/* crypto/ec/ec_curve.c */
/*
* Written by Nils Larsch for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2004 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
* [email protected].
*
* 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
* ([email protected]). This product includes software written by Tim
* Hudson ([email protected]).
*
*/
/* ====================================================================
* 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>
typedef struct ec_curve_data_st {
int field_type; /* either NID_X9_62_prime_field or
* NID_X9_62_characteristic_two_field */
const char *p; /* either a prime number or a polynomial */
const char *a;
const char *b;
const char *x; /* the x coordinate of the generator */
const char *y; /* the y coordinate of the generator */
const char *order; /* the order of the group generated by the
* generator */
const BN_ULONG cofactor;/* the cofactor */
const unsigned char *seed;/* the seed (optional) */
size_t seed_len;
const char *comment; /* a short description of the curve */
} EC_CURVE_DATA;
/* the nist prime curves */
static const unsigned char _EC_NIST_PRIME_192_SEED[] = {
0x30,0x45,0xAE,0x6F,0xC8,0x42,0x2F,0x64,0xED,0x57,
0x95,0x28,0xD3,0x81,0x20,0xEA,0xE1,0x21,0x96,0xD5};
static const EC_CURVE_DATA _EC_NIST_PRIME_192 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
"64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
"188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
"07192b95ffc8da78631011ed6b24cdd573f977a11e794811",
"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",1,
_EC_NIST_PRIME_192_SEED, 20,
"NIST/X9.62/SECG curve over a 192 bit prime field"
};
static const unsigned char _EC_NIST_PRIME_224_SEED[] = {
0xBD,0x71,0x34,0x47,0x99,0xD5,0xC7,0xFC,0xDC,0x45,
0xB5,0x9F,0xA3,0xB9,0xAB,0x8F,0x6A,0x94,0x8B,0xC5};
static const EC_CURVE_DATA _EC_NIST_PRIME_224 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
"bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",1,
_EC_NIST_PRIME_224_SEED, 20,
"NIST/SECG curve over a 224 bit prime field"
};
static const unsigned char _EC_NIST_PRIME_384_SEED[] = {
0xA3,0x35,0x92,0x6A,0xA3,0x19,0xA2,0x7A,0x1D,0x00,
0x89,0x6A,0x67,0x73,0xA4,0x82,0x7A,0xCD,0xAC,0x73};
static const EC_CURVE_DATA _EC_NIST_PRIME_384 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFF"
"FFF0000000000000000FFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFF"
"FFF0000000000000000FFFFFFFC",
"B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC6563"
"98D8A2ED19D2A85C8EDD3EC2AEF",
"AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F"
"25DBF55296C3A545E3872760AB7",
"3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b"
"1ce1d7e819d7a431d7c90ea0e5f",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0"
"DB248B0A77AECEC196ACCC52973",1,
_EC_NIST_PRIME_384_SEED, 20,
"NIST/SECG curve over a 384 bit prime field"
};
static const unsigned char _EC_NIST_PRIME_521_SEED[] = {
0xD0,0x9E,0x88,0x00,0x29,0x1C,0xB8,0x53,0x96,0xCC,
0x67,0x17,0x39,0x32,0x84,0xAA,0xA0,0xDA,0x64,0xBA};
static const EC_CURVE_DATA _EC_NIST_PRIME_521 = {
NID_X9_62_prime_field,
"1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
"1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",
"051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156"
"193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",
"C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14"
"B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",
"011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c9"
"7ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
"1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51"
"868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",1,
_EC_NIST_PRIME_521_SEED, 20,
"NIST/SECG curve over a 521 bit prime field"
};
/* the x9.62 prime curves (minus the nist prime curves) */
static const unsigned char _EC_X9_62_PRIME_192V2_SEED[] = {
0x31,0xA9,0x2E,0xE2,0x02,0x9F,0xD1,0x0D,0x90,0x1B,
0x11,0x3E,0x99,0x07,0x10,0xF0,0xD2,0x1A,0xC6,0xB6};
static const EC_CURVE_DATA _EC_X9_62_PRIME_192V2 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
"CC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953",
"EEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A",
"6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15",
"FFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31",1,
_EC_X9_62_PRIME_192V2_SEED, 20,
"X9.62 curve over a 192 bit prime field"
};
static const unsigned char _EC_X9_62_PRIME_192V3_SEED[] = {
0xC4,0x69,0x68,0x44,0x35,0xDE,0xB3,0x78,0xC4,0xB6,
0x5C,0xA9,0x59,0x1E,0x2A,0x57,0x63,0x05,0x9A,0x2E};
static const EC_CURVE_DATA _EC_X9_62_PRIME_192V3 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
"22123DC2395A05CAA7423DAECCC94760A7D462256BD56916",
"7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896",
"38a90f22637337334b49dcb66a6dc8f9978aca7648a943b0",
"FFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13",1,
_EC_X9_62_PRIME_192V3_SEED, 20,
"X9.62 curve over a 192 bit prime field"
};
static const unsigned char _EC_X9_62_PRIME_239V1_SEED[] = {
0xE4,0x3B,0xB4,0x60,0xF0,0xB8,0x0C,0xC0,0xC0,0xB0,
0x75,0x79,0x8E,0x94,0x80,0x60,0xF8,0x32,0x1B,0x7D};
static const EC_CURVE_DATA _EC_X9_62_PRIME_239V1 = {
NID_X9_62_prime_field,
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
"6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A",
"0FFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF",
"7debe8e4e90a5dae6e4054ca530ba04654b36818ce226b39fccb7b02f1ae",
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B",1,
_EC_X9_62_PRIME_239V1_SEED, 20,
"X9.62 curve over a 239 bit prime field"
};
static const unsigned char _EC_X9_62_PRIME_239V2_SEED[] = {
0xE8,0xB4,0x01,0x16,0x04,0x09,0x53,0x03,0xCA,0x3B,
0x80,0x99,0x98,0x2B,0xE0,0x9F,0xCB,0x9A,0xE6,0x16};
static const EC_CURVE_DATA _EC_X9_62_PRIME_239V2 = {
NID_X9_62_prime_field,
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
"617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C",
"38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7",
"5b0125e4dbea0ec7206da0fc01d9b081329fb555de6ef460237dff8be4ba",
"7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063",1,
_EC_X9_62_PRIME_239V2_SEED, 20,
"X9.62 curve over a 239 bit prime field"
};
static const unsigned char _EC_X9_62_PRIME_239V3_SEED[] = {
0x7D,0x73,0x74,0x16,0x8F,0xFE,0x34,0x71,0xB6,0x0A,
0x85,0x76,0x86,0xA1,0x94,0x75,0xD3,0xBF,0xA2,0xFF};
static const EC_CURVE_DATA _EC_X9_62_PRIME_239V3 = {
NID_X9_62_prime_field,
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF",
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC",
"255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E",
"6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A",
"1607e6898f390c06bc1d552bad226f3b6fcfe48b6e818499af18e3ed6cf3",
"7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551",1,
_EC_X9_62_PRIME_239V3_SEED, 20,
"X9.62 curve over a 239 bit prime field"
};
static const unsigned char _EC_X9_62_PRIME_256V1_SEED[] = {
0xC4,0x9D,0x36,0x08,0x86,0xE7,0x04,0x93,0x6A,0x66,
0x78,0xE1,0x13,0x9D,0x26,0xB7,0x81,0x9F,0x7E,0x90};
static const EC_CURVE_DATA _EC_X9_62_PRIME_256V1 = {
NID_X9_62_prime_field,
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
"4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",1,
_EC_X9_62_PRIME_256V1_SEED, 20,
"X9.62/SECG curve over a 256 bit prime field"
};
/* the secg prime curves (minus the nist and x9.62 prime curves) */
static const unsigned char _EC_SECG_PRIME_112R1_SEED[] = {
0x00,0xF5,0x0B,0x02,0x8E,0x4D,0x69,0x6E,0x67,0x68,
0x75,0x61,0x51,0x75,0x29,0x04,0x72,0x78,0x3F,0xB1};
static const EC_CURVE_DATA _EC_SECG_PRIME_112R1 = {
NID_X9_62_prime_field,
"DB7C2ABF62E35E668076BEAD208B",
"DB7C2ABF62E35E668076BEAD2088",
"659EF8BA043916EEDE8911702B22",
"09487239995A5EE76B55F9C2F098",
"a89ce5af8724c0a23e0e0ff77500",
"DB7C2ABF62E35E7628DFAC6561C5",1,
_EC_SECG_PRIME_112R1_SEED, 20,
"SECG/WTLS curve over a 112 bit prime field"
};
static const unsigned char _EC_SECG_PRIME_112R2_SEED[] = {
0x00,0x27,0x57,0xA1,0x11,0x4D,0x69,0x6E,0x67,0x68,
0x75,0x61,0x51,0x75,0x53,0x16,0xC0,0x5E,0x0B,0xD4};
static const EC_CURVE_DATA _EC_SECG_PRIME_112R2 = {
NID_X9_62_prime_field,
"DB7C2ABF62E35E668076BEAD208B",
"6127C24C05F38A0AAAF65C0EF02C",
"51DEF1815DB5ED74FCC34C85D709",
"4BA30AB5E892B4E1649DD0928643",
"adcd46f5882e3747def36e956e97",
"36DF0AAFD8B8D7597CA10520D04B",4,
_EC_SECG_PRIME_112R2_SEED, 20,
"SECG curve over a 112 bit prime field"
};
static const unsigned char _EC_SECG_PRIME_128R1_SEED[] = {
0x00,0x0E,0x0D,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,
0x51,0x75,0x0C,0xC0,0x3A,0x44,0x73,0xD0,0x36,0x79};
static const EC_CURVE_DATA _EC_SECG_PRIME_128R1 = {
NID_X9_62_prime_field,
"FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",
"FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC",
"E87579C11079F43DD824993C2CEE5ED3",
"161FF7528B899B2D0C28607CA52C5B86",
"cf5ac8395bafeb13c02da292dded7a83",
"FFFFFFFE0000000075A30D1B9038A115",1,
_EC_SECG_PRIME_128R1_SEED, 20,
"SECG curve over a 128 bit prime field"
};
static const unsigned char _EC_SECG_PRIME_128R2_SEED[] = {
0x00,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75,
0x12,0xD8,0xF0,0x34,0x31,0xFC,0xE6,0x3B,0x88,0xF4};
static const EC_CURVE_DATA _EC_SECG_PRIME_128R2 = {
NID_X9_62_prime_field,
"FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",
"D6031998D1B3BBFEBF59CC9BBFF9AEE1",
"5EEEFCA380D02919DC2C6558BB6D8A5D",
"7B6AA5D85E572983E6FB32A7CDEBC140",
"27b6916a894d3aee7106fe805fc34b44",
"3FFFFFFF7FFFFFFFBE0024720613B5A3",4,
_EC_SECG_PRIME_128R2_SEED, 20,
"SECG curve over a 128 bit prime field"
};
static const EC_CURVE_DATA _EC_SECG_PRIME_160K1 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
"0",
"7",
"3B4C382CE37AA192A4019E763036F4F5DD4D7EBB",
"938cf935318fdced6bc28286531733c3f03c4fee",
"0100000000000000000001B8FA16DFAB9ACA16B6B3",1,
NULL, 0,
"SECG curve over a 160 bit prime field"
};
static const unsigned char _EC_SECG_PRIME_160R1_SEED[] = {
0x10,0x53,0xCD,0xE4,0x2C,0x14,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x53,0x3B,0xF3,0xF8,0x33,0x45};
static const EC_CURVE_DATA _EC_SECG_PRIME_160R1 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
"1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
"4A96B5688EF573284664698968C38BB913CBFC82",
"23a628553168947d59dcc912042351377ac5fb32",
"0100000000000000000001F4C8F927AED3CA752257",1,
_EC_SECG_PRIME_160R1_SEED, 20,
"SECG curve over a 160 bit prime field"
};
static const unsigned char _EC_SECG_PRIME_160R2_SEED[] = {
0xB9,0x9B,0x99,0xB0,0x99,0xB3,0x23,0xE0,0x27,0x09,
0xA4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x51};
static const EC_CURVE_DATA _EC_SECG_PRIME_160R2 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70",
"B4E134D3FB59EB8BAB57274904664D5AF50388BA",
"52DCB034293A117E1F4FF11B30F7199D3144CE6D",
"feaffef2e331f296e071fa0df9982cfea7d43f2e",
"0100000000000000000000351EE786A818F3A1A16B",1,
_EC_SECG_PRIME_160R2_SEED, 20,
"SECG/WTLS curve over a 160 bit prime field"
};
static const EC_CURVE_DATA _EC_SECG_PRIME_192K1 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37",
"0",
"3",
"DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D",
"9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d",
"FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D",1,
NULL, 20,
"SECG curve over a 192 bit prime field"
};
static const EC_CURVE_DATA _EC_SECG_PRIME_224K1 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D",
"0",
"5",
"A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C",
"7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5",
"010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",1,
NULL, 20,
"SECG curve over a 224 bit prime field"
};
static const EC_CURVE_DATA _EC_SECG_PRIME_256K1 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
"0",
"7",
"79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",
"483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",1,
NULL, 20,
"SECG curve over a 256 bit prime field"
};
/* some wap/wtls curves */
static const EC_CURVE_DATA _EC_WTLS_8 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFDE7",
"0",
"3",
"1",
"2",
"0100000000000001ECEA551AD837E9",1,
NULL, 20,
"WTLS curve over a 112 bit prime field"
};
static const EC_CURVE_DATA _EC_WTLS_9 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC808F",
"0",
"3",
"1",
"2",
"0100000000000000000001CDC98AE0E2DE574ABF33",1,
NULL, 20,
"WTLS curve over a 160 bit prime field"
};
static const EC_CURVE_DATA _EC_WTLS_12 = {
NID_X9_62_prime_field,
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
"bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", 1,
NULL, 0,
"WTLS curvs over a 224 bit prime field"
};
/* characteristic two curves */
static const unsigned char _EC_SECG_CHAR2_113R1_SEED[] = {
0x10,0xE7,0x23,0xAB,0x14,0xD6,0x96,0xE6,0x76,0x87,
0x56,0x15,0x17,0x56,0xFE,0xBF,0x8F,0xCB,0x49,0xA9};
static const EC_CURVE_DATA _EC_SECG_CHAR2_113R1 = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000201",
"003088250CA6E7C7FE649CE85820F7",
"00E8BEE4D3E2260744188BE0E9C723",
"009D73616F35F4AB1407D73562C10F",
"00A52830277958EE84D1315ED31886",
"0100000000000000D9CCEC8A39E56F", 2,
_EC_SECG_CHAR2_113R1_SEED, 20,
"SECG curve over a 113 bit binary field"
};
static const unsigned char _EC_SECG_CHAR2_113R2_SEED[] = {
0x10,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE,
0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x5D};
static const EC_CURVE_DATA _EC_SECG_CHAR2_113R2 = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000201",
"00689918DBEC7E5A0DD6DFC0AA55C7",
"0095E9A9EC9B297BD4BF36E059184F",
"01A57A6A7B26CA5EF52FCDB8164797",
"00B3ADC94ED1FE674C06E695BABA1D",
"010000000000000108789B2496AF93", 2,
_EC_SECG_CHAR2_113R2_SEED, 20,
"SECG curve over a 113 bit binary field"
};
static const unsigned char _EC_SECG_CHAR2_131R1_SEED[] = {
0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75,0x98,
0x5B,0xD3,0xAD,0xBA,0xDA,0x21,0xB4,0x3A,0x97,0xE2};
static const EC_CURVE_DATA _EC_SECG_CHAR2_131R1 = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000010D",
"07A11B09A76B562144418FF3FF8C2570B8",
"0217C05610884B63B9C6C7291678F9D341",
"0081BAF91FDF9833C40F9C181343638399",
"078C6E7EA38C001F73C8134B1B4EF9E150",
"0400000000000000023123953A9464B54D", 2,
_EC_SECG_CHAR2_131R1_SEED, 20,
"SECG/WTLS curve over a 131 bit binary field"
};
static const unsigned char _EC_SECG_CHAR2_131R2_SEED[] = {
0x98,0x5B,0xD3,0xAD,0xBA,0xD4,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x5A,0x21,0xB4,0x3A,0x97,0xE3};
static const EC_CURVE_DATA _EC_SECG_CHAR2_131R2 = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000010D",
"03E5A88919D7CAFCBF415F07C2176573B2",
"04B8266A46C55657AC734CE38F018F2192",
"0356DCD8F2F95031AD652D23951BB366A8",
"0648F06D867940A5366D9E265DE9EB240F",
"0400000000000000016954A233049BA98F", 2,
_EC_SECG_CHAR2_131R2_SEED, 20,
"SECG curve over a 131 bit binary field"
};
static const EC_CURVE_DATA _EC_NIST_CHAR2_163K = {
NID_X9_62_characteristic_two_field,
"0800000000000000000000000000000000000000C9",
"1",
"1",
"02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
"0289070FB05D38FF58321F2E800536D538CCDAA3D9",
"04000000000000000000020108A2E0CC0D99F8A5EF", 2,
NULL, 0,
"NIST/SECG/WTLS curve over a 163 bit binary field"
};
static const unsigned char _EC_SECG_CHAR2_163R1_SEED[] = {
0x24,0xB7,0xB1,0x37,0xC8,0xA1,0x4D,0x69,0x6E,0x67,
0x68,0x75,0x61,0x51,0x75,0x6F,0xD0,0xDA,0x2E,0x5C};
static const EC_CURVE_DATA _EC_SECG_CHAR2_163R1 = {
NID_X9_62_characteristic_two_field,
"0800000000000000000000000000000000000000C9",
"07B6882CAAEFA84F9554FF8428BD88E246D2782AE2",
"0713612DCDDCB40AAB946BDA29CA91F73AF958AFD9",
"0369979697AB43897789566789567F787A7876A654",
"00435EDB42EFAFB2989D51FEFCE3C80988F41FF883",
"03FFFFFFFFFFFFFFFFFFFF48AAB689C29CA710279B", 2,
/* The algorithm used to derive the curve parameters from
* the seed used here is slightly different than the
* algorithm described in X9.62 .
*/
#if 0
_EC_SECG_CHAR2_163R1_SEED, 20,
#else
NULL, 0,
#endif
"SECG curve over a 163 bit binary field"
};
static const unsigned char _EC_NIST_CHAR2_163B_SEED[] = {
0x85,0xE2,0x5B,0xFE,0x5C,0x86,0x22,0x6C,0xDB,0x12,
0x01,0x6F,0x75,0x53,0xF9,0xD0,0xE6,0x93,0xA2,0x68};
static const EC_CURVE_DATA _EC_NIST_CHAR2_163B ={
NID_X9_62_characteristic_two_field,
"0800000000000000000000000000000000000000C9",
"1",
"020A601907B8C953CA1481EB10512F78744A3205FD",
"03F0EBA16286A2D57EA0991168D4994637E8343E36",
"00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
"040000000000000000000292FE77E70C12A4234C33", 2,
/* The seed here was used to created the curve parameters in normal
* basis representation (and not the polynomial representation used here)
*/
#if 0
_EC_NIST_CHAR2_163B_SEED, 20,
#else
NULL, 0,
#endif
"NIST/SECG curve over a 163 bit binary field"
};
static const unsigned char _EC_SECG_CHAR2_193R1_SEED[] = {
0x10,0x3F,0xAE,0xC7,0x4D,0x69,0x6E,0x67,0x68,0x75,
0x61,0x51,0x75,0x77,0x7F,0xC5,0xB1,0x91,0xEF,0x30};
static const EC_CURVE_DATA _EC_SECG_CHAR2_193R1 = {
NID_X9_62_characteristic_two_field,
"02000000000000000000000000000000000000000000008001",
"0017858FEB7A98975169E171F77B4087DE098AC8A911DF7B01",
"00FDFB49BFE6C3A89FACADAA7A1E5BBC7CC1C2E5D831478814",
"01F481BC5F0FF84A74AD6CDF6FDEF4BF6179625372D8C0C5E1",
"0025E399F2903712CCF3EA9E3A1AD17FB0B3201B6AF7CE1B05",
"01000000000000000000000000C7F34A778F443ACC920EBA49", 2,
_EC_SECG_CHAR2_193R1_SEED, 20,
"SECG curve over a 193 bit binary field"
};
static const unsigned char _EC_SECG_CHAR2_193R2_SEED[] = {
0x10,0xB7,0xB4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,
0x17,0x51,0x37,0xC8,0xA1,0x6F,0xD0,0xDA,0x22,0x11};
static const EC_CURVE_DATA _EC_SECG_CHAR2_193R2 = {
NID_X9_62_characteristic_two_field,
"02000000000000000000000000000000000000000000008001",
"0163F35A5137C2CE3EA6ED8667190B0BC43ECD69977702709B",
"00C9BB9E8927D4D64C377E2AB2856A5B16E3EFB7F61D4316AE",
"00D9B67D192E0367C803F39E1A7E82CA14A651350AAE617E8F",
"01CE94335607C304AC29E7DEFBD9CA01F596F927224CDECF6C",
"010000000000000000000000015AAB561B005413CCD4EE99D5", 2,
_EC_SECG_CHAR2_193R2_SEED, 20,
"SECG curve over a 193 bit binary field"
};
static const EC_CURVE_DATA _EC_NIST_CHAR2_233K = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000000000000000004000000000000000001",
"0",
"1",
"017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
"01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
"008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", 4,
NULL, 0,
"NIST/SECG/WTLS curve over a 233 bit binary field"
};
static const unsigned char _EC_NIST_CHAR2_233B_SEED[] = {
0x74,0xD5,0x9F,0xF0,0x7F,0x6B,0x41,0x3D,0x0E,0xA1,
0x4B,0x34,0x4B,0x20,0xA2,0xDB,0x04,0x9B,0x50,0xC3};
static const EC_CURVE_DATA _EC_NIST_CHAR2_233B = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000000000000000004000000000000000001",
"000000000000000000000000000000000000000000000000000000000001",
"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
"00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
"01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", 2,
_EC_NIST_CHAR2_233B_SEED, 20,
"NIST/SECG/WTLS curve over a 233 bit binary field"
};
static const EC_CURVE_DATA _EC_SECG_CHAR2_239K1 = {
NID_X9_62_characteristic_two_field,
"800000000000000000004000000000000000000000000000000000000001",
"0",
"1",
"29A0B6A887A983E9730988A68727A8B2D126C44CC2CC7B2A6555193035DC",
"76310804F12E549BDB011C103089E73510ACB275FC312A5DC6B76553F0CA",
"2000000000000000000000000000005A79FEC67CB6E91F1C1DA800E478A5", 4,
NULL, 0,
"SECG curve over a 239 bit binary field"
};
static const EC_CURVE_DATA _EC_NIST_CHAR2_283K = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000000000000000000000000000000000000000001"
"0A1",
"0",
"1",
"0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492"
"836",
"01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2"
"259",
"01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163"
"C61", 4,
NULL, 20,
"NIST/SECG curve over a 283 bit binary field"
};
static const unsigned char _EC_NIST_CHAR2_283B_SEED[] = {
0x77,0xE2,0xB0,0x73,0x70,0xEB,0x0F,0x83,0x2A,0x6D,
0xD5,0xB6,0x2D,0xFC,0x88,0xCD,0x06,0xBB,0x84,0xBE};
static const EC_CURVE_DATA _EC_NIST_CHAR2_283B = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000000000000000000000000000000000000000001"
"0A1",
"000000000000000000000000000000000000000000000000000000000000000000000"
"001",
"027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A"
"2F5",
"05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12"
"053",
"03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE811"
"2F4",
"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB"
"307", 2,
_EC_NIST_CHAR2_283B_SEED, 20,
"NIST/SECG curve over a 283 bit binary field"
};
static const EC_CURVE_DATA _EC_NIST_CHAR2_409K = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000000000000000000000000000000000000000000000"
"00000000000008000000000000000000001",
"0",
"1",
"0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C4601"
"89EB5AAAA62EE222EB1B35540CFE9023746",
"01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6"
"C42E9C55215AA9CA27A5863EC48D8E0286B",
"007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400"
"EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", 4,
NULL, 0,
"NIST/SECG curve over a 409 bit binary field"
};
static const unsigned char _EC_NIST_CHAR2_409B_SEED[] = {
0x40,0x99,0xB5,0xA4,0x57,0xF9,0xD6,0x9F,0x79,0x21,
0x3D,0x09,0x4C,0x4B,0xCD,0x4D,0x42,0x62,0x21,0x0B};
static const EC_CURVE_DATA _EC_NIST_CHAR2_409B = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000000000000000000000000000000000000000000000"
"00000000000008000000000000000000001",
"000000000000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000001",
"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A19"
"7B272822F6CD57A55AA4F50AE317B13545F",
"015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255"
"A868A1180515603AEAB60794E54BB7996A7",
"0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514"
"F1FDF4B4F40D2181B3681C364BA0273C706",
"010000000000000000000000000000000000000000000000000001E2AAD6A612F3330"
"7BE5FA47C3C9E052F838164CD37D9A21173", 2,
_EC_NIST_CHAR2_409B_SEED, 20,
"NIST/SECG curve over a 409 bit binary field"
};
static const EC_CURVE_DATA _EC_NIST_CHAR2_571K = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000000000000000000000000"
"000000000000000000000000000000000000000000000000000000000000000000000"
"00425",
"0",
"1",
"026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA443709"
"58493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A0"
"1C8972",
"0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D497"
"9C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143E"
"F1C7A3",
"020000000000000000000000000000000000000000000000000000000000000000000"
"000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F63"
"7C1001", 4,
NULL, 0,
"NIST/SECG curve over a 571 bit binary field"
};
static const unsigned char _EC_NIST_CHAR2_571B_SEED[] = {
0x2A,0xA0,0x58,0xF7,0x3A,0x0E,0x33,0xAB,0x48,0x6B,
0x0F,0x61,0x04,0x10,0xC5,0x3A,0x7F,0x13,0x23,0x10};
static const EC_CURVE_DATA _EC_NIST_CHAR2_571B = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000000000000000000000000"
"000000000000000000000000000000000000000000000000000000000000000000000"
"00425",
"000000000000000000000000000000000000000000000000000000000000000000000"
"000000000000000000000000000000000000000000000000000000000000000000000"
"000001",
"02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFA"
"BBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F29"
"55727A",
"0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53"
"950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8E"
"EC2D19",
"037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423"
"E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B"
"8AC15B",
"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2F"
"E84E47", 2,
_EC_NIST_CHAR2_571B_SEED, 20,
"NIST/SECG curve over a 571 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_163V1_SEED[] = {
0xD2,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE,
0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x54};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_163V1 = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000000000000107",
"072546B5435234A422E0789675F432C89435DE5242",
"00C9517D06D5240D3CFF38C74B20B6CD4D6F9DD4D9",
"07AF69989546103D79329FCC3D74880F33BBE803CB",
"01EC23211B5966ADEA1D3F87F7EA5848AEF0B7CA9F",
"0400000000000000000001E60FC8821CC74DAEAFC1", 2,
_EC_X9_62_CHAR2_163V1_SEED, 20,
"X9.62 curve over a 163 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_163V2_SEED[] = {
0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_163V2 = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000000000000107",
"0108B39E77C4B108BED981ED0E890E117C511CF072",
"0667ACEB38AF4E488C407433FFAE4F1C811638DF20",
"0024266E4EB5106D0A964D92C4860E2671DB9B6CC5",
"079F684DDF6684C5CD258B3890021B2386DFD19FC5",
"03FFFFFFFFFFFFFFFFFFFDF64DE1151ADBB78F10A7", 2,
_EC_X9_62_CHAR2_163V2_SEED, 20,
"X9.62 curve over a 163 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_163V3_SEED[] = {
0x50,0xCB,0xF1,0xD9,0x5C,0xA9,0x4D,0x69,0x6E,0x67,
0x68,0x75,0x61,0x51,0x75,0xF1,0x6A,0x36,0xA3,0xB8};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_163V3 = {
NID_X9_62_characteristic_two_field,
"080000000000000000000000000000000000000107",
"07A526C63D3E25A256A007699F5447E32AE456B50E",
"03F7061798EB99E238FD6F1BF95B48FEEB4854252B",
"02F9F87B7C574D0BDECF8A22E6524775F98CDEBDCB",
"05B935590C155E17EA48EB3FF3718B893DF59A05D0",
"03FFFFFFFFFFFFFFFFFFFE1AEE140F110AFF961309", 2,
_EC_X9_62_CHAR2_163V3_SEED, 20,
"X9.62 curve over a 163 bit binary field"
};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_176V1 = {
NID_X9_62_characteristic_two_field,
"0100000000000000000000000000000000080000000007",
"E4E6DB2995065C407D9D39B8D0967B96704BA8E9C90B",
"5DDA470ABE6414DE8EC133AE28E9BBD7FCEC0AE0FFF2",
"8D16C2866798B600F9F08BB4A8E860F3298CE04A5798",
"6FA4539C2DADDDD6BAB5167D61B436E1D92BB16A562C",
"00010092537397ECA4F6145799D62B0A19CE06FE26AD", 0xFF6E,
NULL, 0,
"X9.62 curve over a 176 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_191V1_SEED[] = {
0x4E,0x13,0xCA,0x54,0x27,0x44,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x55,0x2F,0x27,0x9A,0x8C,0x84};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_191V1 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000201",
"2866537B676752636A68F56554E12640276B649EF7526267",
"2E45EF571F00786F67B0081B9495A3D95462F5DE0AA185EC",
"36B3DAF8A23206F9C4F299D7B21A9C369137F2C84AE1AA0D",
"765BE73433B3F95E332932E70EA245CA2418EA0EF98018FB",
"40000000000000000000000004A20E90C39067C893BBB9A5", 2,
_EC_X9_62_CHAR2_191V1_SEED, 20,
"X9.62 curve over a 191 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_191V2_SEED[] = {
0x08,0x71,0xEF,0x2F,0xEF,0x24,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x58,0xBE,0xE0,0xD9,0x5C,0x15};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_191V2 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000201",
"401028774D7777C7B7666D1366EA432071274F89FF01E718",
"0620048D28BCBD03B6249C99182B7C8CD19700C362C46A01",
"3809B2B7CC1B28CC5A87926AAD83FD28789E81E2C9E3BF10",
"17434386626D14F3DBF01760D9213A3E1CF37AEC437D668A",
"20000000000000000000000050508CB89F652824E06B8173", 4,
_EC_X9_62_CHAR2_191V2_SEED, 20,
"X9.62 curve over a 191 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_191V3_SEED[] = {
0xE0,0x53,0x51,0x2D,0xC6,0x84,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x50,0x67,0xAE,0x78,0x6D,0x1F};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_191V3 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000201",
"6C01074756099122221056911C77D77E77A777E7E7E77FCB",
"71FE1AF926CF847989EFEF8DB459F66394D90F32AD3F15E8",
"375D4CE24FDE434489DE8746E71786015009E66E38A926DD",
"545A39176196575D985999366E6AD34CE0A77CD7127B06BE",
"155555555555555555555555610C0B196812BFB6288A3EA3", 6,
_EC_X9_62_CHAR2_191V3_SEED, 20,
"X9.62 curve over a 191 bit binary field"
};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_208W1 = {
NID_X9_62_characteristic_two_field,
"010000000000000000000000000000000800000000000000000007",
"0000000000000000000000000000000000000000000000000000",
"C8619ED45A62E6212E1160349E2BFA844439FAFC2A3FD1638F9E",
"89FDFBE4ABE193DF9559ECF07AC0CE78554E2784EB8C1ED1A57A",
"0F55B51A06E78E9AC38A035FF520D8B01781BEB1A6BB08617DE3",
"000101BAF95C9723C57B6C21DA2EFF2D5ED588BDD5717E212F9D", 0xFE48,
NULL, 0,
"X9.62 curve over a 208 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_239V1_SEED[] = {
0xD3,0x4B,0x9A,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,
0x51,0x75,0xCA,0x71,0xB9,0x20,0xBF,0xEF,0xB0,0x5D};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_239V1 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000001000000001",
"32010857077C5431123A46B808906756F543423E8D27877578125778AC76",
"790408F2EEDAF392B012EDEFB3392F30F4327C0CA3F31FC383C422AA8C16",
"57927098FA932E7C0A96D3FD5B706EF7E5F5C156E16B7E7C86038552E91D",
"61D8EE5077C33FECF6F1A16B268DE469C3C7744EA9A971649FC7A9616305",
"2000000000000000000000000000000F4D42FFE1492A4993F1CAD666E447", 4,
_EC_X9_62_CHAR2_239V1_SEED, 20,
"X9.62 curve over a 239 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_239V2_SEED[] = {
0x2A,0xA6,0x98,0x2F,0xDF,0xA4,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x5D,0x26,0x67,0x27,0x27,0x7D};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_239V2 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000001000000001",
"4230017757A767FAE42398569B746325D45313AF0766266479B75654E65F",
"5037EA654196CFF0CD82B2C14A2FCF2E3FF8775285B545722F03EACDB74B",
"28F9D04E900069C8DC47A08534FE76D2B900B7D7EF31F5709F200C4CA205",
"5667334C45AFF3B5A03BAD9DD75E2C71A99362567D5453F7FA6E227EC833",
"1555555555555555555555555555553C6F2885259C31E3FCDF154624522D", 6,
_EC_X9_62_CHAR2_239V2_SEED, 20,
"X9.62 curve over a 239 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_239V3_SEED[] = {
0x9E,0x07,0x6F,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,
0x51,0x75,0xE1,0x1E,0x9F,0xDD,0x77,0xF9,0x20,0x41};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_239V3 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000001000000001",
"01238774666A67766D6676F778E676B66999176666E687666D8766C66A9F",
"6A941977BA9F6A435199ACFC51067ED587F519C5ECB541B8E44111DE1D40",
"70F6E9D04D289C4E89913CE3530BFDE903977D42B146D539BF1BDE4E9C92",
"2E5A0EAF6E5E1305B9004DCE5C0ED7FE59A35608F33837C816D80B79F461",
"0CCCCCCCCCCCCCCCCCCCCCCCCCCCCCAC4912D2D9DF903EF9888B8A0E4CFF", 0xA,
_EC_X9_62_CHAR2_239V3_SEED, 20,
"X9.62 curve over a 239 bit binary field"
};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_272W1 = {
NID_X9_62_characteristic_two_field,
"010000000000000000000000000000000000000000000000000000010000000000000"
"B",
"91A091F03B5FBA4AB2CCF49C4EDD220FB028712D42BE752B2C40094DBACDB586FB20",
"7167EFC92BB2E3CE7C8AAAFF34E12A9C557003D7C73A6FAF003F99F6CC8482E540F7",
"6108BABB2CEEBCF787058A056CBE0CFE622D7723A289E08A07AE13EF0D10D171DD8D",
"10C7695716851EEF6BA7F6872E6142FBD241B830FF5EFCACECCAB05E02005DDE9D23",
"000100FAF51354E0E39E4892DF6E319C72C8161603FA45AA7B998A167B8F1E629521",
0xFF06,
NULL, 0,
"X9.62 curve over a 272 bit binary field"
};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_304W1 = {
NID_X9_62_characteristic_two_field,
"010000000000000000000000000000000000000000000000000000000000000000000"
"000000807",
"FD0D693149A118F651E6DCE6802085377E5F882D1B510B44160074C1288078365A039"
"6C8E681",
"BDDB97E555A50A908E43B01C798EA5DAA6788F1EA2794EFCF57166B8C14039601E558"
"27340BE",
"197B07845E9BE2D96ADB0F5F3C7F2CFFBD7A3EB8B6FEC35C7FD67F26DDF6285A644F7"
"40A2614",
"E19FBEB76E0DA171517ECF401B50289BF014103288527A9B416A105E80260B549FDC1"
"B92C03B",
"000101D556572AABAC800101D556572AABAC8001022D5C91DD173F8FB561DA6899164"
"443051D", 0xFE2E,
NULL, 0,
"X9.62 curve over a 304 bit binary field"
};
static const unsigned char _EC_X9_62_CHAR2_359V1_SEED[] = {
0x2B,0x35,0x49,0x20,0xB7,0x24,0xD6,0x96,0xE6,0x76,
0x87,0x56,0x15,0x17,0x58,0x5B,0xA1,0x33,0x2D,0xC6};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_359V1 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000000000000000000000000"
"000100000000000000001",
"5667676A654B20754F356EA92017D946567C46675556F19556A04616B567D223A5E05"
"656FB549016A96656A557",
"2472E2D0197C49363F1FE7F5B6DB075D52B6947D135D8CA445805D39BC34562608968"
"7742B6329E70680231988",
"3C258EF3047767E7EDE0F1FDAA79DAEE3841366A132E163ACED4ED2401DF9C6BDCDE9"
"8E8E707C07A2239B1B097",
"53D7E08529547048121E9C95F3791DD804963948F34FAE7BF44EA82365DC7868FE57E"
"4AE2DE211305A407104BD",
"01AF286BCA1AF286BCA1AF286BCA1AF286BCA1AF286BC9FB8F6B85C556892C20A7EB9"
"64FE7719E74F490758D3B", 0x4C,
_EC_X9_62_CHAR2_359V1_SEED, 20,
"X9.62 curve over a 359 bit binary field"
};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_368W1 = {
NID_X9_62_characteristic_two_field,
"010000000000000000000000000000000000000000000000000000000000000000000"
"0002000000000000000000007",
"E0D2EE25095206F5E2A4F9ED229F1F256E79A0E2B455970D8D0D865BD94778C576D62"
"F0AB7519CCD2A1A906AE30D",
"FC1217D4320A90452C760A58EDCD30C8DD069B3C34453837A34ED50CB54917E1C2112"
"D84D164F444F8F74786046A",
"1085E2755381DCCCE3C1557AFA10C2F0C0C2825646C5B34A394CBCFA8BC16B22E7E78"
"9E927BE216F02E1FB136A5F",
"7B3EB1BDDCBA62D5D8B2059B525797FC73822C59059C623A45FF3843CEE8F87CD1855"
"ADAA81E2A0750B80FDA2310",
"00010090512DA9AF72B08349D98A5DD4C7B0532ECA51CE03E2D10F3B7AC579BD87E90"
"9AE40A6F131E9CFCE5BD967", 0xFF70,
NULL, 0,
"X9.62 curve over a 368 bit binary field"
};
static const EC_CURVE_DATA _EC_X9_62_CHAR2_431R1 = {
NID_X9_62_characteristic_two_field,
"800000000000000000000000000000000000000000000000000000000000000000000"
"000000001000000000000000000000000000001",
"1A827EF00DD6FC0E234CAF046C6A5D8A85395B236CC4AD2CF32A0CADBDC9DDF620B0E"
"B9906D0957F6C6FEACD615468DF104DE296CD8F",
"10D9B4A3D9047D8B154359ABFB1B7F5485B04CEB868237DDC9DEDA982A679A5A919B6"
"26D4E50A8DD731B107A9962381FB5D807BF2618",
"120FC05D3C67A99DE161D2F4092622FECA701BE4F50F4758714E8A87BBF2A658EF8C2"
"1E7C5EFE965361F6C2999C0C247B0DBD70CE6B7",
"20D0AF8903A96F8D5FA2C255745D3C451B302C9346D9B7E485E7BCE41F6B591F3E8F6"
"ADDCBB0BC4C2F947A7DE1A89B625D6A598B3760",
"0340340340340340340340340340340340340340340340340340340323C313FAB5058"
"9703B5EC68D3587FEC60D161CC149C1AD4A91", 0x2760,
NULL, 0,
"X9.62 curve over a 431 bit binary field"
};
static const EC_CURVE_DATA _EC_WTLS_1 = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000201",
"1",
"1",
"01667979A40BA497E5D5C270780617",
"00F44B4AF1ECC2630E08785CEBCC15",
"00FFFFFFFFFFFFFFFDBF91AF6DEA73", 2,
NULL, 0,
"WTLS curve over a 113 bit binary field"
};
/* IPSec curves */
/* NOTE: The of curves over a extension field of non prime degree
* is not recommended (Weil-descent).
* As the group order is not a prime this curve is not suitable
* for ECDSA.
*/
static const EC_CURVE_DATA _EC_IPSEC_155_ID3 = {
NID_X9_62_characteristic_two_field,
"0800000000000000000000004000000000000001",
"0",
"07338f",
"7b",
"1c8",
"2AAAAAAAAAAAAAAAAAAC7F3C7881BD0868FA86C",3,
NULL, 0,
"\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n"
"\tNot suitable for ECDSA.\n\tQuestionable extension field!"
};
/* NOTE: The of curves over a extension field of non prime degree
* is not recommended (Weil-descent).
* As the group order is not a prime this curve is not suitable
* for ECDSA.
*/
static const EC_CURVE_DATA _EC_IPSEC_185_ID4 = {
NID_X9_62_characteristic_two_field,
"020000000000000000000000000000200000000000000001",
"0",
"1ee9",
"18",
"0d",
"FFFFFFFFFFFFFFFFFFFFFFEDF97C44DB9F2420BAFCA75E",2,
NULL, 0,
"\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n"
"\tNot suitable for ECDSA.\n\tQuestionable extension field!"
};
typedef struct _ec_list_element_st {
int nid;
const EC_CURVE_DATA *data;
} ec_list_element;
static const ec_list_element curve_list[] = {
/* prime field curves */
/* secg curves */
{ NID_secp112r1, &_EC_SECG_PRIME_112R1},
{ NID_secp112r2, &_EC_SECG_PRIME_112R2},
{ NID_secp128r1, &_EC_SECG_PRIME_128R1},
{ NID_secp128r2, &_EC_SECG_PRIME_128R2},
{ NID_secp160k1, &_EC_SECG_PRIME_160K1},
{ NID_secp160r1, &_EC_SECG_PRIME_160R1},
{ NID_secp160r2, &_EC_SECG_PRIME_160R2},
/* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */
{ NID_secp192k1, &_EC_SECG_PRIME_192K1},
{ NID_secp224k1, &_EC_SECG_PRIME_224K1},
{ NID_secp224r1, &_EC_NIST_PRIME_224},
{ NID_secp256k1, &_EC_SECG_PRIME_256K1},
/* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */
{ NID_secp384r1, &_EC_NIST_PRIME_384},
{ NID_secp521r1, &_EC_NIST_PRIME_521},
/* X9.62 curves */
{ NID_X9_62_prime192v1, &_EC_NIST_PRIME_192},
{ NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2},
{ NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3},
{ NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1},
{ NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2},
{ NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3},
{ NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1},
/* characteristic two field curves */
/* NIST/SECG curves */
{ NID_sect113r1, &_EC_SECG_CHAR2_113R1},
{ NID_sect113r2, &_EC_SECG_CHAR2_113R2},
{ NID_sect131r1, &_EC_SECG_CHAR2_131R1},
{ NID_sect131r2, &_EC_SECG_CHAR2_131R2},
{ NID_sect163k1, &_EC_NIST_CHAR2_163K },
{ NID_sect163r1, &_EC_SECG_CHAR2_163R1},
{ NID_sect163r2, &_EC_NIST_CHAR2_163B },
{ NID_sect193r1, &_EC_SECG_CHAR2_193R1},
{ NID_sect193r2, &_EC_SECG_CHAR2_193R2},
{ NID_sect233k1, &_EC_NIST_CHAR2_233K },
{ NID_sect233r1, &_EC_NIST_CHAR2_233B },
{ NID_sect239k1, &_EC_SECG_CHAR2_239K1},
{ NID_sect283k1, &_EC_NIST_CHAR2_283K },
{ NID_sect283r1, &_EC_NIST_CHAR2_283B },
{ NID_sect409k1, &_EC_NIST_CHAR2_409K },
{ NID_sect409r1, &_EC_NIST_CHAR2_409B },
{ NID_sect571k1, &_EC_NIST_CHAR2_571K },
{ NID_sect571r1, &_EC_NIST_CHAR2_571B },
/* X9.62 curves */
{ NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1},
{ NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2},
{ NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3},
{ NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1},
{ NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1},
{ NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2},
{ NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3},
{ NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1},
{ NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1},
{ NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2},
{ NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3},
{ NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1},
{ NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1},
{ NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1},
{ NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1},
{ NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1},
/* the WAP/WTLS curves
* [unlike SECG, spec has its own OIDs for curves from X9.62] */
{ NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1},
{ NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K},
{ NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1},
{ NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1},
{ NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1},
{ NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2},
{ NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8},
{ NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9 },
{ NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K},
{ NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B},
{ NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12},
/* IPSec curves */
{ NID_ipsec3, &_EC_IPSEC_155_ID3},
{ NID_ipsec4, &_EC_IPSEC_185_ID4},
};
static size_t curve_list_length = sizeof(curve_list)/sizeof(ec_list_element);
static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data)
{
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;
if ((ctx = BN_CTX_new()) == NULL)
{
ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE);
goto err;
}
if ((p = BN_new()) == NULL || (a = BN_new()) == NULL ||
(b = BN_new()) == NULL || (x = BN_new()) == NULL ||
(y = BN_new()) == NULL || (order = BN_new()) == NULL)
{
ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE);
goto err;
}
if (!BN_hex2bn(&p, data->p) || !BN_hex2bn(&a, data->a)
|| !BN_hex2bn(&b, data->b))
{
ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);
goto err;
}
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;
}
}
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;
}
}
if ((P = EC_POINT_new(group)) == NULL)
{
ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
goto err;
}
if (!BN_hex2bn(&x, data->x) || !BN_hex2bn(&y, data->y))
{
ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);
goto err;
}
if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx))
{
ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
goto err;
}
if (!BN_hex2bn(&order, data->order) || !BN_set_word(x, 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 (data->seed)
{
if (!EC_GROUP_set_seed(group, data->seed, data->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<curve_list_length; i++)
if (curve_list[i].nid == nid)
{
ret = ec_group_new_from_data(curve_list[i].data);
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].data->comment;
}
return curve_list_length;
}
|
