, 1/Z)  into  (X/Z^2, Y/Z^3, 1) */

-

-			if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;

-			if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;

-

-			if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;

-			if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;

-		

-			if (group->meth->field_set_to_one != 0)

-				{

-				if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;

-				}

-			else

-				{

-				if (!BN_one(&p->Z)) goto err;

-				}

-			p->Z_is_one = 1;

-			}

-		}

-

-	ret = 1;

-		

- err:

-	BN_CTX_end(ctx);

-	if (new_ctx != NULL)

-		BN_CTX_free(new_ctx);

-	if (heap != NULL)

-		{

-		/* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */

-		for (i = pow2/2 - 1; i > 0; i--)

-			{

-			if (heap[i] != NULL)

-				BN_clear_free(heap[i]);

-			}

-		OPENSSL_free(heap);

-		}

-	return ret;

-	}

-

-

-int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)

-	{

-	return BN_mod_mul(r, a, b, &group->field, ctx);

-	}

-

-

-int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)

-	{

-	return BN_mod_sqr(r, a, &group->field, ctx);

-	}

+/* crypto/ec/ecp_smpl.c */
+/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
+ * for the OpenSSL project. 
+ * Includes code written by Bodo Moeller for the OpenSSL project.
+*/
+/* ====================================================================
+ * Copyright (c) 1998-2002 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 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ * Portions of this software developed by SUN MICROSYSTEMS, INC.,
+ * and contributed to the OpenSSL project.
+ */
+
+#include <openssl/err.h>
+#include <openssl/symhacks.h>
+
+#include "ec_lcl.h"
+
+const EC_METHOD *EC_GFp_simple_method(void)
+	{
+	static const EC_METHOD ret = {
+		NID_X9_62_prime_field,
+		ec_GFp_simple_group_init,
+		ec_GFp_simple_group_finish,
+		ec_GFp_simple_group_clear_finish,
+		ec_GFp_simple_group_copy,
+		ec_GFp_simple_group_set_curve,
+		ec_GFp_simple_group_get_curve,
+		ec_GFp_simple_group_get_degree,
+		ec_GFp_simple_group_check_discriminant,
+		ec_GFp_simple_point_init,
+		ec_GFp_simple_point_finish,
+		ec_GFp_simple_point_clear_finish,
+		ec_GFp_simple_point_copy,
+		ec_GFp_simple_point_set_to_infinity,
+		ec_GFp_simple_set_Jprojective_coordinates_GFp,
+		ec_GFp_simple_get_Jprojective_coordinates_GFp,
+		ec_GFp_simple_point_set_affine_coordinates,
+		ec_GFp_simple_point_get_affine_coordinates,
+		ec_GFp_simple_set_compressed_coordinates,
+		ec_GFp_simple_point2oct,
+		ec_GFp_simple_oct2point,
+		ec_GFp_simple_add,
+		ec_GFp_simple_dbl,
+		ec_GFp_simple_invert,
+		ec_GFp_simple_is_at_infinity,
+		ec_GFp_simple_is_on_curve,
+		ec_GFp_simple_cmp,
+		ec_GFp_simple_make_affine,
+		ec_GFp_simple_points_make_affine,
+		0 /* mul */,
+		0 /* precompute_mult */,
+		0 /* have_precompute_mult */,	
+		ec_GFp_simple_field_mul,
+		ec_GFp_simple_field_sqr,
+		0 /* field_div */,
+		0 /* field_encode */,
+		0 /* field_decode */,
+		0 /* field_set_to_one */ };
+
+	return &ret;
+	}
+
+
+/* Most method functions in this file are designed to work with
+ * non-trivial representations of field elements if necessary
+ * (see ecp_mont.c): while standard modular addition and subtraction
+ * are used, the field_mul and field_sqr methods will be used for
+ * multiplication, and field_encode and field_decode (if defined)
+ * will be used for converting between representations.
+
+ * Functions ec_GFp_simple_points_make_affine() and
+ * ec_GFp_simple_point_get_affine_coordinates() specifically assume
+ * that if a non-trivial representation is used, it is a Montgomery
+ * representation (i.e. 'encoding' means multiplying by some factor R).
+ */
+
+
+int ec_GFp_simple_group_init(EC_GROUP *group)
+	{
+	BN_init(&group->field);
+	BN_init(&group->a);
+	BN_init(&group->b);
+	group->a_is_minus3 = 0;
+	return 1;
+	}
+
+
+void ec_GFp_simple_group_finish(EC_GROUP *group)
+	{
+	BN_free(&group->field);
+	BN_free(&group->a);
+	BN_free(&group->b);
+	}
+
+
+void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+	{
+	BN_clear_free(&group->field);
+	BN_clear_free(&group->a);
+	BN_clear_free(&group->b);
+	}
+
+
+int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+	{
+	if (!BN_copy(&dest->field, &src->field)) return 0;
+	if (!BN_copy(&dest->a, &src->a)) return 0;
+	if (!BN_copy(&dest->b, &src->b)) return 0;
+
+	dest->a_is_minus3 = src->a_is_minus3;
+
+	return 1;
+	}
+
+
+int ec_GFp_simple_group_set_curve(EC_GROUP *group,
+	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	int ret = 0;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *tmp_a;
+	
+	/* p must be a prime > 3 */
+	if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
+		return 0;
+		}
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	tmp_a = BN_CTX_get(ctx);
+	if (tmp_a == NULL) goto err;
+
+	/* group->field */
+	if (!BN_copy(&group->field, p)) goto err;
+	BN_set_negative(&group->field, 0);
+
+	/* group->a */
+	if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
+	if (group->meth->field_encode)
+		{ if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }	
+	else
+		if (!BN_copy(&group->a, tmp_a)) goto err;
+	
+	/* group->b */
+	if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
+	if (group->meth->field_encode)
+		if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
+	
+	/* group->a_is_minus3 */
+	if (!BN_add_word(tmp_a, 3)) goto err;
+	group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
+	{
+	int ret = 0;
+	BN_CTX *new_ctx = NULL;
+	
+	if (p != NULL)
+		{
+		if (!BN_copy(p, &group->field)) return 0;
+		}
+
+	if (a != NULL || b != NULL)
+		{
+		if (group->meth->field_decode)
+			{
+			if (ctx == NULL)
+				{
+				ctx = new_ctx = BN_CTX_new();
+				if (ctx == NULL)
+					return 0;
+				}
+			if (a != NULL)
+				{
+				if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
+				}
+			if (b != NULL)
+				{
+				if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
+				}
+			}
+		else
+			{
+			if (a != NULL)
+				{
+				if (!BN_copy(a, &group->a)) goto err;
+				}
+			if (b != NULL)
+				{
+				if (!BN_copy(b, &group->b)) goto err;
+				}
+			}
+		}
+	
+	ret = 1;
+	
+ err:
+	if (new_ctx)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
+	{
+	return BN_num_bits(&group->field);
+	}
+
+
+int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
+	{
+	int ret = 0;
+	BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
+	const BIGNUM *p = &group->field;
+	BN_CTX *new_ctx = NULL;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
+			goto err;
+			}
+		}
+	BN_CTX_start(ctx);
+	a = BN_CTX_get(ctx);
+	b = BN_CTX_get(ctx);
+	tmp_1 = BN_CTX_get(ctx);
+	tmp_2 = BN_CTX_get(ctx);
+	order = BN_CTX_get(ctx);
+	if (order == NULL) goto err;
+
+	if (group->meth->field_decode)
+		{
+		if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
+		if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
+		}
+	else
+		{
+		if (!BN_copy(a, &group->a)) goto err;
+		if (!BN_copy(b, &group->b)) goto err;
+		}
+	
+	/* check the discriminant:
+	 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) 
+         * 0 =< a, b < p */
+	if (BN_is_zero(a))
+		{
+		if (BN_is_zero(b)) goto err;
+		}
+	else if (!BN_is_zero(b))
+		{
+		if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
+		if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
+		if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
+		/* tmp_1 = 4*a^3 */
+
+		if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
+		if (!BN_mul_word(tmp_2, 27)) goto err;
+		/* tmp_2 = 27*b^2 */
+
+		if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
+		if (BN_is_zero(a)) goto err;
+		}
+	ret = 1;
+
+err:
+	if (ctx != NULL)
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_point_init(EC_POINT *point)
+	{
+	BN_init(&point->X);
+	BN_init(&point->Y);
+	BN_init(&point->Z);
+	point->Z_is_one = 0;
+
+	return 1;
+	}
+
+
+void ec_GFp_simple_point_finish(EC_POINT *point)
+	{
+	BN_free(&point->X);
+	BN_free(&point->Y);
+	BN_free(&point->Z);
+	}
+
+
+void ec_GFp_simple_point_clear_finish(EC_POINT *point)
+	{
+	BN_clear_free(&point->X);
+	BN_clear_free(&point->Y);
+	BN_clear_free(&point->Z);
+	point->Z_is_one = 0;
+	}
+
+
+int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
+	{
+	if (!BN_copy(&dest->X, &src->X)) return 0;
+	if (!BN_copy(&dest->Y, &src->Y)) return 0;
+	if (!BN_copy(&dest->Z, &src->Z)) return 0;
+	dest->Z_is_one = src->Z_is_one;
+
+	return 1;
+	}
+
+
+int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
+	{
+	point->Z_is_one = 0;
+	BN_zero(&point->Z);
+	return 1;
+	}
+
+
+int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
+	const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	int ret = 0;
+	
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	if (x != NULL)
+		{
+		if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
+		if (group->meth->field_encode)
+			{
+			if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
+			}
+		}
+	
+	if (y != NULL)
+		{
+		if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
+		if (group->meth->field_encode)
+			{
+			if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
+			}
+		}
+	
+	if (z != NULL)
+		{
+		int Z_is_one;
+
+		if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
+		Z_is_one = BN_is_one(&point->Z);
+		if (group->meth->field_encode)
+			{
+			if (Z_is_one && (group->meth->field_set_to_one != 0))
+				{
+				if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
+				}
+			else
+				{
+				if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
+				}
+			}
+		point->Z_is_one = Z_is_one;
+		}
+	
+	ret = 1;
+	
+ err:
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
+	BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	int ret = 0;
+	
+	if (group->meth->field_decode != 0)
+		{
+		if (ctx == NULL)
+			{
+			ctx = new_ctx = BN_CTX_new();
+			if (ctx == NULL)
+				return 0;
+			}
+
+		if (x != NULL)
+			{
+			if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+			}
+		if (y != NULL)
+			{
+			if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+			}
+		if (z != NULL)
+			{
+			if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
+			}
+		}
+	else	
+		{
+		if (x != NULL)
+			{
+			if (!BN_copy(x, &point->X)) goto err;
+			}
+		if (y != NULL)
+			{
+			if (!BN_copy(y, &point->Y)) goto err;
+			}
+		if (z != NULL)
+			{
+			if (!BN_copy(z, &point->Z)) goto err;
+			}
+		}
+	
+	ret = 1;
+
+ err:
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
+	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+	{
+	if (x == NULL || y == NULL)
+		{
+		/* unlike for projective coordinates, we do not tolerate this */
+		ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
+		return 0;
+		}
+
+	return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
+	}
+
+
+int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
+	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *Z, *Z_1, *Z_2, *Z_3;
+	const BIGNUM *Z_;
+	int ret = 0;
+
+	if (EC_POINT_is_at_infinity(group, point))
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
+		return 0;
+		}
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	Z = BN_CTX_get(ctx);
+	Z_1 = BN_CTX_get(ctx);
+	Z_2 = BN_CTX_get(ctx);
+	Z_3 = BN_CTX_get(ctx);
+	if (Z_3 == NULL) goto err;
+
+	/* transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3) */
+	
+	if (group->meth->field_decode)
+		{
+		if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
+		Z_ = Z;
+		}
+	else
+		{
+		Z_ = &point->Z;
+		}
+	
+	if (BN_is_one(Z_))
+		{
+		if (group->meth->field_decode)
+			{
+			if (x != NULL)
+				{
+				if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+				}
+			if (y != NULL)
+				{
+				if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+				}
+			}
+		else
+			{
+			if (x != NULL)
+				{
+				if (!BN_copy(x, &point->X)) goto err;
+				}
+			if (y != NULL)
+				{
+				if (!BN_copy(y, &point->Y)) goto err;
+				}
+			}
+		}
+	else
+		{
+		if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
+			goto err;
+			}
+		
+		if (group->meth->field_encode == 0)
+			{
+			/* field_sqr works on standard representation */
+			if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
+			}
+		else
+			{
+			if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
+			}
+	
+		if (x != NULL)
+			{
+			/* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
+			if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
+			}
+
+		if (y != NULL)
+			{
+			if (group->meth->field_encode == 0)
+				{
+				/* field_mul works on standard representation */
+				if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
+				}
+			else
+				{
+				if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
+				}
+
+			/* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
+			if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
+			}
+		}
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
+	const BIGNUM *x_, int y_bit, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *tmp1, *tmp2, *x, *y;
+	int ret = 0;
+
+	/* clear error queue*/
+	ERR_clear_error();
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	y_bit = (y_bit != 0);
+
+	BN_CTX_start(ctx);
+	tmp1 = BN_CTX_get(ctx);
+	tmp2 = BN_CTX_get(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	if (y == NULL) goto err;
+
+	/* Recover y.  We have a Weierstrass equation
+	 *     y^2 = x^3 + a*x + b,
+	 * so  y  is one of the square roots of  x^3 + a*x + b.
+	 */
+
+	/* tmp1 := x^3 */
+	if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
+	if (group->meth->field_decode == 0)
+		{
+		/* field_{sqr,mul} work on standard representation */
+		if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
+		if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
+		}
+	else
+		{
+		if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
+		if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
+		}
+	
+	/* tmp1 := tmp1 + a*x */
+	if (group->a_is_minus3)
+		{
+		if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
+		if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
+		if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+		}
+	else
+		{
+		if (group->meth->field_decode)
+			{
+			if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
+			if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
+			}
+		else
+			{
+			/* field_mul works on standard representation */
+			if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
+			}
+		
+		if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+		}
+	
+	/* tmp1 := tmp1 + b */
+	if (group->meth->field_decode)
+		{
+		if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
+		if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+		}
+	else
+		{
+		if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
+		}
+	
+	if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
+		{
+		unsigned long err = ERR_peek_last_error();
+		
+		if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
+			{
+			ERR_clear_error();
+			ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+			}
+		else
+			ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
+		goto err;
+		}
+
+	if (y_bit != BN_is_odd(y))
+		{
+		if (BN_is_zero(y))
+			{
+			int kron;
+
+			kron = BN_kronecker(x, &group->field, ctx);
+			if (kron == -2) goto err;
+
+			if (kron == 1)
+				ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
+			else
+				/* BN_mod_sqrt() should have cought this error (not a square) */
+				ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+			goto err;
+			}
+		if (!BN_usub(y, &group->field, y)) goto err;
+		}
+	if (y_bit != BN_is_odd(y))
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
+		goto err;
+		}
+
+	if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
+	unsigned char *buf, size_t len, BN_CTX *ctx)
+	{
+	size_t ret;
+	BN_CTX *new_ctx = NULL;
+	int used_ctx = 0;
+	BIGNUM *x, *y;
+	size_t field_len, i, skip;
+
+	if ((form != POINT_CONVERSION_COMPRESSED)
+		&& (form != POINT_CONVERSION_UNCOMPRESSED)
+		&& (form != POINT_CONVERSION_HYBRID))
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
+		goto err;
+		}
+
+	if (EC_POINT_is_at_infinity(group, point))
+		{
+		/* encodes to a single 0 octet */
+		if (buf != NULL)
+			{
+			if (len < 1)
+				{
+				ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
+				return 0;
+				}
+			buf[0] = 0;
+			}
+		return 1;
+		}
+
+
+	/* ret := required output buffer length */
+	field_len = BN_num_bytes(&group->field);
+	ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
+
+	/* if 'buf' is NULL, just return required length */
+	if (buf != NULL)
+		{
+		if (len < ret)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
+			goto err;
+			}
+
+		if (ctx == NULL)
+			{
+			ctx = new_ctx = BN_CTX_new();
+			if (ctx == NULL)
+				return 0;
+			}
+
+		BN_CTX_start(ctx);
+		used_ctx = 1;
+		x = BN_CTX_get(ctx);
+		y = BN_CTX_get(ctx);
+		if (y == NULL) goto err;
+
+		if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+
+		if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
+			buf[0] = form + 1;
+		else
+			buf[0] = form;
+	
+		i = 1;
+		
+		skip = field_len - BN_num_bytes(x);
+		if (skip > field_len)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+			goto err;
+			}
+		while (skip > 0)
+			{
+			buf[i++] = 0;
+			skip--;
+			}
+		skip = BN_bn2bin(x, buf + i);
+		i += skip;
+		if (i != 1 + field_len)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+			goto err;
+			}
+
+		if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
+			{
+			skip = field_len - BN_num_bytes(y);
+			if (skip > field_len)
+				{
+				ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+				goto err;
+				}
+			while (skip > 0)
+				{
+				buf[i++] = 0;
+				skip--;
+				}
+			skip = BN_bn2bin(y, buf + i);
+			i += skip;
+			}
+
+		if (i != ret)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
+			goto err;
+			}
+		}
+	
+	if (used_ctx)
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+
+ err:
+	if (used_ctx)
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return 0;
+	}
+
+
+int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
+	const unsigned char *buf, size_t len, BN_CTX *ctx)
+	{
+	point_conversion_form_t form;
+	int y_bit;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *x, *y;
+	size_t field_len, enc_len;
+	int ret = 0;
+
+	if (len == 0)
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
+		return 0;
+		}
+	form = buf[0];
+	y_bit = form & 1;
+	form = form & ~1U;
+	if ((form != 0)	&& (form != POINT_CONVERSION_COMPRESSED)
+		&& (form != POINT_CONVERSION_UNCOMPRESSED)
+		&& (form != POINT_CONVERSION_HYBRID))
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		return 0;
+		}
+	if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		return 0;
+		}
+
+	if (form == 0)
+		{
+		if (len != 1)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+			return 0;
+			}
+
+		return EC_POINT_set_to_infinity(group, point);
+		}
+	
+	field_len = BN_num_bytes(&group->field);
+	enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
+
+	if (len != enc_len)
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		return 0;
+		}
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	if (y == NULL) goto err;
+
+	if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
+	if (BN_ucmp(x, &group->field) >= 0)
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+		goto err;
+		}
+
+	if (form == POINT_CONVERSION_COMPRESSED)
+		{
+		if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
+		}
+	else
+		{
+		if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
+		if (BN_ucmp(y, &group->field) >= 0)
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+			goto err;
+			}
+		if (form == POINT_CONVERSION_HYBRID)
+			{
+			if (y_bit != BN_is_odd(y))
+				{
+				ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
+				goto err;
+				}
+			}
+
+		if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+		}
+	
+	if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
+		goto err;
+		}
+
+	ret = 1;
+	
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+	{
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+	const BIGNUM *p;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
+	int ret = 0;
+	
+	if (a == b)
+		return EC_POINT_dbl(group, r, a, ctx);
+	if (EC_POINT_is_at_infinity(group, a))
+		return EC_POINT_copy(r, b);
+	if (EC_POINT_is_at_infinity(group, b))
+		return EC_POINT_copy(r, a);
+	
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;
+	p = &group->field;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	n0 = BN_CTX_get(ctx);
+	n1 = BN_CTX_get(ctx);
+	n2 = BN_CTX_get(ctx);
+	n3 = BN_CTX_get(ctx);
+	n4 = BN_CTX_get(ctx);
+	n5 = BN_CTX_get(ctx);
+	n6 = BN_CTX_get(ctx);
+	if (n6 == NULL) goto end;
+
+	/* Note that in this function we must not read components of 'a' or 'b'
+	 * once we have written the corresponding components of 'r'.
+	 * ('r' might be one of 'a' or 'b'.)
+	 */
+
+	/* n1, n2 */
+	if (b->Z_is_one)
+		{
+		if (!BN_copy(n1, &a->X)) goto end;
+		if (!BN_copy(n2, &a->Y)) goto end;
+		/* n1 = X_a */
+		/* n2 = Y_a */
+		}
+	else
+		{
+		if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
+		if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
+		/* n1 = X_a * Z_b^2 */
+
+		if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
+		if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
+		/* n2 = Y_a * Z_b^3 */
+		}
+
+	/* n3, n4 */
+	if (a->Z_is_one)
+		{
+		if (!BN_copy(n3, &b->X)) goto end;
+		if (!BN_copy(n4, &b->Y)) goto end;
+		/* n3 = X_b */
+		/* n4 = Y_b */
+		}
+	else
+		{
+		if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
+		if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
+		/* n3 = X_b * Z_a^2 */
+
+		if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
+		if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
+		/* n4 = Y_b * Z_a^3 */
+		}
+
+	/* n5, n6 */
+	if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
+	if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
+	/* n5 = n1 - n3 */
+	/* n6 = n2 - n4 */
+
+	if (BN_is_zero(n5))
+		{
+		if (BN_is_zero(n6))
+			{
+			/* a is the same point as b */
+			BN_CTX_end(ctx);
+			ret = EC_POINT_dbl(group, r, a, ctx);
+			ctx = NULL;
+			goto end;
+			}
+		else
+			{
+			/* a is the inverse of b */
+			BN_zero(&r->Z);
+			r->Z_is_one = 0;
+			ret = 1;
+			goto end;
+			}
+		}
+
+	/* 'n7', 'n8' */
+	if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
+	if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
+	/* 'n7' = n1 + n3 */
+	/* 'n8' = n2 + n4 */
+
+	/* Z_r */
+	if (a->Z_is_one && b->Z_is_one)
+		{
+		if (!BN_copy(&r->Z, n5)) goto end;
+		}
+	else
+		{
+		if (a->Z_is_one)
+			{ if (!BN_copy(n0, &b->Z)) goto end; }
+		else if (b->Z_is_one)
+			{ if (!BN_copy(n0, &a->Z)) goto end; }
+		else
+			{ if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
+		if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
+		}
+	r->Z_is_one = 0;
+	/* Z_r = Z_a * Z_b * n5 */
+
+	/* X_r */
+	if (!field_sqr(group, n0, n6, ctx)) goto end;
+	if (!field_sqr(group, n4, n5, ctx)) goto end;
+	if (!field_mul(group, n3, n1, n4, ctx)) goto end;
+	if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
+	/* X_r = n6^2 - n5^2 * 'n7' */
+	
+	/* 'n9' */
+	if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
+	if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
+	/* n9 = n5^2 * 'n7' - 2 * X_r */
+
+	/* Y_r */
+	if (!field_mul(group, n0, n0, n6, ctx)) goto end;
+	if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
+	if (!field_mul(group, n1, n2, n5, ctx)) goto end;
+	if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
+	if (BN_is_odd(n0))
+		if (!BN_add(n0, n0, p)) goto end;
+	/* now  0 <= n0 < 2*p,  and n0 is even */
+	if (!BN_rshift1(&r->Y, n0)) goto end;
+	/* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
+
+	ret = 1;
+
+ end:
+	if (ctx) /* otherwise we already called BN_CTX_end */
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
+	{
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+	const BIGNUM *p;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *n0, *n1, *n2, *n3;
+	int ret = 0;
+	
+	if (EC_POINT_is_at_infinity(group, a))
+		{
+		BN_zero(&r->Z);
+		r->Z_is_one = 0;
+		return 1;
+		}
+
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;
+	p = &group->field;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	n0 = BN_CTX_get(ctx);
+	n1 = BN_CTX_get(ctx);
+	n2 = BN_CTX_get(ctx);
+	n3 = BN_CTX_get(ctx);
+	if (n3 == NULL) goto err;
+
+	/* Note that in this function we must not read components of 'a'
+	 * once we have written the corresponding components of 'r'.
+	 * ('r' might the same as 'a'.)
+	 */
+
+	/* n1 */
+	if (a->Z_is_one)
+		{
+		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
+		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
+		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
+		if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
+		/* n1 = 3 * X_a^2 + a_curve */
+		}
+	else if (group->a_is_minus3)
+		{
+		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
+		if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
+		if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
+		if (!field_mul(group, n1, n0, n2, ctx)) goto err;
+		if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
+		if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
+		/* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
+		 *    = 3 * X_a^2 - 3 * Z_a^4 */
+		}
+	else
+		{
+		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
+		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
+		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
+		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
+		if (!field_sqr(group, n1, n1, ctx)) goto err;
+		if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
+		if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
+		/* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
+		}
+
+	/* Z_r */
+	if (a->Z_is_one)
+		{
+		if (!BN_copy(n0, &a->Y)) goto err;
+		}
+	else
+		{
+		if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
+		}
+	if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
+	r->Z_is_one = 0;
+	/* Z_r = 2 * Y_a * Z_a */
+
+	/* n2 */
+	if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
+	if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
+	if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
+	/* n2 = 4 * X_a * Y_a^2 */
+
+	/* X_r */
+	if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
+	if (!field_sqr(group, &r->X, n1, ctx)) goto err;
+	if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
+	/* X_r = n1^2 - 2 * n2 */
+	
+	/* n3 */
+	if (!field_sqr(group, n0, n3, ctx)) goto err;
+	if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
+	/* n3 = 8 * Y_a^4 */
+	
+	/* Y_r */
+	if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
+	if (!field_mul(group, n0, n1, n0, ctx)) goto err;
+	if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
+	/* Y_r = n1 * (n2 - X_r) - n3 */
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+	{
+	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
+		/* point is its own inverse */
+		return 1;
+	
+	return BN_usub(&point->Y, &group->field, &point->Y);
+	}
+
+
+int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
+	{
+	return BN_is_zero(&point->Z);
+	}
+
+
+int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
+	{
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+	const BIGNUM *p;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *rh, *tmp, *Z4, *Z6;
+	int ret = -1;
+
+	if (EC_POINT_is_at_infinity(group, point))
+		return 1;
+	
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;
+	p = &group->field;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return -1;
+		}
+
+	BN_CTX_start(ctx);
+	rh = BN_CTX_get(ctx);
+	tmp = BN_CTX_get(ctx);
+	Z4 = BN_CTX_get(ctx);
+	Z6 = BN_CTX_get(ctx);
+	if (Z6 == NULL) goto err;
+
+	/* We have a curve defined by a Weierstrass equation
+	 *      y^2 = x^3 + a*x + b.
+	 * The point to consider is given in Jacobian projective coordinates
+	 * where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).
+	 * Substituting this and multiplying by  Z^6  transforms the above equation into
+	 *      Y^2 = X^3 + a*X*Z^4 + b*Z^6.
+	 * To test this, we add up the right-hand side in 'rh'.
+	 */
+
+	/* rh := X^2 */
+	if (!field_sqr(group, rh, &point->X, ctx)) goto err;
+
+	if (!point->Z_is_one)
+		{
+		if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
+		if (!field_sqr(group, Z4, tmp, ctx)) goto err;
+		if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
+
+		/* rh := (rh + a*Z^4)*X */
+		if (group->a_is_minus3)
+			{
+			if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
+			if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
+			if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
+			if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
+			}
+		else
+			{
+			if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
+			if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
+			if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
+			}
+
+		/* rh := rh + b*Z^6 */
+		if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
+		if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
+		}
+	else
+		{
+		/* point->Z_is_one */
+
+		/* rh := (rh + a)*X */
+		if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
+		if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
+		/* rh := rh + b */
+		if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
+		}
+
+	/* 'lh' := Y^2 */
+	if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
+
+	ret = (0 == BN_ucmp(tmp, rh));
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+	{
+	/* return values:
+	 *  -1   error
+	 *   0   equal (in affine coordinates)
+	 *   1   not equal
+	 */
+
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
+	const BIGNUM *tmp1_, *tmp2_;
+	int ret = -1;
+	
+	if (EC_POINT_is_at_infinity(group, a))
+		{
+		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
+		}
+
+	if (EC_POINT_is_at_infinity(group, b))
+		return 1;
+	
+	if (a->Z_is_one && b->Z_is_one)
+		{
+		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
+		}
+
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return -1;
+		}
+
+	BN_CTX_start(ctx);
+	tmp1 = BN_CTX_get(ctx);
+	tmp2 = BN_CTX_get(ctx);
+	Za23 = BN_CTX_get(ctx);
+	Zb23 = BN_CTX_get(ctx);
+	if (Zb23 == NULL) goto end;
+
+	/* We have to decide whether
+	 *     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
+	 * or equivalently, whether
+	 *     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
+	 */
+
+	if (!b->Z_is_one)
+		{
+		if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
+		if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
+		tmp1_ = tmp1;
+		}
+	else
+		tmp1_ = &a->X;
+	if (!a->Z_is_one)
+		{
+		if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
+		if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
+		tmp2_ = tmp2;
+		}
+	else
+		tmp2_ = &b->X;
+	
+	/* compare  X_a*Z_b^2  with  X_b*Z_a^2 */
+	if (BN_cmp(tmp1_, tmp2_) != 0)
+		{
+		ret = 1; /* points differ */
+		goto end;
+		}
+
+
+	if (!b->Z_is_one)
+		{
+		if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
+		if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
+		/* tmp1_ = tmp1 */
+		}
+	else
+		tmp1_ = &a->Y;
+	if (!a->Z_is_one)
+		{
+		if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
+		if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
+		/* tmp2_ = tmp2 */
+		}
+	else
+		tmp2_ = &b->Y;
+
+	/* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */
+	if (BN_cmp(tmp1_, tmp2_) != 0)
+		{
+		ret = 1; /* points differ */
+		goto end;
+		}
+
+	/* points are equal */
+	ret = 0;
+
+ end:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *x, *y;
+	int ret = 0;
+
+	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
+		return 1;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	x = BN_CTX_get(ctx);
+	y = BN_CTX_get(ctx);
+	if (y == NULL) goto err;
+
+	if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+	if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+	if (!point->Z_is_one)
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
+		goto err;
+		}
+	
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
+	{
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *tmp0, *tmp1;
+	size_t pow2 = 0;
+	BIGNUM **heap = NULL;
+	size_t i;
+	int ret = 0;
+
+	if (num == 0)
+		return 1;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+
+	BN_CTX_start(ctx);
+	tmp0 = BN_CTX_get(ctx);
+	tmp1 = BN_CTX_get(ctx);
+	if (tmp0  == NULL || tmp1 == NULL) goto err;
+
+	/* Before converting the individual points, compute inverses of all Z values.
+	 * Modular inversion is rather slow, but luckily we can do with a single
+	 * explicit inversion, plus about 3 multiplications per input value.
+	 */
+
+	pow2 = 1;
+	while (num > pow2)
+		pow2 <<= 1;
+	/* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
+	 * We need twice that. */
+	pow2 <<= 1;
+
+	heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
+	if (heap == NULL) goto err;
+	
+	/* The array is used as a binary tree, exactly as in heapsort:
+	 *
+	 *                               heap[1]
+	 *                 heap[2]                     heap[3]
+	 *          heap[4]       heap[5]       heap[6]       heap[7]
+	 *   heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
+	 *
+	 * We put the Z's in the last line;
+	 * then we set each other node to the product of its two child-nodes (where
+	 * empty or 0 entries are treated as ones);
+	 * then we invert heap[1];
+	 * then we invert each other node by replacing it by the product of its
+	 * parent (after inversion) and its sibling (before inversion).
+	 */
+	heap[0] = NULL;
+	for (i = pow2/2 - 1; i > 0; i--)
+		heap[i] = NULL;
+	for (i = 0; i < num; i++)
+		heap[pow2/2 + i] = &points[i]->Z;
+	for (i = pow2/2 + num; i < pow2; i++)
+		heap[i] = NULL;
+	
+	/* set each node to the product of its children */
+	for (i = pow2/2 - 1; i > 0; i--)
+		{
+		heap[i] = BN_new();
+		if (heap[i] == NULL) goto err;
+		
+		if (heap[2*i] != NULL)
+			{
+			if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
+				{
+				if (!BN_copy(heap[i], heap[2*i])) goto err;
+				}
+			else
+				{
+				if (BN_is_zero(heap[2*i]))
+					{
+					if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
+					}
+				else
+					{
+					if (!group->meth->field_mul(group, heap[i],
+						heap[2*i], heap[2*i + 1], ctx)) goto err;
+					}
+				}
+			}
+		}
+
+	/* invert heap[1] */
+	if (!BN_is_zero(heap[1]))
+		{
+		if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
+			{
+			ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
+			goto err;
+			}
+		}
+	if (group->meth->field_encode != 0)
+		{
+		/* in the Montgomery case, we just turned  R*H  (representing H)
+		 * into  1/(R*H),  but we need  R*(1/H)  (representing 1/H);
+		 * i.e. we have need to multiply by the Montgomery factor twice */
+		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+		}
+
+	/* set other heap[i]'s to their inverses */
+	for (i = 2; i < pow2/2 + num; i += 2)
+		{
+		/* i is even */
+		if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
+			{
+			if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
+			if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
+			if (!BN_copy(heap[i], tmp0)) goto err;
+			if (!BN_copy(heap[i + 1], tmp1)) goto err;
+			}
+		else
+			{
+			if (!BN_copy(heap[i], heap[i/2])) goto err;
+			}
+		}
+
+	/* we have replaced all non-zero Z's by their inverses, now fix up all the points */
+	for (i = 0; i < num; i++)
+		{
+		EC_POINT *p = points[i];
+		
+		if (!BN_is_zero(&p->Z))
+			{
+			/* turn  (X, Y, 1/Z)  into  (X/Z^2, Y/Z^3, 1) */
+
+			if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
+			if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
+
+			if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
+			if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
+		
+			if (group->meth->field_set_to_one != 0)
+				{
+				if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
+				}
+			else
+				{
+				if (!BN_one(&p->Z)) goto err;
+				}
+			p->Z_is_one = 1;
+			}
+		}
+
+	ret = 1;
+		
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	if (heap != NULL)
+		{
+		/* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
+		for (i = pow2/2 - 1; i > 0; i--)
+			{
+			if (heap[i] != NULL)
+				BN_clear_free(heap[i]);
+			}
+		OPENSSL_free(heap);
+		}
+	return ret;
+	}
+
+
+int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	return BN_mod_mul(r, a, b, &group->field, ctx);
+	}
+
+
+int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
+	{
+	return BN_mod_sqr(r, a, &group->field, ctx);
+	}