ec_secp192r1.js

/* jscrypto library, ellitpic curve cryptography
 *   by GUAN Zhi <guanzhi at guanzhi dot org>
 */

var secp192r1_curve_name = "secp192r1";
var secp192r1_p = bn_nistp192;
var secp192r1_a = bn_from_hex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC");
var secp192r1_b = bn_from_hex("64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1");
var secp192r1_n = bn_from_hex("FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831");
var secp192r1_x = bn_from_hex("188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012");
var secp192r1_y = bn_from_hex("07192b95ffc8da78631011ed6b24cdd573f977a11e794811");
var secp192r1_h = 1;

function secp192r1_to_affine(A) {
	var z_1 = bn_mod_invert(A.z, secp192r1_p);
	var z_2 = bn_mod_nistp192_sqr(z_1);
	var z_3 = bn_mod_nistp192_mul(z_1, z_2);
	return new ecpoint(
		bn_mod_nistp192_mul(A.x, z_2),
		bn_mod_nistp192_mul(A.y, z_3));
}

function secp192r1_is_on_curve(A) {
	if (!bn_is_one(A.z))
		A = secp192r1_to_affine(A);
	var t0, t1, t2;
	t0 = bn_mod_nistp192_sqr(A.y);	
	t1 = bn_mod_nistp192_sqr(A.x);
	t1 = bn_mod_nistp192_mul(t1, A.x);
	t2 = bn_mod_nistp192_mul(A.x, secp192r1_a);
	t1 = bn_mod_nistp192_add(t1, t2);
	t1 = bn_mod_nistp192_add(t1, secp192r1_b);
	return bn_cmp(t0, t1) == 0;
}

function secp192r1_double(A) {
	var x1 = A.x, y1 = A.y, z1 = A.z;
	var t1, t2, t3;
	var x3, y3, z3;
	t1 = bn_mod_nistp192_sqr(z1);
	t2 = bn_mod_nistp192_sub(x1, t1);
	t1 = bn_mod_nistp192_add(x1, t1);
	t2 = bn_mod_nistp192_mul(t2, t1);
	t2 = bn_mod_nistp192_add(bn_mod_nistp192_add(t2, t2), t2);
	y3 = bn_mod_nistp192_add(y1, y1);
	z3 = bn_mod_nistp192_mul(y3, z1);
	y3 = bn_mod_nistp192_sqr(y3);
	t3 = bn_mod_nistp192_mul(y3, x1);
	y3 = bn_mod_nistp192_sqr(y3);
	y3 = bn_mod_nistp192_div2(y3);
	x3 = bn_mod_nistp192_sqr(t2);
	t1 = bn_mod_nistp192_add(t3, t3);
	x3 = bn_mod_nistp192_sub(x3, t1);
	t1 = bn_mod_nistp192_sub(t3, x3);
	t1 = bn_mod_nistp192_mul(t1, t2);
	y3 = bn_mod_nistp192_sub(t1, y3);
	return new ecpoint(x3, y3, z3);
}

function secp192r1_add_affine(A, x2, y2) {
	if (A.is_infinity == true)
		return new ecpoint(x2, y2, bn_one.slice(0, 13));
	var x1 = A.x, y1 = A.y, z1 = A.z;
	var t1, t2, t3, t4;
	var x3, y3, z3;
	
	t1 = bn_mod_nistp192_sqr(z1);
	t2 = bn_mod_nistp192_mul(t1, z1);
	t1 = bn_mod_nistp192_mul(t1, x2);
	t2 = bn_mod_nistp192_mul(t2, y2);
	t1 = bn_mod_nistp192_sub(t1, x1);
	t2 = bn_mod_nistp192_sub(t2, y1);
	if (bn_is_zero(t1)) {
		return bn_is_zero(t2) ? 
			secp192r1_double(new ecpoint(x2, y2, bn_one.slice(0, 13))) : 
			new ecpoint();
	}
	z3 = bn_mod_nistp192_mul(z1, t1);
	t3 = bn_mod_nistp192_sqr(t1);
	t4 = bn_mod_nistp192_mul(t3, t1);
	t3 = bn_mod_nistp192_mul(t3, x1);
	t1 = bn_mod_nistp192_add(t3, t3);
	x3 = bn_mod_nistp192_sqr(t2);
	x3 = bn_mod_nistp192_sub(x3, t1);
	x3 = bn_mod_nistp192_sub(x3, t4);
	t3 = bn_mod_nistp192_sub(t3, x3);
	t3 = bn_mod_nistp192_mul(t3, t2);
	t4 = bn_mod_nistp192_mul(t4, y1);
	y3 = bn_mod_nistp192_sub(t3, t4);
	return new ecpoint(x3, y3, z3);
}

function secp192r1_mul(k, P) {
	var bits = bn_to_bits(k);
	var R = ecpoint_new();
	var Q = ecpoint_dup(P);
	for (var i = bits.length - 1; i >= 0; i--) {
		if (bits[i] == 1) {
			R = secp192r1_add_affine(R, Q.x, Q.y);
		}
		Q = secp192r1_double(Q);
		secp192r1_to_affine(Q);
	}
	return R;
}

function secp192r1_mul_G(k) {
	var R = new ecpoint();
	var bits = bn_to_le_bits(k);
	for (var i = 0; i < 192; i++) {
		if (bits[i] == '1') {
			R = secp192r1_add_affine(R, 
			bn_from_hex(secp192r1_kG[i].slice(0, 48)), 
			bn_from_hex(secp192r1_kG[i].slice(48,96)));
		}
	}
	return R;
}



function secp192r1_ecdsa_pre_compute() {
	var k, Q;
	do {
		do {
			k = bn_pseudo_rand(secp192r1_n);
		} while (bn_is_zero(k));
		
		Q = secp192r1_mul_G(k);
		secp192r1_to_affine(Q);		
		while (bn_cmp(Q.x, n) >= 0) {
			Q.x = bn_sub(Q.x, n);
		}
		
	} while (bn_is_zero(Q.x));
	
	return {"k_1": bn_mod_invert(k, secp192r1_n), "r":Q.x};
}

function secp192r1_ecdsa_sign(digest, pri_key, k_1, r) {

	if (k_1 == null || r == null) {
		var pc = secp192r1_ecdsa_pre_compute();
		k_1 = pc.k_1;
		r = pc.r;
	}
	
	var d = pri_key;
	var n = secp192r1.n;
	var e = bn_from_bytes(digest);
	
	var s;
	s = bn_div(bn_mul(d, r), secp192r1_n)[1];
	s = bn_mod_add(e, s, secp192r1_n);
	s = bn_div(bn_mul(k_1, s), secp192r1_n)[1];

	return {"r":r, "s":s};
}

function secp192r1_ecdsa_verify(digest, sig, pub_key) {
	var r = sig.r;
	var s = sig.s;

	var e = bn_from_bytes(digest);
	
	w = bn_mod_invert(s, n);
	u = bn_mod_barrett_mul(e, w, secp192r1.barrett);
	v = bn_mod_barrett_mul(r, w, secp192r1.barrett);
	Q = secp192r1_mul_add(u, G, v, P);
	
	
	x = secp192r1_get_affine_x(Q);
	while (bn_cmp(x, secp192r1.n) >= 0) {
		x = bn_sub(x, n);
	}
	
	return (bn_cmp(x, r) == 0);
}


/*
 * the secp192r1_kG is generated by the C program with openssl
 *

#include <openssl/ec.h>
#include <openssl/objects.h>
#include <stdio.h>

int main()
{
	int i = 0;
	BN_CTX *bn_ctx = BN_CTX_new();
	const EC_GROUP *ec_group = EC_GROUP_new_by_curve_name(NID_X9_62_prime192v1);
	EC_POINT *Q = EC_POINT_dup(EC_GROUP_get0_generator(ec_group), ec_group);	
	do {
		printf("\"%s\",\n", EC_POINT_point2hex(ec_group, Q, 4, bn_ctx) + 2);
		EC_POINT_dbl(ec_group, Q, Q, bn_ctx);
	} while (i++ < 191);	
	return 0;
}


 */
var secp192r1_kG = [
"188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF101207192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
"DAFEBF5828783F2AD35534631588A3F629A70FB16982A888DD6BDA0D993DA0FA46B27BBC141B868F59331AFA5C7E93AB",
"35433907297CC378B0015703374729D7A4FE46647084E4BAA2649984F2135C301EA3ACB0776CD4F125389B311DB3BE32",
"2FA1F92D1ECCE92014771993CC14899D4B5977883397EDDEA338AFDEF78B7214273B8B5978EF733FF2DD8A8E9738F6C0",
"B7310B4548FBFDBD29005092A5355BFCD99473733048AFDFFF9EAE9EDCD27C1E42D8585C4546D9491845C56629CF2290",
"C5A5972D9C055918B48023EA50E5AD979FB98448420880A26038FB784A780F5396CE0EDB96CFA1B8B320F86384188C55",
"E73B3792BFC59E8D09827DE8BA1B61AEB4A39F7EB97FA4345CCC1DF588A0F8F9F28B2B5DD7EFB0D8EC1A76CFAE20FB95",
"ACED16C30FE2DCCCF8BFF138D87CF00BEFC377F2A3F770D0C07FDF90AB9BE9881CA4CCCB42DB1EED9CBB7122CAFF09F1",
"9FF5229D3B61EDD21FA5302B22355286D812EFFF0DCB2EAAA8A8B331E844B4D16E8BD096D13B7B8CFFDFCCFC026164F6",
"319B54BF674E0C57538BCCB5DF6E8F6250AD0F1B5C04B276F73E1F13CDD6912FD41A42CBDB2DA3617EAD6781DCC394AA",
"BA24EE6052819109A387348D114B0DA9514623145C9AE29F08ED5F359918498A62B4DDAF52E9B2707773081F07DA2E76",
"78C2C6FDDCE72683FA0720ABC68ADE81FF4D11F8668593F1D4A79AE5A49793BE918897B80AA3638D9E24421C55FA0969",
"EE355E9C6A392603FAD7710DE187C91AF1C803E9CE1D0DB64F71B1C6A0299F7B862F7135E93FBF85B1FA412321D2CFDA",
"65A227C5877B02F953A0A39F19492F60AD8D55491B64893B058B0B001D301D23D9AB8FDAA5B536AF4397BE70EA781017",
"40F41C5E37E3224418C5CB3E06550ACF363EF54571892F0228A8B5ECDFC45AB939A312BE903C0D84E6293B415E45FA71",
"814CD305431A62FC95646970F0626EEFD8B2D9D915B0F1AFEF22EFAEBC94691D665781A6D16CFF052EFD43F88B35DB84",
"7D23ED578C0B10CD2CBA22F71FA93AE2A6AC7B9F131406AD8B8311DCBCA5DF183E989364EC8BEC0D262A3B0BF2525D64",
"D1B67325E76E186452EDAC84E9C519BC0613B9A38C69CBDFE86D14F4521628545986DD64B5858DD8B479163E1910EA26",
"52FBE4131E101D514E02A647C694B9035F40C00030FEDD08A70DAE1C4D387E8A5676AF1FCEF6D4D95D36CBD0511BE925",
"B6BB074BE06F99D0EDB2763A3DE9664355AA9AE07E8D5397E57A7163FB166944E3E8FCF9393C60CA8457C376CC7FED97",
"C7580802AFFEE06347789236A3E36A89BF6CD8B820AC893B1B14A0068C3173751BF320F4A122527AEFAF2D9EC1857578",
"5F1817849F76834719354E483D80FF0DF57DEF4C24451FED69E265E2B49DEA91B7F05DEA343993FF09EE782A27397C84",
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"FC8EF8111F98AA0341CD1CE38E53C43067DC3DE8CF6862EBFAFCA79A7444F9A7DBDCD7CB296152AB0805C9104EAFBE3E",
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"1920A4DF0F402C03C1807F71063C12ED6759D191FA3B41F037DF506AB873ECF6A3FB9E2EDA869C53F9F7D2EC1F571F2D",
"CC99E6476BE141969FC1C1D997FD281AB947A1BB2C8F0B4F3977AA4ED0CDB89343E69772FB53086F665B2AE4F335D7AA",
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"33EA57CB2E84057AF83515D5B4684B3B6CA2E20D9F0F4410A15D3A0ACB0BF7C50DB72C53FCB2FD66F558C87AA5276F35",
"ED68FC779960F89F7967D3B9914191D3CE0F39EA9F29990E0187AEEB483501671BF6794E51ECF20B5A8512BC278A8105",
"205759C95E280A9ED7B36007627CAD09027AB959CD36A12BC5C1C42DAAE3D4502E82D1CAE95D96061F442BDD44FDDC5A",
"67E30CBDCBA671FBEB2CDFAE5A927C35C39649C55D7C48D8A93549C45810F5C3CE32D03C063015777A83CEE1ECBFBE7D",
"2B6CACB0C600C45CB37D3FCE1C31929AF7451A7257B5F01DE065AFCC4DF109DD294C91BF1450564308242B4547A577B6",
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"4F2581091D7378AF11558B5B213A102B53840CC8231935EC52387E2DBA59071B0B6510F50AC140DEAE017AB8A8BF3B75",
"73CADCA6BE975F8A92E85F81953A4C5B74930470A386A9C608D99BCAC671B9879CEF856C2320739D008240A9EEC70948",
"DB4DAF19FA965E21B0CEF52038DB569517E4CEE4013010DA7EC9D95463FF3934257F4493160D03D30489BA87EE625F7E",
"898EF4A1756502023646BAFE2009C502EF7F1B6BBB3629964A0A158BA74C525465794634B0B7EF6AFC888B99945F30A1",
"0AA38ED480AA3074B916B12E26AA0B60760805CDD0920EC8BDA447FAB8213C1417A778FCA094EA2FA8B49AC2C68B7610",
"BD12EBD12AE54D508BEE2C1D00914A56E9A045F1B2B87BE3AC2BD78D9E7D57B3ECC58FAFE7CE8F40B283A79315349181",
"E49AA20224FD6B114FFE7680D5B5C0CC6EBD7E46F5566C979F28C9EECEE9D5694F904E197E9C550007BBB826C1A909DA",
"E7897F12B5AD4207E9ACCF64590267C84516CAE42D7E182768B64D8B9BA0DF2B7C5D3FCBD7F7C0111EF20C93BE19E9D6",
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"F4110D1D500DCC19D5416D4BAE78CFA169C05C3AC5E3F5593AAAA4F1165ACAB1C75E9CA73F6038C433B45ADCE0710102",
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