ec_curve.c

/* crypto/ec/ec_curve.c */
/* ====================================================================
 * 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).
 *
 */

#include "ec_lcl.h"
#include <openssl/err.h>
#include <openssl/obj_mac.h>
#include <openssl/asn1.h>
#include <openssl/asn1t.h>

/* #define _EC_GROUP_EXAMPLE_PRIME_CURVE	\
 *		"the prime number p", "a", "b", "the compressed base point", "y-bit", "order", "cofactor"
 */
/* the nist prime curves */
#define _EC_GROUP_NIST_PRIME_192	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",\
		"64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",\
		"188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",1,\
		"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",1
#define _EC_GROUP_NIST_PRIME_224	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",\
		"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",\
		"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",0,\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",1
#define _EC_GROUP_NIST_PRIME_384	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",\
		"B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",\
		"AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",1,\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",1
#define _EC_GROUP_NIST_PRIME_521	\
		"1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",\
		"1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",\
		"051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"\
		"315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",\
		"C6858E06B70404E9CD9E3ECB662395B4429C648139053F"\
		"B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",0,\
		"1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"\
		"FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",1
/* the x9.62 prime curves (minus the nist prime curves) */
#define _EC_GROUP_X9_62_PRIME_192V2	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",\
		"CC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953",\
		"EEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A",1,\
		"FFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31",1
#define _EC_GROUP_X9_62_PRIME_192V3	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",\
		"22123DC2395A05CAA7423DAECCC94760A7D462256BD56916",\
		"7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896",0,\
		"FFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13",1
#define _EC_GROUP_X9_62_PRIME_239V1	\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",\
		"6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A",\
		"0FFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF",0,\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B",1
#define _EC_GROUP_X9_62_PRIME_239V2	\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",\
		"617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C",\
		"38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7",0,\
		"7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063",1
#define _EC_GROUP_X9_62_PRIME_239V3	\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",\
		"255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E",\
		"6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A",1,\
		"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551",1
#define _EC_GROUP_X9_62_PRIME_256V1	\
		"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",\
		"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",\
		"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",\
		"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",1,\
		"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",1
/* the secg prime curves (minus the nist and x9.62 prime curves) */
#define _EC_GROUP_SECG_PRIME_112R1	\
		"DB7C2ABF62E35E668076BEAD208B",\
		"DB7C2ABF62E35E668076BEAD2088",\
		"659EF8BA043916EEDE8911702B22",\
		"09487239995A5EE76B55F9C2F098",0,\
		"DB7C2ABF62E35E7628DFAC6561C5",1
#define _EC_GROUP_SECG_PRIME_112R2	\
		"DB7C2ABF62E35E668076BEAD208B",\
		"6127C24C05F38A0AAAF65C0EF02C",\
		"51DEF1815DB5ED74FCC34C85D709",\
		"4BA30AB5E892B4E1649DD0928643",1,\
		"36DF0AAFD8B8D7597CA10520D04B",4
#define _EC_GROUP_SECG_PRIME_128R1	\
		"FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",\
		"FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC",\
		"E87579C11079F43DD824993C2CEE5ED3",\
		"161FF7528B899B2D0C28607CA52C5B86",1,\
		"FFFFFFFE0000000075A30D1B9038A115",1
#define _EC_GROUP_SECG_PRIME_128R2	\
		"FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",\
		"D6031998D1B3BBFEBF59CC9BBFF9AEE1",\
		"5EEEFCA380D02919DC2C6558BB6D8A5D",\
		"7B6AA5D85E572983E6FB32A7CDEBC140",0,\
		"3FFFFFFF7FFFFFFFBE0024720613B5A3",4
#define _EC_GROUP_SECG_PRIME_160K1	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",\
		"0",\
		"7",\
		"3B4C382CE37AA192A4019E763036F4F5DD4D7EBB",0,\
		"0100000000000000000001B8FA16DFAB9ACA16B6B3",1
#define _EC_GROUP_SECG_PRIME_160R1	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",\
		"1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",\
		"4A96B5688EF573284664698968C38BB913CBFC82",0,\
		"0100000000000000000001F4C8F927AED3CA752257",1
#define _EC_GROUP_SECG_PRIME_160R2	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70",\
		"B4E134D3FB59EB8BAB57274904664D5AF50388BA",\
		"52DCB034293A117E1F4FF11B30F7199D3144CE6D",0,\
		"0100000000000000000000351EE786A818F3A1A16B",1
#define _EC_GROUP_SECG_PRIME_192K1	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37",\
		"0",\
		"3",\
		"DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D",1,\
		"FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D",1
#define _EC_GROUP_SECG_PRIME_224K1	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D",\
		"0",\
		"5",\
		"A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C",1,\
		"010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",1
#define _EC_GROUP_SECG_PRIME_256K1	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",\
		"0",\
		"7",\
		"79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",0,\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",1
/* some wap/wtls curves */
#define _EC_GROUP_WTLS_6	\
		"DB7C2ABF62E35E668076BEAD208B",\
		"DB7C2ABF62E35E668076BEAD2088",\
		"659EF8BA043916EEDE8911702B22",\
		"09487239995A5EE76B55F9C2F098",0,\
		"DB7C2ABF62E35E7628DFAC6561C5",1
#define _EC_GROUP_WTLS_8	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFDE7",\
		"0",\
		"3",\
		"1",0,\
		"0100000000000001ECEA551AD837E9",1
#define _EC_GROUP_WTLS_9	\
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC808F",\
		"0",\
		"3",\
		"1",0,\
		"0100000000000000000001CDC98AE0E2DE574ABF33",1

static EC_GROUP *ec_group_new_GFp_from_hex(const char *prime_in,
	    const char *a_in, const char *b_in,
	    const char *x_in, const int y_bit, const char *order_in, const BN_ULONG cofac_in)
	{
	EC_GROUP *group=NULL;
	EC_POINT *P=NULL;
	BN_CTX	 *ctx=NULL;
	BIGNUM 	 *prime=NULL,*a=NULL,*b=NULL,*x=NULL,*order=NULL;
	int	 ok=0;

	if ((ctx = BN_CTX_new()) == NULL) goto bn_err;
	if ((prime = BN_new()) == NULL || (a = BN_new()) == NULL || (b = BN_new()) == NULL ||
		(x = BN_new()) == NULL || (order = BN_new()) == NULL) goto bn_err;
	
	if (!BN_hex2bn(&prime, prime_in)) goto bn_err;
	if (!BN_hex2bn(&a, a_in)) goto bn_err;
	if (!BN_hex2bn(&b, b_in)) goto bn_err;

	if ((group = EC_GROUP_new_curve_GFp(prime, a, b, ctx)) == NULL) goto err;
	if ((P = EC_POINT_new(group)) == NULL) goto err;
	
	if (!BN_hex2bn(&x, x_in)) goto bn_err;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, y_bit, ctx)) goto err;
	if (!BN_hex2bn(&order, order_in)) goto bn_err;
	if (!BN_set_word(x, cofac_in)) goto bn_err;
	if (!EC_GROUP_set_generator(group, P, order, x)) goto err;
	ok=1;
bn_err:
	if (!ok)
		ECerr(EC_F_EC_GROUP_NEW_GFP_FROM_HEX, ERR_R_BN_LIB);
err:
	if (!ok)
		{
		EC_GROUP_free(group);
		group = NULL;
		}
	if (P) 	   EC_POINT_free(P);
	if (ctx)   BN_CTX_free(ctx);
	if (prime) BN_free(prime);
	if (a)     BN_free(a);
	if (b)     BN_free(b);
	if (order) BN_free(order);
	if (x)     BN_free(x);
	return(group);
	}

EC_GROUP *EC_GROUP_new_by_name(int name)
	{
	EC_GROUP *ret = NULL;
	switch (name)
		{
	case EC_GROUP_NO_CURVE:
		return NULL;
	/* some nist curves */
	case EC_GROUP_NIST_PRIME_224: /* EC_GROUP_NIST_PRIME_224 == EC_GROUP_SECG_PRIME_224R1 */
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_224);
		break;

	case EC_GROUP_NIST_PRIME_384: /* EC_GROUP_NIST_PRIME_384 == EC_GROUP_SECG_PRIME_384R1 */
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_384);
		break;

	case EC_GROUP_NIST_PRIME_521: /* EC_GROUP_NIST_PRIME_521 == EC_GROUP_SECG_PRIME_521R1 */
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_521);
		break;
	/* x9.62 prime curves */
	case EC_GROUP_X9_62_PRIME_192V1: /* == EC_GROUP_NIST_PRIME_192 == EC_GROUP_SECG_PRIME_192R1 */
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_NIST_PRIME_192);
		break;

	case EC_GROUP_X9_62_PRIME_192V2:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_192V2);
		break;

	case EC_GROUP_X9_62_PRIME_192V3:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_192V3);
		break;

	case EC_GROUP_X9_62_PRIME_239V1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_239V1);
		break;

	case EC_GROUP_X9_62_PRIME_239V2:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_239V2);
		break;

	case EC_GROUP_X9_62_PRIME_239V3:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_239V3);
		break;

	case EC_GROUP_X9_62_PRIME_256V1: /* == EC_GROUP_NIST_PRIME_256 == EC_GROUP_SECG_PRIME_256R1 */
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_X9_62_PRIME_256V1);
		break;
	/* the remaining secg curves */
	case EC_GROUP_SECG_PRIME_112R1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_112R1);
		break;
	case EC_GROUP_SECG_PRIME_112R2:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_112R2);
		break;
	case EC_GROUP_SECG_PRIME_128R1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_128R1);
		break;
	case EC_GROUP_SECG_PRIME_128R2:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_128R2);
		break;
	case EC_GROUP_SECG_PRIME_160K1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_160K1);
		break;
	case EC_GROUP_SECG_PRIME_160R1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_160R1);
		break;
	case EC_GROUP_SECG_PRIME_160R2:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_160R2);
		break;
	case EC_GROUP_SECG_PRIME_192K1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_192K1);
		break;
	case EC_GROUP_SECG_PRIME_224K1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_224K1);
		break;
	case EC_GROUP_SECG_PRIME_256K1:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_SECG_PRIME_256K1);
		break;
	/* some wap/wtls curves */
	case EC_GROUP_WTLS_6:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_WTLS_6);
		break;
	case EC_GROUP_WTLS_8:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_WTLS_8);
		break;
	case EC_GROUP_WTLS_9:
		ret = ec_group_new_GFp_from_hex(_EC_GROUP_WTLS_9);
		break;

		}
	if (ret == NULL)
		{
		ECerr(EC_F_EC_GROUP_NEW_BY_NAME, EC_R_UNKNOWN_GROUP);
		return NULL;
		}
	EC_GROUP_set_nid(ret, name);
	return ret;
	}


EC_GROUP *EC_GROUP_new_by_nid(int nid)
	{
	return EC_GROUP_new_by_name(nid);
	}