/* crypto/ec/ec_curve.c */

/*

 * Written by Nils Larsch for the OpenSSL project.

 */

/* ====================================================================

 * Copyright (c) 1998-2010 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 the attached software ("Contribution") are developed by 

 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.

 *

 * The Contribution is licensed pursuant to the OpenSSL open source

 * license provided above.

 *

 * The elliptic curve binary polynomial software is originally written by 

 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.

 *

 */

#include "ec_lcl.h"

#include <openssl/err.h>

#include <openssl/obj_mac.h>

#include <openssl/opensslconf.h>

typedef struct {

	int	field_type,	/* either NID_X9_62_prime_field or

				 * NID_X9_62_characteristic_two_field */

		seed_len,

		param_len;

	unsigned int cofactor;	/* promoted to BN_ULONG */

} EC_CURVE_DATA;

static const struct { EC_CURVE_DATA h; unsigned char data[20+48*6]; }

	_EC_NIST_PRIME_384 = {

	{ NID_X9_62_prime_field,20,48,1 },

	{ 0xA3,0x35,0x92,0x6A,0xA3,0x19,0xA2,0x7A,0x1D,0x00,	/* seed */

	  0x89,0x6A,0x67,0x73,0xA4,0x82,0x7A,0xCD,0xAC,0x73,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,	/* p */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,

	  0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,	/* a */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,

	  0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFC,

	  0xB3,0x31,0x2F,0xA7,0xE2,0x3E,0xE7,0xE4,0x98,0x8E,	/* b */

	  0x05,0x6B,0xE3,0xF8,0x2D,0x19,0x18,0x1D,0x9C,0x6E,

	  0xFE,0x81,0x41,0x12,0x03,0x14,0x08,0x8F,0x50,0x13,

	  0x87,0x5A,0xC6,0x56,0x39,0x8D,0x8A,0x2E,0xD1,0x9D,

	  0x2A,0x85,0xC8,0xED,0xD3,0xEC,0x2A,0xEF,

	  0xAA,0x87,0xCA,0x22,0xBE,0x8B,0x05,0x37,0x8E,0xB1,	/* x */

	  0xC7,0x1E,0xF3,0x20,0xAD,0x74,0x6E,0x1D,0x3B,0x62,

	  0x8B,0xA7,0x9B,0x98,0x59,0xF7,0x41,0xE0,0x82,0x54,

	  0x2A,0x38,0x55,0x02,0xF2,0x5D,0xBF,0x55,0x29,0x6C,

	  0x3A,0x54,0x5E,0x38,0x72,0x76,0x0A,0xB7,

	  0x36,0x17,0xde,0x4a,0x96,0x26,0x2c,0x6f,0x5d,0x9e,	/* y */

	  0x98,0xbf,0x92,0x92,0xdc,0x29,0xf8,0xf4,0x1d,0xbd,

	  0x28,0x9a,0x14,0x7c,0xe9,0xda,0x31,0x13,0xb5,0xf0,

	  0xb8,0xc0,0x0a,0x60,0xb1,0xce,0x1d,0x7e,0x81,0x9d,

	  0x7a,0x43,0x1d,0x7c,0x90,0xea,0x0e,0x5f,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,	/* order */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xC7,0x63,0x4D,0x81,0xF4,0x37,

	  0x2D,0xDF,0x58,0x1A,0x0D,0xB2,0x48,0xB0,0xA7,0x7A,

	  0xEC,0xEC,0x19,0x6A,0xCC,0xC5,0x29,0x73 }

	};

static const struct { EC_CURVE_DATA h; unsigned char data[20+66*6]; }

	_EC_NIST_PRIME_521 = {

	{ NID_X9_62_prime_field,20,66,1 },

	{ 0xD0,0x9E,0x88,0x00,0x29,0x1C,0xB8,0x53,0x96,0xCC,	/* seed */

	  0x67,0x17,0x39,0x32,0x84,0xAA,0xA0,0xDA,0x64,0xBA,

	  0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,	/* p */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,	/* a */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFC,

	  0x00,0x51,0x95,0x3E,0xB9,0x61,0x8E,0x1C,0x9A,0x1F,	/* b */

	  0x92,0x9A,0x21,0xA0,0xB6,0x85,0x40,0xEE,0xA2,0xDA,

	  0x72,0x5B,0x99,0xB3,0x15,0xF3,0xB8,0xB4,0x89,0x91,

	  0x8E,0xF1,0x09,0xE1,0x56,0x19,0x39,0x51,0xEC,0x7E,

	  0x93,0x7B,0x16,0x52,0xC0,0xBD,0x3B,0xB1,0xBF,0x07,

	  0x35,0x73,0xDF,0x88,0x3D,0x2C,0x34,0xF1,0xEF,0x45,

	  0x1F,0xD4,0x6B,0x50,0x3F,0x00,

	  0x00,0xC6,0x85,0x8E,0x06,0xB7,0x04,0x04,0xE9,0xCD,	/* x */

	  0x9E,0x3E,0xCB,0x66,0x23,0x95,0xB4,0x42,0x9C,0x64,

	  0x81,0x39,0x05,0x3F,0xB5,0x21,0xF8,0x28,0xAF,0x60,

	  0x6B,0x4D,0x3D,0xBA,0xA1,0x4B,0x5E,0x77,0xEF,0xE7,

	  0x59,0x28,0xFE,0x1D,0xC1,0x27,0xA2,0xFF,0xA8,0xDE,

	  0x33,0x48,0xB3,0xC1,0x85,0x6A,0x42,0x9B,0xF9,0x7E,

	  0x7E,0x31,0xC2,0xE5,0xBD,0x66,

	  0x01,0x18,0x39,0x29,0x6a,0x78,0x9a,0x3b,0xc0,0x04,	/* y */

	  0x5c,0x8a,0x5f,0xb4,0x2c,0x7d,0x1b,0xd9,0x98,0xf5,

	  0x44,0x49,0x57,0x9b,0x44,0x68,0x17,0xaf,0xbd,0x17,

	  0x27,0x3e,0x66,0x2c,0x97,0xee,0x72,0x99,0x5e,0xf4,

	  0x26,0x40,0xc5,0x50,0xb9,0x01,0x3f,0xad,0x07,0x61,

	  0x35,0x3c,0x70,0x86,0xa2,0x72,0xc2,0x40,0x88,0xbe,

	  0x94,0x76,0x9f,0xd1,0x66,0x50,

	  0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,	/* order */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFA,0x51,0x86,0x87,0x83,0xBF,0x2F,

	  0x96,0x6B,0x7F,0xCC,0x01,0x48,0xF7,0x09,0xA5,0xD0,

	  0x3B,0xB5,0xC9,0xB8,0x89,0x9C,0x47,0xAE,0xBB,0x6F,

	  0xB7,0x1E,0x91,0x38,0x64,0x09 }

	};

static const struct { EC_CURVE_DATA h; unsigned char data[20+32*6]; }

	_EC_X9_62_PRIME_256V1 = {

	{ NID_X9_62_prime_field,20,32,1 },

	{ 0xC4,0x9D,0x36,0x08,0x86,0xE7,0x04,0x93,0x6A,0x66,	/* seed */

	  0x78,0xE1,0x13,0x9D,0x26,0xB7,0x81,0x9F,0x7E,0x90,

	  0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00,	/* p */

	  0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFF,

	  0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00,	/* a */

	  0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

	  0xFF,0xFC,

	  0x5A,0xC6,0x35,0xD8,0xAA,0x3A,0x93,0xE7,0xB3,0xEB,	/* b */

	  0xBD,0x55,0x76,0x98,0x86,0xBC,0x65,0x1D,0x06,0xB0,

	  0xCC,0x53,0xB0,0xF6,0x3B,0xCE,0x3C,0x3E,0x27,0xD2,

	  0x60,0x4B,

	  0x6B,0x17,0xD1,0xF2,0xE1,0x2C,0x42,0x47,0xF8,0xBC,	/* x */

	  0xE6,0xE5,0x63,0xA4,0x40,0xF2,0x77,0x03,0x7D,0x81,

	  0x2D,0xEB,0x33,0xA0,0xF4,0xA1,0x39,0x45,0xD8,0x98,

	  0xC2,0x96,

	  0x4f,0xe3,0x42,0xe2,0xfe,0x1a,0x7f,0x9b,0x8e,0xe7,	/* y */

	  0xeb,0x4a,0x7c,0x0f,0x9e,0x16,0x2b,0xce,0x33,0x57,

	  0x6b,0x31,0x5e,0xce,0xcb,0xb6,0x40,0x68,0x37,0xbf,

	  0x51,0xf5,

	  0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0xFF,0xFF,	/* order */

	  0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xBC,0xE6,0xFA,0xAD,

	  0xA7,0x17,0x9E,0x84,0xF3,0xB9,0xCA,0xC2,0xFC,0x63,

	  0x25,0x51 }

	};

typedef struct _ec_list_element_st {

	int	nid;

	const EC_CURVE_DATA *data;

	const EC_METHOD *(*meth)(void);

	const char *comment;

	} ec_list_element;

static const ec_list_element curve_list[] = {

	/* prime field curves */

	/* secg curves */

	/* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */

	{ NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" },

#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128

	{ NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" },

#else

	{ NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" },

#endif

#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128

	{ NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" },

#else

	{ NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" },

#endif

};

#define curve_list_length (sizeof(curve_list)/sizeof(ec_list_element))

static EC_GROUP *ec_group_new_from_data(const ec_list_element curve)

	{

	EC_GROUP *group=NULL;

	EC_POINT *P=NULL;

	BN_CTX	 *ctx=NULL;

	BIGNUM	 *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL;

	int	 ok=0;

	int	 seed_len,param_len;

	const EC_METHOD *meth;

	const EC_CURVE_DATA *data;

	const unsigned char *params;

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

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE);

		goto err;

		}

	data = curve.data;

	seed_len  = data->seed_len;

	param_len = data->param_len;

	params	  = (const unsigned char *)(data+1);	/* skip header */

	params	 += seed_len;				/* skip seed   */

	if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL))

		|| !(a = BN_bin2bn(params+1*param_len, param_len, NULL))

		|| !(b = BN_bin2bn(params+2*param_len, param_len, NULL)))

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);

		goto err;

		}

	if (curve.meth != 0)

		{

		meth = curve.meth();

		if (((group = EC_GROUP_new(meth)) == NULL) ||

			(!(group->meth->group_set_curve(group, p, a, b, ctx))))

			{

			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

			goto err;

			}

		}

	else if (data->field_type == NID_X9_62_prime_field)

		{

		if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL)

			{

			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

			goto err;

			}

		}

#ifndef OPENSSL_NO_EC2M

	else	/* field_type == NID_X9_62_characteristic_two_field */

		{

		if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL)

			{

			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

			goto err;

			}

		}

#endif

	if ((P = EC_POINT_new(group)) == NULL)

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

		goto err;

		}

	if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL))

		|| !(y = BN_bin2bn(params+4*param_len, param_len, NULL)))

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);

		goto err;

		}

	if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

		goto err;

		}

	if (!(order = BN_bin2bn(params+5*param_len, param_len, NULL))

		|| !BN_set_word(x, (BN_ULONG)data->cofactor))

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);

		goto err;

		}

	if (!EC_GROUP_set_generator(group, P, order, x))

		{

		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

		goto err;

		}

	if (seed_len)

		{

		if (!EC_GROUP_set_seed(group, params-seed_len, seed_len))

			{

			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);

			goto err;

			}

		}

	ok=1;

err:

	if (!ok)

		{

		EC_GROUP_free(group);

		group = NULL;

		}

	if (P)

		EC_POINT_free(P);

	if (ctx)

		BN_CTX_free(ctx);

	if (p)

		BN_free(p);

	if (a)

		BN_free(a);

	if (b)

		BN_free(b);

	if (order)

		BN_free(order);

	if (x)

		BN_free(x);

	if (y)

		BN_free(y);

	return group;

	}

EC_GROUP *EC_GROUP_new_by_curve_name(int nid)

	{

	size_t i;

	EC_GROUP *ret = NULL;

	if (nid <= 0)

		return NULL;

	for (i=0; i

		if (curve_list[i].nid == nid)

			{

			ret = ec_group_new_from_data(curve_list[i]);

			break;

			}

	if (ret == NULL)

		{

		ECerr(EC_F_EC_GROUP_NEW_BY_CURVE_NAME, EC_R_UNKNOWN_GROUP);

		return NULL;

		}

	EC_GROUP_set_curve_name(ret, nid);

	return ret;

	}

size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems)

	{

	size_t	i, min;

	if (r == NULL || nitems == 0)

		return curve_list_length;

	min = nitems < curve_list_length ? nitems : curve_list_length;

	for (i = 0; i < min; i++)

		{

		r[i].nid = curve_list[i].nid;

		r[i].comment = curve_list[i].comment;

		}

	return curve_list_length;

	}