eccrypto.cpp

lots Elliptic curve cryptography codes. Use Visual c++ to compile

// eccrypto.cpp - written and placed in the public domain by Wei Dai

#include "pch.h"

#ifndef CRYPTOPP_IMPORTS

#include "eccrypto.h"
#include "nbtheory.h"
#include "oids.h"
#include "hex.h"
#include "argnames.h"
#include "ec2n.h"

NAMESPACE_BEGIN(CryptoPP)

#if 0
static void ECDSA_TestInstantiations()
{
	ECDSA<EC2N>::Signer t1;
	ECDSA<EC2N>::Verifier t2(t1);
	ECNR<ECP>::Signer t3;
	ECNR<ECP>::Verifier t4(t3);
	ECIES<ECP>::Encryptor t5;
	ECIES<EC2N>::Decryptor t6;
	ECDH<ECP>::Domain t7;
	ECMQV<ECP>::Domain t8;
}
#endif

// VC60 workaround: complains when these functions are put into an anonymous namespace
static Integer ConvertToInteger(const PolynomialMod2 &x)
{
	unsigned int l = x.ByteCount();
	SecByteBlock temp(l);
	x.Encode(temp, l);
	return Integer(temp, l);
}

static inline Integer ConvertToInteger(const Integer &x)
{
	return x;
}

static bool CheckMOVCondition(const Integer &q, const Integer &r)
{
	// see "Updated standards for validating elliptic curves", http://eprint.iacr.org/2007/343
	Integer t = 1;
	unsigned int n = q.IsEven() ? 1 : q.BitCount(), m = r.BitCount();

	for (unsigned int i=n; DiscreteLogWorkFactor(i)<m/2; i+=n)
	{
		if (q.IsEven())
			t = (t+t)%r;
		else
			t = (t*q)%r;
		if (t == 1)
			return false;
	}
	return true;
}

// ******************************************************************

template <class T> struct EcRecommendedParameters;

template<> struct EcRecommendedParameters<EC2N>
{
	EcRecommendedParameters(const OID &oid, unsigned int t2, unsigned int t3, unsigned int t4, const char *a, const char *b, const char *g, const char *n, unsigned int h)
		: oid(oid), t0(0), t1(0), t2(t2), t3(t3), t4(t4), a(a), b(b), g(g), n(n), h(h) {}
	EcRecommendedParameters(const OID &oid, unsigned int t0, unsigned int t1, unsigned int t2, unsigned int t3, unsigned int t4, const char *a, const char *b, const char *g, const char *n, unsigned int h)
		: oid(oid), t0(t0), t1(t1), t2(t2), t3(t3), t4(t4), a(a), b(b), g(g), n(n), h(h) {}
	EC2N *NewEC() const
	{
		StringSource ssA(a, true, new HexDecoder);
		StringSource ssB(b, true, new HexDecoder);
		if (t0 == 0)
			return new EC2N(GF2NT(t2, t3, t4), EC2N::FieldElement(ssA, (size_t)ssA.MaxRetrievable()), EC2N::FieldElement(ssB, (size_t)ssB.MaxRetrievable()));
		else
			return new EC2N(GF2NPP(t0, t1, t2, t3, t4), EC2N::FieldElement(ssA, (size_t)ssA.MaxRetrievable()), EC2N::FieldElement(ssB, (size_t)ssB.MaxRetrievable()));
	};

	OID oid;
	unsigned int t0, t1, t2, t3, t4;
	const char *a, *b, *g, *n;
	unsigned int h;
};

template<> struct EcRecommendedParameters<ECP>
{
	EcRecommendedParameters(const OID &oid, const char *p, const char *a, const char *b, const char *g, const char *n, unsigned int h)
		: oid(oid), p(p), a(a), b(b), g(g), n(n), h(h) {}
	ECP *NewEC() const
	{
		StringSource ssP(p, true, new HexDecoder);
		StringSource ssA(a, true, new HexDecoder);
		StringSource ssB(b, true, new HexDecoder);
		return new ECP(Integer(ssP, (size_t)ssP.MaxRetrievable()), ECP::FieldElement(ssA, (size_t)ssA.MaxRetrievable()), ECP::FieldElement(ssB, (size_t)ssB.MaxRetrievable()));
	};

	OID oid;
	const char *p;
	const char *a, *b, *g, *n;
	unsigned int h;
};

struct OIDLessThan
{
	template <typename T>
	inline bool operator()(const EcRecommendedParameters<T>& a, const OID& b) {return a.oid < b;}
	template <typename T>
	inline bool operator()(const OID& a, const EcRecommendedParameters<T>& b) {return a < b.oid;}
	template <typename T>
	inline bool operator()(const EcRecommendedParameters<T>& a, const EcRecommendedParameters<T>& b) {return a.oid < b.oid;}
};

static void GetRecommendedParameters(const EcRecommendedParameters<EC2N> *&begin, const EcRecommendedParameters<EC2N> *&end)
{
	// this array must be sorted by OID
	static const EcRecommendedParameters<EC2N> rec[] = {
		EcRecommendedParameters<EC2N>(ASN1::sect163k1(), 
			163, 7, 6, 3, 0,
			"000000000000000000000000000000000000000001",
			"000000000000000000000000000000000000000001",
			"0402FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE80289070FB05D38FF58321F2E800536D538CCDAA3D9",
			"04000000000000000000020108A2E0CC0D99F8A5EF",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect163r1(), 
			163, 7, 6, 3, 0,
			"07B6882CAAEFA84F9554FF8428BD88E246D2782AE2",
			"0713612DCDDCB40AAB946BDA29CA91F73AF958AFD9",
			"040369979697AB43897789566789567F787A7876A65400435EDB42EFAFB2989D51FEFCE3C80988F41FF883",
			"03FFFFFFFFFFFFFFFFFFFF48AAB689C29CA710279B",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect239k1(), 
			239, 158, 0,
			"000000000000000000000000000000000000000000000000000000000000",
			"000000000000000000000000000000000000000000000000000000000001",
			"0429A0B6A887A983E9730988A68727A8B2D126C44CC2CC7B2A6555193035DC76310804F12E549BDB011C103089E73510ACB275FC312A5DC6B76553F0CA",
			"2000000000000000000000000000005A79FEC67CB6E91F1C1DA800E478A5",
			4),
		EcRecommendedParameters<EC2N>(ASN1::sect113r1(),
			113, 9, 0,
			"003088250CA6E7C7FE649CE85820F7",
			"00E8BEE4D3E2260744188BE0E9C723",
			"04009D73616F35F4AB1407D73562C10F00A52830277958EE84D1315ED31886",
			"0100000000000000D9CCEC8A39E56F",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect113r2(), 
			113, 9, 0,
			"00689918DBEC7E5A0DD6DFC0AA55C7",
			"0095E9A9EC9B297BD4BF36E059184F",
			"0401A57A6A7B26CA5EF52FCDB816479700B3ADC94ED1FE674C06E695BABA1D",
			"010000000000000108789B2496AF93",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect163r2(), 
			163, 7, 6, 3, 0,
			"000000000000000000000000000000000000000001",
			"020A601907B8C953CA1481EB10512F78744A3205FD",
			"0403F0EBA16286A2D57EA0991168D4994637E8343E3600D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
			"040000000000000000000292FE77E70C12A4234C33",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect283k1(), 
			283, 12, 7, 5, 0,
			"000000000000000000000000000000000000000000000000000000000000000000000000",
			"000000000000000000000000000000000000000000000000000000000000000000000001",
			"040503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC245849283601CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
			"01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
			4),
		EcRecommendedParameters<EC2N>(ASN1::sect283r1(), 
			283, 12, 7, 5, 0,
			"000000000000000000000000000000000000000000000000000000000000000000000001",
			"027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
			"0405F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B1205303676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
			"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect131r1(), 
			131, 8, 3, 2, 0,
			"07A11B09A76B562144418FF3FF8C2570B8",
			"0217C05610884B63B9C6C7291678F9D341",
			"040081BAF91FDF9833C40F9C181343638399078C6E7EA38C001F73C8134B1B4EF9E150",
			"0400000000000000023123953A9464B54D",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect131r2(), 
			131, 8, 3, 2, 0,
			"03E5A88919D7CAFCBF415F07C2176573B2",
			"04B8266A46C55657AC734CE38F018F2192",
			"040356DCD8F2F95031AD652D23951BB366A80648F06D867940A5366D9E265DE9EB240F",
			"0400000000000000016954A233049BA98F",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect193r1(), 
			193, 15, 0,
			"0017858FEB7A98975169E171F77B4087DE098AC8A911DF7B01",
			"00FDFB49BFE6C3A89FACADAA7A1E5BBC7CC1C2E5D831478814",
			"0401F481BC5F0FF84A74AD6CDF6FDEF4BF6179625372D8C0C5E10025E399F2903712CCF3EA9E3A1AD17FB0B3201B6AF7CE1B05",
			"01000000000000000000000000C7F34A778F443ACC920EBA49",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect193r2(), 
			193, 15, 0,
			"0163F35A5137C2CE3EA6ED8667190B0BC43ECD69977702709B",
			"00C9BB9E8927D4D64C377E2AB2856A5B16E3EFB7F61D4316AE",
			"0400D9B67D192E0367C803F39E1A7E82CA14A651350AAE617E8F01CE94335607C304AC29E7DEFBD9CA01F596F927224CDECF6C",
			"010000000000000000000000015AAB561B005413CCD4EE99D5",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect233k1(), 
			233, 74, 0,
			"000000000000000000000000000000000000000000000000000000000000",
			"000000000000000000000000000000000000000000000000000000000001",
			"04017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD612601DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
			"8000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
			4),
		EcRecommendedParameters<EC2N>(ASN1::sect233r1(), 
			233, 74, 0,
			"000000000000000000000000000000000000000000000000000000000001",
			"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
			"0400FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
			"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect409k1(), 
			409, 87, 0,
			"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
			"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
			"040060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE902374601E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
			"7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
			4),
		EcRecommendedParameters<EC2N>(ASN1::sect409r1(), 
			409, 87, 0,
			"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
			"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
			"04015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A70061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
			"010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
			2),
		EcRecommendedParameters<EC2N>(ASN1::sect571k1(), 
			571, 10, 5, 2, 0,
			"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
			"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
			"04026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C89720349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
			"020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
			4),
		EcRecommendedParameters<EC2N>(ASN1::sect571r1(), 
			571, 10, 5, 2, 0,
			"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
			"02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
			"040303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
			"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
			2),
	};
	begin = rec;
	end = rec + sizeof(rec)/sizeof(rec[0]);
}

static void GetRecommendedParameters(const EcRecommendedParameters<ECP> *&begin, const EcRecommendedParameters<ECP> *&end)
{
	// this array must be sorted by OID
	static const EcRecommendedParameters<ECP> rec[] = {
		EcRecommendedParameters<ECP>(ASN1::secp192r1(),
			"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
			"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
			"64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
			"04188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF101207192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
			"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
			1),
		EcRecommendedParameters<ECP>(ASN1::secp256r1(),
			"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
			"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
			"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
			"046B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C2964FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
			"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP160r1(),
			"E95E4A5F737059DC60DFC7AD95B3D8139515620F",
			"340E7BE2A280EB74E2BE61BADA745D97E8F7C300",
			"1E589A8595423412134FAA2DBDEC95C8D8675E58",
			"04BED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC31667CB477A1A8EC338F94741669C976316DA6321",
			"E95E4A5F737059DC60DF5991D45029409E60FC09",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP192r1(),
			"C302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297",
			"6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF",
			"469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9",
			"04C0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD614B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F",
			"C302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP224r1(),
			"D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF",
			"68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43",
			"2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B",
			"040D9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD",
			"D7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP256r1(),
			"A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377",
			"7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9",
			"26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6",
			"048BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997",
			"A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP320r1(),
			"D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC28FCD412B1F1B32E27",
			"3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9F492F375A97D860EB4",
			"520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD884539816F5EB4AC8FB1F1A6",
			"0443BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599C710AF8D0D39E2061114FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6AC7D35245D1692E8EE1",
			"D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658E98691555B44C59311",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP384r1(),
			"8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53",
			"7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F90F8AA5814A503AD4EB04A8C7DD22CE2826",
			"04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62D57CB4390295DBC9943AB78696FA504C11",
			"041D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315",
			"8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565",
			1),
		EcRecommendedParameters<ECP>(ASN1::brainpoolP512r1(),
			"AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3",
			"7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA",
			"3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723",
			"0481AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F8227DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892",
			"AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069",
			1),
		EcRecommendedParameters<ECP>(ASN1::secp112r1(),
			"DB7C2ABF62E35E668076BEAD208B",
			"DB7C2ABF62E35E668076BEAD2088",
			"659EF8BA043916EEDE8911702B22",
			"0409487239995A5EE76B55F9C2F098A89CE5AF8724C0A23E0E0FF77500",
			"DB7C2ABF62E35E7628DFAC6561C5",
			1),
		EcRecommendedParameters<ECP>(ASN1::secp112r2(),
			"DB7C2ABF62E35E668076BEAD208B",
			"6127C24C05F38A0AAAF65C0EF02C",
			"51DEF1815DB5ED74FCC34C85D709",
			"044BA30AB5E892B4E1649DD0928643ADCD46F5882E3747DEF36E956E97",
			"36DF0AAFD8B8D7597CA10520D04B",
			4),
		EcRecommendedParameters<ECP>(ASN1::secp160r1(),
			"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
			"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
			"1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
			"044A96B5688EF573284664698968C38BB913CBFC8223A628553168947D59DCC912042351377AC5FB32",
			"0100000000000000000001F4C8F927AED3CA752257",
			1),
		EcRecommendedParameters<ECP>(ASN1::secp160k1(),
			"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73",
			"0000000000000000000000000000000000000000",
			"0000000000000000000000000000000000000007",
			"043B4C382CE37AA192A4019E763036F4F5DD4D7EBB938CF935318FDCED6BC28286531733C3F03C4FEE",
			"0100000000000000000001B8FA16DFAB9ACA16B6B3",
			1),
		EcRecommendedParameters<ECP>(ASN1::secp256k1(),
			"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
			"0000000000000000000000000000000000000000000000000000000000000000",