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strict';\n\nvar curve = exports;\n\ncurve.base = require('./base');\ncurve.short = require('./short');\ncurve.mont = require('./mont');\ncurve.edwards = require('./edwards');\n","'use strict';\n\nvar hash = require('hash.js');\nvar curves = require('../curves');\nvar utils = require('../utils');\nvar assert = utils.assert;\nvar parseBytes = utils.parseBytes;\nvar KeyPair = require('./key');\nvar Signature = require('./signature');\n\nfunction EDDSA(curve) {\n assert(curve === 'ed25519', 'only tested with ed25519 so far');\n\n if (!(this instanceof EDDSA))\n return new EDDSA(curve);\n\n curve = curves[curve].curve;\n this.curve = curve;\n this.g = curve.g;\n this.g.precompute(curve.n.bitLength() + 1);\n\n this.pointClass = curve.point().constructor;\n this.encodingLength = Math.ceil(curve.n.bitLength() / 8);\n this.hash = hash.sha512;\n}\n\nmodule.exports = EDDSA;\n\n/**\n* @param {Array|String} message - message bytes\n* @param {Array|String|KeyPair} secret - secret bytes or a keypair\n* @returns {Signature} - signature\n*/\nEDDSA.prototype.sign = function sign(message, secret) {\n message = parseBytes(message);\n var key = this.keyFromSecret(secret);\n var r = this.hashInt(key.messagePrefix(), message);\n var R = this.g.mul(r);\n var Rencoded = this.encodePoint(R);\n var s_ = this.hashInt(Rencoded, key.pubBytes(), message)\n .mul(key.priv());\n var S = r.add(s_).umod(this.curve.n);\n return this.makeSignature({ R: R, S: S, Rencoded: Rencoded });\n};\n\n/**\n* @param {Array} message - message bytes\n* @param {Array|String|Signature} sig - sig bytes\n* @param {Array|String|Point|KeyPair} pub - public key\n* @returns {Boolean} - true if public key matches sig of message\n*/\nEDDSA.prototype.verify = function verify(message, sig, pub) {\n message = parseBytes(message);\n sig = this.makeSignature(sig);\n var key = this.keyFromPublic(pub);\n var h = this.hashInt(sig.Rencoded(), key.pubBytes(), message);\n var SG = this.g.mul(sig.S());\n var RplusAh = sig.R().add(key.pub().mul(h));\n return RplusAh.eq(SG);\n};\n\nEDDSA.prototype.hashInt = function hashInt() {\n var hash = this.hash();\n for (var i = 0; i < arguments.length; i++)\n hash.update(arguments[i]);\n return utils.intFromLE(hash.digest()).umod(this.curve.n);\n};\n\nEDDSA.prototype.keyFromPublic = function keyFromPublic(pub) {\n return KeyPair.fromPublic(this, pub);\n};\n\nEDDSA.prototype.keyFromSecret = function keyFromSecret(secret) {\n return KeyPair.fromSecret(this, secret);\n};\n\nEDDSA.prototype.makeSignature = function makeSignature(sig) {\n if (sig instanceof Signature)\n return sig;\n return new Signature(this, sig);\n};\n\n/**\n* * https://tools.ietf.org/html/draft-josefsson-eddsa-ed25519-03#section-5.2\n*\n* EDDSA defines methods for encoding and decoding points and integers. These are\n* helper convenience methods, that pass along to utility functions implied\n* parameters.\n*\n*/\nEDDSA.prototype.encodePoint = function encodePoint(point) {\n var enc = point.getY().toArray('le', this.encodingLength);\n enc[this.encodingLength - 1] |= point.getX().isOdd() ? 0x80 : 0;\n return enc;\n};\n\nEDDSA.prototype.decodePoint = function decodePoint(bytes) {\n bytes = utils.parseBytes(bytes);\n\n var lastIx = bytes.length - 1;\n var normed = bytes.slice(0, lastIx).concat(bytes[lastIx] & ~0x80);\n var xIsOdd = (bytes[lastIx] & 0x80) !== 0;\n\n var y = utils.intFromLE(normed);\n return this.curve.pointFromY(y, xIsOdd);\n};\n\nEDDSA.prototype.encodeInt = function encodeInt(num) {\n return num.toArray('le', this.encodingLength);\n};\n\nEDDSA.prototype.decodeInt = function decodeInt(bytes) {\n return utils.intFromLE(bytes);\n};\n\nEDDSA.prototype.isPoint = function isPoint(val) {\n return val instanceof this.pointClass;\n};\n","'use strict';\n\nvar BN = require('bn.js');\n\nvar utils = require('../utils');\nvar assert = utils.assert;\n\nfunction Signature(options, enc) {\n if (options instanceof Signature)\n return options;\n\n if (this._importDER(options, enc))\n return;\n\n assert(options.r && options.s, 'Signature without r or s');\n this.r = new BN(options.r, 16);\n this.s = new BN(options.s, 16);\n if (options.recoveryParam === undefined)\n this.recoveryParam = null;\n else\n this.recoveryParam = options.recoveryParam;\n}\nmodule.exports = Signature;\n\nfunction Position() {\n this.place = 0;\n}\n\nfunction getLength(buf, p) {\n var initial = buf[p.place++];\n if (!(initial & 0x80)) {\n return initial;\n }\n var octetLen = initial & 0xf;\n\n // Indefinite length or overflow\n if (octetLen === 0 || octetLen > 4) {\n return false;\n }\n\n var val = 0;\n for (var i = 0, off = p.place; i < octetLen; i++, off++) {\n val <<= 8;\n val |= buf[off];\n val >>>= 0;\n }\n\n // Leading zeroes\n if (val <= 0x7f) {\n return false;\n }\n\n p.place = off;\n return val;\n}\n\nfunction rmPadding(buf) {\n var i = 0;\n var len = buf.length - 1;\n while (!buf[i] && !(buf[i + 1] & 0x80) && i < len) {\n i++;\n }\n if (i === 0) {\n return buf;\n }\n return buf.slice(i);\n}\n\nSignature.prototype._importDER = function _importDER(data, enc) {\n data = utils.toArray(data, enc);\n var p = new Position();\n if (data[p.place++] !== 0x30) {\n return false;\n }\n var len = getLength(data, p);\n if (len === false) {\n return false;\n }\n if ((len + p.place) !== data.length) {\n return false;\n }\n if (data[p.place++] !== 0x02) {\n return false;\n }\n var rlen = getLength(data, p);\n if (rlen === false) {\n return false;\n }\n var r = data.slice(p.place, rlen + p.place);\n p.place += rlen;\n if (data[p.place++] !== 0x02) {\n return false;\n }\n var slen = getLength(data, p);\n if (slen === false) {\n return false;\n }\n if (data.length !== slen + p.place) {\n return false;\n }\n var s = data.slice(p.place, slen + p.place);\n if (r[0] === 0) {\n if (r[1] & 0x80) {\n r = r.slice(1);\n } else {\n // Leading zeroes\n return false;\n }\n }\n if (s[0] === 0) {\n if (s[1] & 0x80) {\n s = s.slice(1);\n } else {\n // Leading zeroes\n return false;\n }\n }\n\n this.r = new BN(r);\n this.s = new BN(s);\n this.recoveryParam = null;\n\n return true;\n};\n\nfunction constructLength(arr, len) {\n if (len < 0x80) {\n arr.push(len);\n return;\n }\n var octets = 1 + (Math.log(len) / Math.LN2 >>> 3);\n arr.push(octets | 0x80);\n while (--octets) {\n arr.push((len >>> (octets << 3)) & 0xff);\n }\n arr.push(len);\n}\n\nSignature.prototype.toDER = function toDER(enc) {\n var r = this.r.toArray();\n var s = this.s.toArray();\n\n // Pad values\n if (r[0] & 0x80)\n r = [ 0 ].concat(r);\n // Pad values\n if (s[0] & 0x80)\n s = [ 0 ].concat(s);\n\n r = rmPadding(r);\n s = rmPadding(s);\n\n while (!s[0] && !(s[1] & 0x80)) {\n s = s.slice(1);\n }\n var arr = [ 0x02 ];\n constructLength(arr, r.length);\n arr = arr.concat(r);\n arr.push(0x02);\n constructLength(arr, s.length);\n var backHalf = arr.concat(s);\n var res = [ 0x30 ];\n constructLength(res, backHalf.length);\n res = res.concat(backHalf);\n return utils.encode(res, enc);\n};\n","'use strict';\n\nvar BN = require('bn.js');\nvar inherits = require('inherits');\nvar Base = require('./base');\n\nvar utils = require('../utils');\n\nfunction MontCurve(conf) {\n Base.call(this, 'mont', conf);\n\n this.a = new BN(conf.a, 16).toRed(this.red);\n this.b = new BN(conf.b, 16).toRed(this.red);\n this.i4 = new BN(4).toRed(this.red).redInvm();\n this.two = new BN(2).toRed(this.red);\n this.a24 = this.i4.redMul(this.a.redAdd(this.two));\n}\ninherits(MontCurve, Base);\nmodule.exports = MontCurve;\n\nMontCurve.prototype.validate = function validate(point) {\n var x = point.normalize().x;\n var x2 = x.redSqr();\n var rhs = x2.redMul(x).redAdd(x2.redMul(this.a)).redAdd(x);\n var y = rhs.redSqrt();\n\n return y.redSqr().cmp(rhs) === 0;\n};\n\nfunction Point(curve, x, z) {\n Base.BasePoint.call(this, curve, 'projective');\n if (x === null && z === null) {\n this.x = this.curve.one;\n this.z = this.curve.zero;\n } else {\n this.x = new BN(x, 16);\n this.z = new BN(z, 16);\n if (!this.x.red)\n this.x = this.x.toRed(this.curve.red);\n if (!this.z.red)\n this.z = this.z.toRed(this.curve.red);\n }\n}\ninherits(Point, Base.BasePoint);\n\nMontCurve.prototype.decodePoint = function decodePoint(bytes, enc) {\n return this.point(utils.toArray(bytes, enc), 1);\n};\n\nMontCurve.prototype.point = function point(x, z) {\n return new Point(this, x, z);\n};\n\nMontCurve.prototype.pointFromJSON = function pointFromJSON(obj) {\n return Point.fromJSON(this, obj);\n};\n\nPoint.prototype.precompute = function precompute() {\n // No-op\n};\n\nPoint.prototype._encode = function _encode() {\n return this.getX().toArray('be', this.curve.p.byteLength());\n};\n\nPoint.fromJSON = function fromJSON(curve, obj) {\n return new Point(curve, obj[0], obj[1] || curve.one);\n};\n\nPoint.prototype.inspect = function inspect() {\n if (this.isInfinity())\n return '<EC Point Infinity>';\n return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +\n ' z: ' + this.z.fromRed().toString(16, 2) + '>';\n};\n\nPoint.prototype.isInfinity = function isInfinity() {\n // XXX This code assumes that zero is always zero in red\n return this.z.cmpn(0) === 0;\n};\n\nPoint.prototype.dbl = function dbl() {\n // http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#doubling-dbl-1987-m-3\n // 2M + 2S + 4A\n\n // A = X1 + Z1\n var a = this.x.redAdd(this.z);\n // AA = A^2\n var aa = a.redSqr();\n // B = X1 - Z1\n var b = this.x.redSub(this.z);\n // BB = B^2\n var bb = b.redSqr();\n // C = AA - BB\n var c = aa.redSub(bb);\n // X3 = AA * BB\n var nx = aa.redMul(bb);\n // Z3 = C * (BB + A24 * C)\n var nz = c.redMul(bb.redAdd(this.curve.a24.redMul(c)));\n return this.curve.point(nx, nz);\n};\n\nPoint.prototype.add = function add() {\n throw new Error('Not supported on Montgomery curve');\n};\n\nPoint.prototype.diffAdd = function diffAdd(p, diff) {\n // http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#diffadd-dadd-1987-m-3\n // 4M + 2S + 6A\n\n // A = X2 + Z2\n var a = this.x.redAdd(this.z);\n // B = X2 - Z2\n var b = this.x.redSub(this.z);\n // C = X3 + Z3\n var c = p.x.redAdd(p.z);\n // D = X3 - Z3\n var d = p.x.redSub(p.z);\n // DA = D * A\n var da = d.redMul(a);\n // CB = C * B\n var cb = c.redMul(b);\n // X5 = Z1 * (DA + CB)^2\n var nx = diff.z.redMul(da.redAdd(cb).redSqr());\n // Z5 = X1 * (DA - CB)^2\n var nz = diff.x.redMul(da.redISub(cb).redSqr());\n return this.curve.point(nx, nz);\n};\n\nPoint.prototype.mul = function mul(k) {\n var t = k.clone();\n var a = this; // (N / 2) * Q + Q\n var b = this.curve.point(null, null); // (N / 2) * Q\n var c = this; // Q\n\n for (var bits = []; t.cmpn(0) !== 0; t.iushrn(1))\n bits.push(t.andln(1));\n\n for (var i = bits.length - 1; i >= 0; i--) {\n if (bits[i] === 0) {\n // N * Q + Q = ((N / 2) * Q + Q)) + (N / 2) * Q\n a = a.diffAdd(b, c);\n // N * Q = 2 * ((N / 2) * Q + Q))\n b = b.dbl();\n } else {\n // N * Q = ((N / 2) * Q + Q) + ((N / 2) * Q)\n b = a.diffAdd(b, c);\n // N * Q + Q = 2 * ((N / 2) * Q + Q)\n a = a.dbl();\n }\n }\n return b;\n};\n\nPoint.prototype.mulAdd = function mulAdd() {\n throw new Error('Not supported on Montgomery curve');\n};\n\nPoint.prototype.jumlAdd = function jumlAdd() {\n throw new Error('Not supported on Montgomery curve');\n};\n\nPoint.prototype.eq = function eq(other) {\n return this.getX().cmp(other.getX()) === 0;\n};\n\nPoint.prototype.normalize = function normalize() {\n this.x = this.x.redMul(this.z.redInvm());\n this.z = this.curve.one;\n return this;\n};\n\nPoint.prototype.getX = function getX() {\n // Normalize coordinates\n this.normalize();\n\n return this.x.fromRed();\n};\n","'use strict';\n\nvar utils = require('../utils');\nvar BN = require('bn.js');\nvar inherits = require('inherits');\nvar Base = require('./base');\n\nvar assert = utils.assert;\n\nfunction EdwardsCurve(conf) {\n // NOTE: Important as we are creating point in Base.call()\n this.twisted = (conf.a | 0) !== 1;\n this.mOneA = this.twisted && (conf.a | 0) === -1;\n this.extended = this.mOneA;\n\n Base.call(this, 'edwards', conf);\n\n this.a = new BN(conf.a, 16).umod(this.red.m);\n this.a = this.a.toRed(this.red);\n this.c = new BN(conf.c, 16).toRed(this.red);\n this.c2 = this.c.redSqr();\n this.d = new BN(conf.d, 16).toRed(this.red);\n this.dd = this.d.redAdd(this.d);\n\n assert(!this.twisted || this.c.fromRed().cmpn(1) === 0);\n this.oneC = (conf.c | 0) === 1;\n}\ninherits(EdwardsCurve, Base);\nmodule.exports = EdwardsCurve;\n\nEdwardsCurve.prototype._mulA = function _mulA(num) {\n if (this.mOneA)\n return num.redNeg();\n else\n return this.a.redMul(num);\n};\n\nEdwardsCurve.prototype._mulC = function _mulC(num) {\n if (this.oneC)\n return num;\n else\n return this.c.redMul(num);\n};\n\n// Just for compatibility with Short curve\nEdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {\n return this.point(x, y, z, t);\n};\n\nEdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {\n x = new BN(x, 16);\n if (!x.red)\n x = x.toRed(this.red);\n\n var x2 = x.redSqr();\n var rhs = this.c2.redSub(this.a.redMul(x2));\n var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));\n\n var y2 = rhs.redMul(lhs.redInvm());\n var y = y2.redSqrt();\n if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)\n throw new Error('invalid point');\n\n var isOdd = y.fromRed().isOdd();\n if (odd && !isOdd || !odd && isOdd)\n y = y.redNeg();\n\n return this.point(x, y);\n};\n\nEdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {\n y = new BN(y, 16);\n if (!y.red)\n y = y.toRed(this.red);\n\n // x^2 = (y^2 - c^2) / (c^2 d y^2 - a)\n var y2 = y.redSqr();\n var lhs = y2.redSub(this.c2);\n var rhs = y2.redMul(this.d).redMul(this.c2).redSub(this.a);\n var x2 = lhs.redMul(rhs.redInvm());\n\n if (x2.cmp(this.zero) === 0) {\n if (odd)\n throw new Error('invalid point');\n else\n return this.point(this.zero, y);\n }\n\n var x = x2.redSqrt();\n if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)\n throw new Error('invalid point');\n\n if (x.fromRed().isOdd() !== odd)\n x = x.redNeg();\n\n return this.point(x, y);\n};\n\nEdwardsCurve.prototype.validate = function validate(point) {\n if (point.isInfinity())\n return true;\n\n // Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)\n point.normalize();\n\n var x2 = point.x.redSqr();\n var y2 = point.y.redSqr();\n var lhs = x2.redMul(this.a).redAdd(y2);\n var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));\n\n return lhs.cmp(rhs) === 0;\n};\n\nfunction Point(curve, x, y, z, t) {\n Base.BasePoint.call(this, curve, 'projective');\n if (x === null && y === null && z === null) {\n this.x = this.curve.zero;\n this.y = this.curve.one;\n this.z = this.curve.one;\n this.t = this.curve.zero;\n this.zOne = true;\n } else {\n this.x = new BN(x, 16);\n this.y = new BN(y, 16);\n this.z = z ? new BN(z, 16) : this.curve.one;\n this.t = t && new BN(t, 16);\n if (!this.x.red)\n this.x = this.x.toRed(this.curve.red);\n if (!this.y.red)\n this.y = this.y.toRed(this.curve.red);\n if (!this.z.red)\n this.z = this.z.toRed(this.curve.red);\n if (this.t && !this.t.red)\n this.t = this.t.toRed(this.curve.red);\n this.zOne = this.z === this.curve.one;\n\n // Use extended coordinates\n if (this.curve.extended && !this.t) {\n this.t = this.x.redMul(this.y);\n if (!this.zOne)\n this.t = this.t.redMul(this.z.redInvm());\n }\n }\n}\ninherits(Point, Base.BasePoint);\n\nEdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {\n return Point.fromJSON(this, obj);\n};\n\nEdwardsCurve.prototype.point = function point(x, y, z, t) {\n return new Point(this, x, y, z, t);\n};\n\nPoint.fromJSON = function fromJSON(curve, obj) {\n return new Point(curve, obj[0], obj[1], obj[2]);\n};\n\nPoint.prototype.inspect = function inspect() {\n if (this.isInfinity())\n return '<EC Point Infinity>';\n return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +\n ' y: ' + this.y.fromRed().toString(16, 2) +\n ' z: ' + this.z.fromRed().toString(16, 2) + '>';\n};\n\nPoint.prototype.isInfinity = function isInfinity() {\n // XXX This code assumes that zero is always zero in red\n return this.x.cmpn(0) === 0 &&\n (this.y.cmp(this.z) === 0 ||\n (this.zOne && this.y.cmp(this.curve.c) === 0));\n};\n\nPoint.prototype._extDbl = function _extDbl() {\n // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html\n // #doubling-dbl-2008-hwcd\n // 4M + 4S\n\n // A = X1^2\n var a = this.x.redSqr();\n // B = Y1^2\n var b = this.y.redSqr();\n // C = 2 * Z1^2\n var c = this.z.redSqr();\n c = c.redIAdd(c);\n // D = a * A\n var d = this.curve._mulA(a);\n // E = (X1 + Y1)^2 - A - B\n var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);\n // G = D + B\n var g = d.redAdd(b);\n // F = G - C\n var f = g.redSub(c);\n // H = D - B\n var h = d.redSub(b);\n // X3 = E * F\n var nx = e.redMul(f);\n // Y3 = G * H\n var ny = g.redMul(h);\n // T3 = E * H\n var nt = e.redMul(h);\n // Z3 = F * G\n var nz = f.redMul(g);\n return this.curve.point(nx, ny, nz, nt);\n};\n\nPoint.prototype._projDbl = function _projDbl() {\n // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html\n // #doubling-dbl-2008-bbjlp\n // #doubling-dbl-2007-bl\n // and others\n // Generally 3M + 4S or 2M + 4S\n\n // B = (X1 + Y1)^2\n var b = this.x.redAdd(this.y).redSqr();\n // C = X1^2\n var c = this.x.redSqr();\n // D = Y1^2\n var d = this.y.redSqr();\n\n var nx;\n var ny;\n var nz;\n var e;\n var h;\n var j;\n if (this.curve.twisted) {\n // E = a * C\n e = this.curve._mulA(c);\n // F = E + D\n var f = e.redAdd(d);\n if (this.zOne) {\n // X3 = (B - C - D) * (F - 2)\n nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));\n // Y3 = F * (E - D)\n ny = f.redMul(e.redSub(d));\n // Z3 = F^2 - 2 * F\n nz = f.redSqr().redSub(f).redSub(f);\n } else {\n // H = Z1^2\n h = this.z.redSqr();\n // J = F - 2 * H\n j = f.redSub(h).redISub(h);\n // X3 = (B-C-D)*J\n nx = b.redSub(c).redISub(d).redMul(j);\n // Y3 = F * (E - D)\n ny = f.redMul(e.redSub(d));\n // Z3 = F * J\n nz = f.redMul(j);\n }\n } else {\n // E = C + D\n e = c.redAdd(d);\n // H = (c * Z1)^2\n h = this.curve._mulC(this.z).redSqr();\n // J = E - 2 * H\n j = e.redSub(h).redSub(h);\n // X3 = c * (B - E) * J\n nx = this.curve._mulC(b.redISub(e)).redMul(j);\n // Y3 = c * E * (C - D)\n ny = this.curve._mulC(e).redMul(c.redISub(d));\n // Z3 = E * J\n nz = e.redMul(j);\n }\n return this.curve.point(nx, ny, nz);\n};\n\nPoint.prototype.dbl = function dbl() {\n if (this.isInfinity())\n return this;\n\n // Double in extended coordinates\n if (this.curve.extended)\n return this._extDbl();\n else\n return this._projDbl();\n};\n\nPoint.prototype._extAdd = function _extAdd(p) {\n // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html\n // #addition-add-2008-hwcd-3\n // 8M\n\n // A = (Y1 - X1) * (Y2 - X2)\n var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));\n // B = (Y1 + X1) * (Y2 + X2)\n var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));\n // C = T1 * k * T2\n var c = this.t.redMul(this.curve.dd).redMul(p.t);\n // D = Z1 * 2 * Z2\n var d = this.z.redMul(p.z.redAdd(p.z));\n // E = B - A\n var e = b.redSub(a);\n // F = D - C\n var f = d.redSub(c);\n // G = D + C\n var g = d.redAdd(c);\n // H = B + A\n var h = b.redAdd(a);\n // X3 = E * F\n var nx = e.redMul(f);\n // Y3 = G * H\n var ny = g.redMul(h);\n // T3 = E * H\n var nt = e.redMul(h);\n // Z3 = F * G\n var nz = f.redMul(g);\n return this.curve.point(nx, ny, nz, nt);\n};\n\nPoint.prototype._projAdd = function _projAdd(p) {\n // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html\n // #addition-add-2008-bbjlp\n // #addition-add-2007-bl\n // 10M + 1S\n\n // A = Z1 * Z2\n var a = this.z.redMul(p.z);\n // B = A^2\n var b = a.redSqr();\n // C = X1 * X2\n var c = this.x.redMul(p.x);\n // D = Y1 * Y2\n var d = this.y.redMul(p.y);\n // E = d * C * D\n var e = this.curve.d.redMul(c).redMul(d);\n // F = B - E\n var f = b.redSub(e);\n // G = B + E\n var g = b.redAdd(e);\n // X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)\n var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);\n var nx = a.redMul(f).redMul(tmp);\n var ny;\n var nz;\n if (this.curve.twisted) {\n // Y3 = A * G * (D - a * C)\n ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));\n // Z3 = F * G\n nz = f.redMul(g);\n } else {\n // Y3 = A * G * (D - C)\n ny = a.redMul(g).redMul(d.redSub(c));\n // Z3 = c * F * G\n nz = this.curve._mulC(f).redMul(g);\n }\n return this.curve.point(nx, ny, nz);\n};\n\nPoint.prototype.add = function add(p) {\n if (this.isInfinity())\n return p;\n if (p.isInfinity())\n return this;\n\n if (this.curve.extended)\n return this._extAdd(p);\n else\n return this._projAdd(p);\n};\n\nPoint.prototype.mul = function mul(k) {\n if (this._hasDoubles(k))\n return this.curve._fixedNafMul(this, k);\n else\n return this.curve._wnafMul(this, k);\n};\n\nPoint.prototype.mulAdd = function mulAdd(k1, p, k2) {\n return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, false);\n};\n\nPoint.prototype.jmulAdd = function jmulAdd(k1, p, k2) {\n return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, true);\n};\n\nPoint.prototype.normalize = function normalize() {\n if (this.zOne)\n return this;\n\n // Normalize coordinates\n var zi = this.z.redInvm();\n this.x = this.x.redMul(zi);\n this.y = this.y.redMul(zi);\n if (this.t)\n this.t = this.t.redMul(zi);\n this.z = this.curve.one;\n this.zOne = true;\n return this;\n};\n\nPoint.prototype.neg = function neg() {\n return this.curve.point(this.x.redNeg(),\n this.y,\n this.z,\n this.t && this.t.redNeg());\n};\n\nPoint.prototype.getX = function getX() {\n this.normalize();\n return this.x.fromRed();\n};\n\nPoint.prototype.getY = function getY() {\n this.normalize();\n return this.y.fromRed();\n};\n\nPoint.prototype.eq = function eq(other) {\n return this === other ||\n this.getX().cmp(other.getX()) === 0 &&\n this.getY().cmp(other.getY()) === 0;\n};\n\nPoint.prototype.eqXToP = function eqXToP(x) {\n var rx = x.toRed(this.curve.red).redMul(this.z);\n if (this.x.cmp(rx) === 0)\n return true;\n\n var xc = x.clone();\n var t = this.curve.redN.redMul(this.z);\n for (;;) {\n xc.iadd(this.curve.n);\n if (xc.cmp(this.curve.p) >= 0)\n return false;\n\n rx.redIAdd(t);\n if (this.x.cmp(rx) === 0)\n return true;\n }\n};\n\n// Compatibility with BaseCurve\nPoint.prototype.toP = Point.prototype.normalize;\nPoint.prototype.mixedAdd = Point.prototype.add;\n","'use strict';\n\nvar BN = require('bn.js');\nvar utils = require('../utils');\nvar getNAF = utils.getNAF;\nvar getJSF = utils.getJSF;\nvar assert = utils.assert;\n\nfunction BaseCurve(type, conf) {\n this.type = type;\n this.p = new BN(conf.p, 16);\n\n // Use Montgomery, when there is no fast reduction for the prime\n this.red = conf.prime ? BN.red(conf.prime) : BN.mont(this.p);\n\n // Useful for many curves\n this.zero = new BN(0).toRed(this.red);\n this.one = new BN(1).toRed(this.red);\n this.two = new BN(2).toRed(this.red);\n\n // Curve configuration, optional\n this.n = conf.n && new BN(conf.n, 16);\n this.g = conf.g && this.pointFromJSON(conf.g, conf.gRed);\n\n // Temporary arrays\n this._wnafT1 = new Array(4);\n this._wnafT2 = new Array(4);\n this._wnafT3 = new Array(4);\n this._wnafT4 = new Array(4);\n\n this._bitLength = this.n ? this.n.bitLength() : 0;\n\n // Generalized Greg Maxwell's trick\n var adjustCount = this.n && this.p.div(this.n);\n if (!adjustCount || adjustCount.cmpn(100) > 0) {\n this.redN = null;\n } else {\n this._maxwellTrick = true;\n this.redN = this.n.toRed(this.red);\n }\n}\nmodule.exports = BaseCurve;\n\nBaseCurve.prototype.point = function point() {\n throw new Error('Not implemented');\n};\n\nBaseCurve.prototype.validate = function validate() {\n throw new Error('Not implemented');\n};\n\nBaseCurve.prototype._fixedNafMul = function _fixedNafMul(p, k) {\n assert(p.precomputed);\n var doubles = p._getDoubles();\n\n var naf = getNAF(k, 1, this._bitLength);\n var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1);\n I /= 3;\n\n // Translate into more windowed form\n var repr = [];\n var j;\n var nafW;\n for (j = 0; j < naf.length; j += doubles.step) {\n nafW = 0;\n for (var l = j + doubles.step - 1; l >= j; l--)\n nafW = (nafW << 1) + naf[l];\n repr.push(nafW);\n }\n\n var a = this.jpoint(null, null, null);\n var b = this.jpoint(null, null, null);\n for (var i = I; i > 0; i--) {\n for (j = 0; j < repr.length; j++) {\n nafW = repr[j];\n if (nafW === i)\n b = b.mixedAdd(doubles.points[j]);\n else if (nafW === -i)\n b = b.mixedAdd(doubles.points[j].neg());\n }\n a = a.add(b);\n }\n return a.toP();\n};\n\nBaseCurve.prototype._wnafMul = function _wnafMul(p, k) {\n var w = 4;\n\n // Precompute window\n var nafPoints = p._getNAFPoints(w);\n w = nafPoints.wnd;\n var wnd = nafPoints.points;\n\n // Get NAF form\n var naf = getNAF(k, w, this._bitLength);\n\n // Add `this`*(N+1) for every w-NAF index\n var acc = this.jpoint(null, null, null);\n for (var i = naf.length - 1; i >= 0; i--) {\n // Count zeroes\n for (var l = 0; i >= 0 && naf[i] === 0; i--)\n l++;\n if (i >= 0)\n l++;\n acc = acc.dblp(l);\n\n if (i < 0)\n break;\n var z = naf[i];\n assert(z !== 0);\n if (p.type === 'affine') {\n // J +- P\n if (z > 0)\n acc = acc.mixedAdd(wnd[(z - 1) >> 1]);\n else\n acc = acc.mixedAdd(wnd[(-z - 1) >> 1].neg());\n } else {\n // J +- J\n if (z > 0)\n acc = acc.add(wnd[(z - 1) >> 1]);\n else\n acc = acc.add(wnd[(-z - 1) >> 1].neg());\n }\n }\n return p.type === 'affine' ? acc.toP() : acc;\n};\n\nBaseCurve.prototype._wnafMulAdd = function _wnafMulAdd(defW,\n points,\n coeffs,\n len,\n jacobianResult) {\n var wndWidth = this._wnafT1;\n var wnd = this._wnafT2;\n var naf = this._wnafT3;\n\n // Fill all arrays\n var max = 0;\n var i;\n var j;\n var p;\n for (i = 0; i < len; i++) {\n p = points[i];\n var nafPoints = p._getNAFPoints(defW);\n wndWidth[i] = nafPoints.wnd;\n wnd[i] = nafPoints.points;\n }\n\n // Comb small window NAFs\n for (i = len - 1; i >= 1; i -= 2) {\n var a = i - 1;\n var b = i;\n if (wndWidth[a] !== 1 || wndWidth[b] !== 1) {\n naf[a] = getNAF(coeffs[a], wndWidth[a], this._bitLength);\n naf[b] = getNAF(coeffs[b], wndWidth[b], this._bitLength);\n max = Math.max(naf[a].length, max);\n max = Math.max(naf[b].length, max);\n continue;\n }\n\n var comb = [\n points[a], /* 1 */\n null, /* 3 */\n null, /* 5 */\n points[b], /* 7 */\n ];\n\n // Try to avoid Projective points, if possible\n if (points[a].y.cmp(points[b].y) === 0) {\n comb[1] = points[a].add(points[b]);\n comb[2] = points[a].toJ().mixedAdd(points[b].neg());\n } else if (points[a].y.cmp(points[b].y.redNeg()) === 0) {\n comb[1] = points[a].toJ().mixedAdd(points[b]);\n comb[2] = points[a].add(points[b].neg());\n } else {\n comb[1] = points[a].toJ().mixedAdd(points[b]);\n comb[2] = points[a].toJ().mixedAdd(points[b].neg());\n }\n\n var index = [\n -3, /* -1 -1 */\n -1, /* -1 0 */\n -5, /* -1 1 */\n -7, /* 0 -1 */\n 0, /* 0 0 */\n 7, /* 0 1 */\n 5, /* 1 -1 */\n 1, /* 1 0 */\n 3, /* 1 1 */\n ];\n\n var jsf = getJSF(coeffs[a], coeffs[b]);\n max = Math.max(jsf[0].length, max);\n naf[a] = new Array(max);\n naf[b] = new Array(max);\n for (j = 0; j < max; j++) {\n var ja = jsf[0][j] | 0;\n var jb = jsf[1][j] | 0;\n\n naf[a][j] = index[(ja + 1) * 3 + (jb + 1)];\n naf[b][j] = 0;\n wnd[a] = comb;\n }\n }\n\n var acc = this.jpoint(null, null, null);\n var tmp = this._wnafT4;\n for (i = max; i >= 0; i--) {\n var k = 0;\n\n while (i >= 0) {\n var zero = true;\n for (j = 0; j < len; j++) {\n tmp[j] = naf[j][i] | 0;\n if (tmp[j] !== 0)\n zero = false;\n }\n if (!zero)\n break;\n k++;\n i--;\n }\n if (i >= 0)\n k++;\n acc = acc.dblp(k);\n if (i < 0)\n break;\n\n for (j = 0; j < len; j++) {\n var z = tmp[j];\n p;\n if (z === 0)\n continue;\n else if (z > 0)\n p = wnd[j][(z - 1) >> 1];\n else if (z < 0)\n p = wnd[j][(-z - 1) >> 1].neg();\n\n if (p.type === 'affine')\n acc = acc.mixedAdd(p);\n else\n acc = acc.add(p);\n }\n }\n // Zeroify references\n for (i = 0; i < len; i++)\n wnd[i] = null;\n\n if (jacobianResult)\n return acc;\n else\n return acc.toP();\n};\n\nfunction BasePoint(curve, type) {\n this.curve = curve;\n this.type = type;\n this.precomputed = null;\n}\nBaseCurve.BasePoint = BasePoint;\n\nBasePoint.prototype.eq = function eq(/*other*/) {\n throw new Error('Not implemented');\n};\n\nBasePoint.prototype.validate = function validate() {\n return this.curve.validate(this);\n};\n\nBaseCurve.prototype.decodePoint = function decodePoint(bytes, enc) {\n bytes = utils.toArray(bytes, enc);\n\n var len = this.p.byteLength();\n\n // uncompressed, hybrid-odd, hybrid-even\n if ((bytes[0] === 0x04 || bytes[0] === 0x06 || bytes[0] === 0x07) &&\n bytes.length - 1 === 2 * len) {\n if (bytes[0] === 0x06)\n assert(bytes[bytes.length - 1] % 2 === 0);\n else if (bytes[0] === 0x07)\n assert(bytes[bytes.length - 1] % 2 === 1);\n\n var res = this.point(bytes.slice(1, 1 + len),\n bytes.slice(1 + len, 1 + 2 * len));\n\n return res;\n } else if ((bytes[0] === 0x02 || bytes[0] === 0x03) &&\n bytes.length - 1 === len) {\n return this.pointFromX(bytes.slice(1, 1 + len), bytes[0] === 0x03);\n }\n throw new Error('Unknown point format');\n};\n\nBasePoint.prototype.encodeCompressed = function encodeCompressed(enc) {\n return this.encode(enc, true);\n};\n\nBasePoint.prototype._encode = function _encode(compact) {\n var len = this.curve.p.byteLength();\n var x = this.getX().toArray('be', len);\n\n if (compact)\n return [ this.getY().isEven() ? 0x02 : 0x03 ].concat(x);\n\n return [ 0x04 ].concat(x, this.getY().toArray('be', len));\n};\n\nBasePoint.prototype.encode = function encode(enc, compact) {\n return utils.encode(this._encode(compact), enc);\n};\n\nBasePoint.prototype.precompute = function precompute(power) {\n if (this.precomputed)\n return this;\n\n var precomputed = {\n doubles: null,\n naf: null,\n beta: null,\n };\n precomputed.naf = this._getNAFPoints(8);\n precomputed.doubles = this._getDoubles(4, power);\n precomputed.beta = this._getBeta();\n this.precomputed = precomputed;\n\n return this;\n};\n\nBasePoint.prototype._hasDoubles = function _hasDoubles(k) {\n if (!this.precomputed)\n return false;\n\n var doubles = this.precomputed.doubles;\n if (!doubles)\n return false;\n\n return doubles.points.length >= Math.ceil((k.bitLength() + 1) / doubles.step);\n};\n\nBasePoint.prototype._getDoubles = function _getDoubles(step, power) {\n if (this.precomputed && this.precomputed.doubles)\n return this.precomputed.doubles;\n\n var doubles = [ this ];\n var acc = this;\n for (var i = 0; i < power; i += step) {\n for (var j = 0; j < step; j++)\n acc = acc.dbl();\n doubles.push(acc);\n }\n return {\n step: step,\n points: doubles,\n };\n};\n\nBasePoint.prototype._getNAFPoints = function _getNAFPoints(wnd) {\n if (this.precomputed && this.precomputed.naf)\n return this.precomputed.naf;\n\n var res = [ this ];\n var max = (1 << wnd) - 1;\n var dbl = max === 1 ? null : this.dbl();\n for (var i = 1; i < max; i++)\n res[i] = res[i - 1].add(dbl);\n return {\n wnd: wnd,\n points: res,\n };\n};\n\nBasePoint.prototype._getBeta = function _getBeta() {\n return null;\n};\n\nBasePoint.prototype.dblp = function dblp(k) {\n var r = this;\n for (var i = 0; i < k; i++)\n r = r.dbl();\n return r;\n};\n","'use strict';\n\nvar utils = require('../utils');\nvar BN = require('bn.js');\nvar inherits = require('inherits');\nvar Base = require('./base');\n\nvar assert = utils.assert;\n\nfunction ShortCurve(conf) {\n Base.call(this, 'short', conf);\n\n this.a = new BN(conf.a, 16).toRed(this.red);\n this.b = new BN(conf.b, 16).toRed(this.red);\n this.tinv = this.two.redInvm();\n\n this.zeroA = this.a.fromRed().cmpn(0) === 0;\n this.threeA = this.a.fromRed().sub(this.p).cmpn(-3) === 0;\n\n // If the curve is endomorphic, precalculate beta and lambda\n this.endo = this._getEndomorphism(conf);\n this._endoWnafT1 = new Array(4);\n this._endoWnafT2 = new Array(4);\n}\ninherits(ShortCurve, Base);\nmodule.exports = ShortCurve;\n\nShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {\n // No efficient endomorphism\n if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)\n return;\n\n // Compute beta and lambda, that lambda * P = (beta * Px; Py)\n var beta;\n var lambda;\n if (conf.beta) {\n beta = new BN(conf.beta, 16).toRed(this.red);\n } else {\n var betas = this._getEndoRoots(this.p);\n // Choose the smallest beta\n beta = betas[0].cmp(betas[1]) < 0 ? betas[0] : betas[1];\n beta = beta.toRed(this.red);\n }\n if (conf.lambda) {\n lambda = new BN(conf.lambda, 16);\n } else {\n // Choose the lambda that is matching selected beta\n var lambdas = this._getEndoRoots(this.n);\n if (this.g.mul(lambdas[0]).x.cmp(this.g.x.redMul(beta)) === 0) {\n lambda = lambdas[0];\n } else {\n lambda = lambdas[1];\n assert(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);\n }\n }\n\n // Get basis vectors, used for balanced length-two representation\n var basis;\n if (conf.basis) {\n basis = conf.basis.map(function(vec) {\n return {\n a: new BN(vec.a, 16),\n b: new BN(vec.b, 16),\n };\n });\n } else {\n basis = this._getEndoBasis(lambda);\n }\n\n return {\n beta: beta,\n lambda: lambda,\n basis: basis,\n };\n};\n\nShortCurve.prototype._getEndoRoots = function _getEndoRoots(num) {\n // Find roots of for x^2 + x + 1 in F\n // Root = (-1 +- Sqrt(-3)) / 2\n //\n var red = num === this.p ? this.red : BN.mont(num);\n var tinv = new BN(2).toRed(red).redInvm();\n var ntinv = tinv.redNeg();\n\n var s = new BN(3).toRed(red).redNeg().redSqrt().redMul(tinv);\n\n var l1 = ntinv.redAdd(s).fromRed();\n var l2 = ntinv.redSub(s).fromRed();\n return [ l1, l2 ];\n};\n\nShortCurve.prototype._getEndoBasis = function _getEndoBasis(lambda) {\n // aprxSqrt >= sqrt(this.n)\n var aprxSqrt = this.n.ushrn(Math.floor(this.n.bitLength() / 2));\n\n // 3.74\n // Run EGCD, until r(L + 1) < aprxSqrt\n var u = lambda;\n var v = this.n.clone();\n var x1 = new BN(1);\n var y1 = new BN(0);\n var x2 = new BN(0);\n var y2 = new BN(1);\n\n // NOTE: all vectors are roots of: a + b * lambda = 0 (mod n)\n var a0;\n var b0;\n // First vector\n var a1;\n var b1;\n // Second vector\n var a2;\n var b2;\n\n var prevR;\n var i = 0;\n var r;\n var x;\n while (u.cmpn(0) !== 0) {\n var q = v.div(u);\n r = v.sub(q.mul(u));\n x = x2.sub(q.mul(x1));\n var y = y2.sub(q.mul(y1));\n\n if (!a1 && r.cmp(aprxSqrt) < 0) {\n a0 = prevR.neg();\n b0 = x1;\n a1 = r.neg();\n b1 = x;\n } else if (a1 && ++i === 2) {\n break;\n }\n prevR = r;\n\n v = u;\n u = r;\n x2 = x1;\n x1 = x;\n y2 = y1;\n y1 = y;\n }\n a2 = r.neg();\n b2 = x;\n\n var len1 = a1.sqr().add(b1.sqr());\n var len2 = a2.sqr().add(b2.sqr());\n if (len2.cmp(len1) >= 0) {\n a2 = a0;\n b2 = b0;\n }\n\n // Normalize signs\n if (a1.negative) {\n a1 = a1.neg();\n b1 = b1.neg();\n }\n if (a2.negative) {\n a2 = a2.neg();\n b2 = b2.neg();\n }\n\n return [\n { a: a1, b: b1 },\n { a: a2, b: b2 },\n ];\n};\n\nShortCurve.prototype._endoSplit = function _endoSplit(k) {\n var basis = this.endo.basis;\n var v1 = basis[0];\n var v2 = basis[1];\n\n var c1 = v2.b.mul(k).divRound(this.n);\n var c2 = v1.b.neg().mul(k).divRound(this.n);\n\n var p1 = c1.mul(v1.a);\n var p2 = c2.mul(v2.a);\n var q1 = c1.mul(v1.b);\n var q2 = c2.mul(v2.b);\n\n // Calculate answer\n var k1 = k.sub(p1).sub(p2);\n var k2 = q1.add(q2).neg();\n return { k1: k1, k2: k2 };\n};\n\nShortCurve.prototype.pointFromX = function pointFromX(x, odd) {\n x = new BN(x, 16);\n if (!x.red)\n x = x.toRed(this.red);\n\n var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);\n var y = y2.redSqrt();\n if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)\n throw new Error('invalid point');\n\n // XXX Is there any way to tell if the number is odd without converting it\n // to non-red form?\n var isOdd = y.fromRed().isOdd();\n if (odd && !isOdd || !odd && isOdd)\n y = y.redNeg();\n\n return this.point(x, y);\n};\n\nShortCurve.prototype.validate = function validate(point) {\n if (point.inf)\n return true;\n\n var x = point.x;\n var y = point.y;\n\n var ax = this.a.redMul(x);\n var rhs = x.redSqr().redMul(x).redIAdd(ax).redIAdd(this.b);\n return y.redSqr().redISub(rhs).cmpn(0) === 0;\n};\n\nShortCurve.prototype._endoWnafMulAdd =\n function _endoWnafMulAdd(points, coeffs, jacobianResult) {\n var npoints = this._endoWnafT1;\n var ncoeffs = this._endoWnafT2;\n for (var i = 0; i < points.length; i++) {\n var split = this._endoSplit(coeffs[i]);\n var p = points[i];\n var beta = p._getBeta();\n\n if (split.k1.negative) {\n split.k1.ineg();\n p = p.neg(true);\n }\n if (split.k2.negative) {\n split.k2.ineg();\n beta = beta.neg(true);\n }\n\n npoints[i * 2] = p;\n npoints[i * 2 + 1] = beta;\n ncoeffs[i * 2] = split.k1;\n ncoeffs[i * 2 + 1] = split.k2;\n }\n var res = this._wnafMulAdd(1, npoints, ncoeffs, i * 2, jacobianResult);\n\n // Clean-up references to points and coefficients\n for (var j = 0; j < i * 2; j++) {\n npoints[j] = null;\n ncoeffs[j] = null;\n }\n return res;\n };\n\nfunction Point(curve, x, y, isRed) {\n Base.BasePoint.call(this, curve, 'affine');\n if (x === null && y === null) {\n this.x = null;\n this.y = null;\n this.inf = true;\n } else {\n this.x = new BN(x, 16);\n this.y = new BN(y, 16);\n // Force redgomery representation when loading from JSON\n if (isRed) {\n this.x.forceRed(this.curve.red);\n this.y.forceRed(this.curve.red);\n }\n if (!this.x.red)\n this.x = this.x.toRed(this.curve.red);\n if (!this.y.red)\n this.y = this.y.toRed(this.curve.red);\n this.inf = false;\n }\n}\ninherits(Point, Base.BasePoint);\n\nShortCurve.prototype.point = function point(x, y, isRed) {\n return new Point(this, x, y, isRed);\n};\n\nShortCurve.prototype.pointFromJSON = function pointFromJSON(obj, red) {\n return Point.fromJSON(this, obj, red);\n};\n\nPoint.prototype._getBeta = function _getBeta() {\n if (!this.curve.endo)\n return;\n\n var pre = this.precomputed;\n if (pre && pre.beta)\n return pre.beta;\n\n var beta = this.curve.point(this.x.redMul(this.curve.endo.beta), this.y);\n if (pre) {\n var curve = this.curve;\n var endoMul = function(p) {\n return curve.point(p.x.redMul(curve.endo.beta), p.y);\n };\n pre.beta = beta;\n beta.precomputed = {\n beta: null,\n naf: pre.naf && {\n wnd: pre.naf.wnd,\n points: pre.naf.points.map(endoMul),\n },\n doubles: pre.doubles && {\n step: pre.doubles.step,\n points: pre.doubles.points.map(endoMul),\n },\n };\n }\n return beta;\n};\n\nPoint.prototype.toJSON = function toJSON() {\n if (!this.precomputed)\n return [ this.x, this.y ];\n\n return [ this.x, this.y, this.precomputed && {\n doubles: this.precomputed.doubles && {\n step: this.precomputed.doubles.step,\n points: this.precomputed.doubles.points.slice(1),\n },\n naf: this.precomputed.naf && {\n wnd: this.precomputed.naf.wnd,\n points: this.precomputed.naf.points.slice(1),\n },\n } ];\n};\n\nPoint.fromJSON = function fromJSON(curve, obj, red) {\n if (typeof obj === 'string')\n obj = JSON.parse(obj);\n var res = curve.point(obj[0], obj[1], red);\n if (!obj[2])\n return res;\n\n function obj2point(obj) {\n return curve.point(obj[0], obj[1], red);\n }\n\n var pre = obj[2];\n res.precomputed = {\n beta: null,\n doubles: pre.doubles && {\n step: pre.doubles.step,\n points: [ res ].concat(pre.doubles.points.map(obj2point)),\n },\n naf: pre.naf && {\n wnd: pre.naf.wnd,\n points: [ res ].concat(pre.naf.points.map(obj2point)),\n },\n };\n return res;\n};\n\nPoint.prototype.inspect = function inspect() {\n if (this.isInfinity())\n return '<EC Point Infinity>';\n return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +\n ' y: ' + this.y.fromRed().toString(16, 2) + '>';\n};\n\nPoint.prototype.isInfinity = function isInfinity() {\n return this.inf;\n};\n\nPoint.prototype.add = function add(p) {\n // O + P = P\n if (this.inf)\n return p;\n\n // P + O = P\n if (p.inf)\n return this;\n\n // P + P = 2P\n if (this.eq(p))\n return this.dbl();\n\n // P + (-P) = O\n if (this.neg().eq(p))\n return this.curve.point(null, null);\n\n // P + Q = O\n if (this.x.cmp(p.x) === 0)\n return this.curve.point(null, null);\n\n var c = this.y.redSub(p.y);\n if (c.cmpn(0) !== 0)\n c = c.redMul(this.x.redSub(p.x).redInvm());\n var nx = c.redSqr().redISub(this.x).redISub(p.x);\n var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);\n return this.curve.point(nx, ny);\n};\n\nPoint.prototype.dbl = function dbl() {\n if (this.inf)\n return this;\n\n // 2P = O\n var ys1 = this.y.redAdd(this.y);\n if (ys1.cmpn(0) === 0)\n return this.curve.point(null, null);\n\n var a = this.curve.a;\n\n var x2 = this.x.redSqr();\n var dyinv = ys1.redInvm();\n var c = x2.redAdd(x2).redIAdd(x2).redIAdd(a).redMul(dyinv);\n\n var nx = c.redSqr().redISub(this.x.redAdd(this.x));\n var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);\n return this.curve.point(nx, ny);\n};\n\nPoint.prototype.getX = function getX() {\n return this.x.fromRed();\n};\n\nPoint.prototype.getY = function getY() {\n return this.y.fromRed();\n};\n\nPoint.prototype.mul = function mul(k) {\n k = new BN(k, 16);\n if (this.isInfinity())\n return this;\n else if (this._hasDoubles(k))\n return this.curve._fixedNafMul(this, k);\n else if (this.curve.endo)\n return this.curve._endoWnafMulAdd([ this ], [ k ]);\n else\n return this.curve._wnafMul(this, k);\n};\n\nPoint.prototype.mulAdd = function mulAdd(k1, p2, k2) {\n var points = [ this, p2 ];\n var coeffs = [ k1, k2 ];\n if (this.curve.endo)\n return this.curve._endoWnafMulAdd(points, coeffs);\n else\n return this.curve._wnafMulAdd(1, points, coeffs, 2);\n};\n\nPoint.prototype.jmulAdd = function jmulAdd(k1, p2, k2) {\n var points = [ this, p2 ];\n var coeffs = [ k1, k2 ];\n if (this.curve.endo)\n return this.curve._endoWnafMulAdd(points, coeffs, true);\n else\n return this.curve._wnafMulAdd(1, points, coeffs, 2, true);\n};\n\nPoint.prototype.eq = function eq(p) {\n return this === p ||\n this.inf === p.inf &&\n (this.inf || this.x.cmp(p.x) === 0 && this.y.cmp(p.y) === 0);\n};\n\nPoint.prototype.neg = function neg(_precompute) {\n if (this.inf)\n return this;\n\n var res = this.curve.point(this.x, this.y.redNeg());\n if (_precompute && this.precomputed) {\n var pre = this.precomputed;\n var negate = function(p) {\n return p.neg();\n };\n res.precomputed = {\n naf: pre.naf && {\n wnd: pre.naf.wnd,\n points: pre.naf.points.map(negate),\n },\n doubles: pre.doubles && {\n step: pre.doubles.step,\n points: pre.doubles.points.map(negate),\n },\n };\n }\n return res;\n};\n\nPoint.prototype.toJ = function toJ() {\n if (this.inf)\n return this.curve.jpoint(null, null, null);\n\n var res = this.curve.jpoint(this.x, this.y, this.curve.one);\n return res;\n};\n\nfunction JPoint(curve, x, y, z) {\n Base.BasePoint.call(this, curve, 'jacobian');\n if (x === null && y === null && z === null) {\n this.x = this.curve.one;\n this.y = this.curve.one;\n this.z = new BN(0);\n } else {\n this.x = new BN(x, 16);\n this.y = new BN(y, 16);\n this.z = new BN(z, 16);\n }\n if (!this.x.red)\n this.x = this.x.toRed(this.curve.red);\n if (!this.y.red)\n this.y = this.y.toRed(this.curve.red);\n if (!this.z.red)\n this.z = this.z.toRed(this.curve.red);\n\n this.zOne = this.z === this.curve.one;\n}\ninherits(JPoint, Base.BasePoint);\n\nShortCurve.prototype.jpoint = function jpoint(x, y, z) {\n return new JPoint(this, x, y, z);\n};\n\nJPoint.prototype.toP = function toP() {\n if (this.isInfinity())\n return this.curve.point(null, null);\n\n var zinv = this.z.redInvm();\n var zinv2 = zinv.redSqr();\n var ax = this.x.redMul(zinv2);\n var ay = this.y.redMul(zinv2).redMul(zinv);\n\n return this.curve.point(ax, ay);\n};\n\nJPoint.prototype.neg = function neg() {\n return this.curve.jpoint(this.x, this.y.redNeg(), this.z);\n};\n\nJPoint.prototype.add = function add(p) {\n // O + P = P\n if (this.isInfinity())\n return p;\n\n // P + O = P\n if (p.isInfinity())\n return this;\n\n // 12M + 4S + 7A\n var pz2 = p.z.redSqr();\n var z2 = this.z.redSqr();\n var u1 = this.x.redMul(pz2);\n var u2 = p.x.redMul(z2);\n var s1 = this.y.redMul(pz2.redMul(p.z));\n var s2 = p.y.redMul(z2.redMul(this.z));\n\n var h = u1.redSub(u2);\n var r = s1.redSub(s2);\n if (h.cmpn(0) === 0) {\n if (r.cmpn(0) !== 0)\n return this.curve.jpoint(null, null, null);\n else\n return this.dbl();\n }\n\n var h2 = h.redSqr();\n var h3 = h2.redMul(h);\n var v = u1.redMul(h2);\n\n var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);\n var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));\n var nz = this.z.redMul(p.z).redMul(h);\n\n return this.curve.jpoint(nx, ny, nz);\n};\n\nJPoint.prototype.mixedAdd = function mixedAdd(p) {\n // O + P = P\n if (this.isInfinity())\n return p.toJ();\n\n // P + O = P\n if (p.isInfinity())\n return this;\n\n // 8M + 3S + 7A\n var z2 = this.z.redSqr();\n var u1 = this.x;\n var u2 = p.x.redMul(z2);\n var s1 = this.y;\n var s2 = p.y.redMul(z2).redMul(this.z);\n\n var h = u1.redSub(u2);\n var r = s1.redSub(s2);\n if (h.cmpn(0) === 0) {\n if (r.cmpn(0) !== 0)\n return this.curve.jpoint(null, null, null);\n else\n return this.dbl();\n }\n\n var h2 = h.redSqr();\n var h3 = h2.redMul(h);\n var v = u1.redMul(h2);\n\n var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);\n var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));\n var nz = this.z.redMul(h);\n\n return this.curve.jpoint(nx, ny, nz);\n};\n\nJPoint.prototype.dblp = function dblp(pow) {\n if (pow === 0)\n return this;\n if (this.isInfinity())\n return this;\n if (!pow)\n return this.dbl();\n\n var i;\n if (this.curve.zeroA || this.curve.threeA) {\n var r = this;\n for (i = 0; i < pow; i++)\n r = r.dbl();\n return r;\n }\n\n // 1M + 2S + 1A + N * (4S + 5M + 8A)\n // N = 1 => 6M + 6S + 9A\n var a = this.curve.a;\n var tinv = this.curve.tinv;\n\n var jx = this.x;\n var jy = this.y;\n var jz = this.z;\n var jz4 = jz.redSqr().redSqr();\n\n // Reuse results\n var jyd = jy.redAdd(jy);\n for (i = 0; i < pow; i++) {\n var jx2 = jx.redSqr();\n var jyd2 = jyd.redSqr();\n var jyd4 = jyd2.redSqr();\n var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));\n\n var t1 = jx.redMul(jyd2);\n var nx = c.redSqr().redISub(t1.redAdd(t1));\n var t2 = t1.redISub(nx);\n var dny = c.redMul(t2);\n dny = dny.redIAdd(dny).redISub(jyd4);\n var nz = jyd.redMul(jz);\n if (i + 1 < pow)\n jz4 = jz4.redMul(jyd4);\n\n jx = nx;\n jz = nz;\n jyd = dny;\n }\n\n return this.curve.jpoint(jx, jyd.redMul(tinv), jz);\n};\n\nJPoint.prototype.dbl = function dbl() {\n if (this.isInfinity())\n return this;\n\n if (this.curve.zeroA)\n return this._zeroDbl();\n else if (this.curve.threeA)\n return this._threeDbl();\n else\n return this._dbl();\n};\n\nJPoint.prototype._zeroDbl = function _zeroDbl() {\n var nx;\n var ny;\n var nz;\n // Z = 1\n if (this.zOne) {\n // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html\n // #doubling-mdbl-2007-bl\n // 1M + 5S + 14A\n\n // XX = X1^2\n var xx = this.x.redSqr();\n // YY = Y1^2\n var yy = this.y.redSqr();\n // YYYY = YY^2\n var yyyy = yy.redSqr();\n // S = 2 * ((X1 + YY)^2 - XX - YYYY)\n var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);\n s = s.redIAdd(s);\n // M = 3 * XX + a; a = 0\n var m = xx.redAdd(xx).redIAdd(xx);\n // T = M ^ 2 - 2*S\n var t = m.redSqr().redISub(s).redISub(s);\n\n // 8 * YYYY\n var yyyy8 = yyyy.redIAdd(yyyy);\n yyyy8 = yyyy8.redIAdd(yyyy8);\n yyyy8 = yyyy8.redIAdd(yyyy8);\n\n // X3 = T\n nx = t;\n // Y3 = M * (S - T) - 8 * YYYY\n ny = m.redMul(s.redISub(t)).redISub(yyyy8);\n // Z3 = 2*Y1\n nz = this.y.redAdd(this.y);\n } else {\n // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html\n // #doubling-dbl-2009-l\n // 2M + 5S + 13A\n\n // A = X1^2\n var a = this.x.redSqr();\n // B = Y1^2\n var b = this.y.redSqr();\n // C = B^2\n var c = b.redSqr();\n // D = 2 * ((X1 + B)^2 - A - C)\n var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);\n d = d.redIAdd(d);\n // E = 3 * A\n var e = a.redAdd(a).redIAdd(a);\n // F = E^2\n var f = e.redSqr();\n\n // 8 * C\n var c8 = c.redIAdd(c);\n c8 = c8.redIAdd(c8);\n c8 = c8.redIAdd(c8);\n\n // X3 = F - 2 * D\n nx = f.redISub(d).redISub(d);\n // Y3 = E * (D - X3) - 8 * C\n ny = e.redMul(d.redISub(nx)).redISub(c8);\n // Z3 = 2 * Y1 * Z1\n nz = this.y.redMul(this.z);\n nz = nz.redIAdd(nz);\n }\n\n return this.curve.jpoint(nx, ny, nz);\n};\n\nJPoint.prototype._threeDbl = function _threeDbl() {\n var nx;\n var ny;\n var nz;\n // Z = 1\n if (this.zOne) {\n // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html\n // #doubling-mdbl-2007-bl\n // 1M + 5S + 15A\n\n // XX = X1^2\n var xx = this.x.redSqr();\n // YY = Y1^2\n var yy = this.y.redSqr();\n // YYYY = YY^2\n var yyyy = yy.redSqr();\n // S = 2 * ((X1 + YY)^2 - XX - YYYY)\n var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);\n s = s.redIAdd(s);\n // M = 3 * XX + a\n var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);\n // T = M^2 - 2 * S\n var t = m.redSqr().redISub(s).redISub(s);\n // X3 = T\n nx = t;\n // Y3 = M * (S - T) - 8 * YYYY\n var yyyy8 = yyyy.redIAdd(yyyy);\n yyyy8 = yyyy8.redIAdd(yyyy8);\n yyyy8 = yyyy8.redIAdd(yyyy8);\n ny = m.redMul(s.redISub(t)).redISub(yyyy8);\n // Z3 = 2 * Y1\n nz = this.y.redAdd(this.y);\n } else {\n // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b\n // 3M + 5S\n\n // delta = Z1^2\n var delta = this.z.redSqr();\n // gamma = Y1^2\n var gamma = this.y.redSqr();\n // beta = X1 * gamma\n var beta = this.x.redMul(gamma);\n // alpha = 3 * (X1 - delta) * (X1 + delta)\n var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));\n alpha = alpha.redAdd(alpha).redIAdd(alpha);\n // X3 = alpha^2 - 8 * beta\n var beta4 = beta.redIAdd(beta);\n beta4 = beta4.redIAdd(beta4);\n var beta8 = beta4.redAdd(beta4);\n nx = alpha.redSqr().redISub(beta8);\n // Z3 = (Y1 + Z1)^2 - gamma - delta\n nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);\n // Y3 = alpha * (4 * beta - X3) - 8 * gamma^2\n var ggamma8 = gamma.redSqr();\n ggamma8 = ggamma8.redIAdd(ggamma8);\n ggamma8 = ggamma8.redIAdd(ggamma8);\n ggamma8 = ggamma8.redIAdd(ggamma8);\n ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);\n }\n\n return this.curve.jpoint(nx, ny, nz);\n};\n\nJPoint.prototype._dbl = function _dbl() {\n var a = this.curve.a;\n\n // 4M + 6S + 10A\n var jx = this.x;\n var jy = this.y;\n var jz = this.z;\n var jz4 = jz.redSqr().redSqr();\n\n var jx2 = jx.redSqr();\n var jy2 = jy.redSqr();\n\n var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));\n\n var jxd4 = jx.redAdd(jx);\n jxd4 = jxd4.redIAdd(jxd4);\n var t1 = jxd4.redMul(jy2);\n var nx = c.redSqr().redISub(t1.redAdd(t1));\n var t2 = t1.redISub(nx);\n\n var jyd8 = jy2.redSqr();\n jyd8 = jyd8.redIAdd(jyd8);\n jyd8 = jyd8.redIAdd(jyd8);\n jyd8 = jyd8.redIAdd(jyd8);\n var ny = c.redMul(t2).redISub(jyd8);\n var nz = jy.redAdd(jy).redMul(jz);\n\n return this.curve.jpoint(nx, ny, nz);\n};\n\nJPoint.prototype.trpl = function trpl() {\n if (!this.curve.zeroA)\n return this.dbl().add(this);\n\n // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#tripling-tpl-2007-bl\n // 5M + 10S + ...\n\n // XX = X1^2\n var xx = this.x.redSqr();\n // YY = Y1^2\n var yy = this.y.redSqr();\n // ZZ = Z1^2\n var zz = this.z.redSqr();\n // YYYY = YY^2\n var yyyy = yy.redSqr();\n // M = 3 * XX + a * ZZ2; a = 0\n var m = xx.redAdd(xx).redIAdd(xx);\n // MM = M^2\n var mm = m.redSqr();\n // E = 6 * ((X1 + YY)^2 - XX - YYYY) - MM\n var e = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);\n e = e.redIAdd(e);\n e = e.redAdd(e).redIAdd(e);\n e = e.redISub(mm);\n // EE = E^2\n var ee = e.redSqr();\n // T = 16*YYYY\n var t = yyyy.redIAdd(yyyy);\n t = t.redIAdd(t);\n t = t.redIAdd(t);\n t = t.redIAdd(t);\n // U = (M + E)^2 - MM - EE - T\n var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);\n // X3 = 4 * (X1 * EE - 4 * YY * U)\n var yyu4 = yy.redMul(u);\n yyu4 = yyu4.redIAdd(yyu4);\n yyu4 = yyu4.redIAdd(yyu4);\n var nx = this.x.redMul(ee).redISub(yyu4);\n nx = nx.redIAdd(nx);\n nx = nx.redIAdd(nx);\n // Y3 = 8 * Y1 * (U * (T - U) - E * EE)\n var ny = this.y.redMul(u.redMul(t.redISub(u)).redISub(e.redMul(ee)));\n ny = ny.redIAdd(ny);\n ny = ny.redIAdd(ny);\n ny = ny.redIAdd(ny);\n // Z3 = (Z1 + E)^2 - ZZ - EE\n var nz = this.z.redAdd(e).redSqr().redISub(zz).redISub(ee);\n\n return this.curve.jpoint(nx, ny, nz);\n};\n\nJPoint.prototype.mul = function mul(k, kbase) {\n k = new BN(k, kbase);\n\n return this.curve._wnafMul(this, k);\n};\n\nJPoint.prototype.eq = function eq(p) {\n if (p.type === 'affine')\n return this.eq(p.toJ());\n\n if (this === p)\n return true;\n\n // x1 * z2^2 == x2 * z1^2\n var z2 = this.z.redSqr();\n var pz2 = p.z.redSqr();\n if (this.x.redMul(pz2).redISub(p.x.redMul(z2)).cmpn(0) !== 0)\n return false;\n\n // y1 * z2^3 == y2 * z1^3\n var z3 = z2.redMul(this.z);\n var pz3 = pz2.redMul(p.z);\n return this.y.redMul(pz3).redISub(p.y.redMul(z3)).cmpn(0) === 0;\n};\n\nJPoint.prototype.eqXToP = function eqXToP(x) {\n var zs = this.z.redSqr();\n var rx = x.toRed(this.curve.red).redMul(zs);\n if (this.x.cmp(rx) === 0)\n return true;\n\n var xc = x.clone();\n var t = this.curve.redN.redMul(zs);\n for (;;) {\n xc.iadd(this.curve.n);\n if (xc.cmp(this.curve.p) >= 0)\n return false;\n\n rx.redIAdd(t);\n if (this.x.cmp(rx) === 0)\n return true;\n }\n};\n\nJPoint.prototype.inspect = function inspect() {\n if (this.isInfinity())\n return '<EC JPoint Infinity>';\n return '<EC JPoint x: ' + this.x.toString(16, 2) +\n ' y: ' + this.y.toString(16, 2) +\n ' z: ' + this.z.toString(16, 2) + '>';\n};\n\nJPoint.prototype.isInfinity = function isInfinity() {\n // XXX This code assumes that zero is always zero in red\n return this.z.cmpn(0) === 0;\n};\n","'use strict';\n\nvar utils = require('../utils');\nvar assert = utils.assert;\nvar parseBytes = utils.parseBytes;\nvar cachedProperty = utils.cachedProperty;\n\n/**\n* @param {EDDSA} eddsa - instance\n* @param {Object} params - public/private key parameters\n*\n* @param {Array<Byte>} [params.secret] - secret seed bytes\n* @param {Point} [params.pub] - public key point (aka `A` in eddsa terms)\n* @param {Array<Byte>} [params.pub] - public key point encoded as bytes\n*\n*/\nfunction KeyPair(eddsa, params) {\n this.eddsa = eddsa;\n this._secret = parseBytes(params.secret);\n if (eddsa.isPoint(params.pub))\n this._pub = params.pub;\n else\n this._pubBytes = parseBytes(params.pub);\n}\n\nKeyPair.fromPublic = function fromPublic(eddsa, pub) {\n if (pub instanceof KeyPair)\n return pub;\n return new KeyPair(eddsa, { pub: pub });\n};\n\nKeyPair.fromSecret = function fromSecret(eddsa, secret) {\n if (secret instanceof KeyPair)\n return secret;\n return new KeyPair(eddsa, { secret: secret });\n};\n\nKeyPair.prototype.secret = function secret() {\n return this._secret;\n};\n\ncachedProperty(KeyPair, 'pubBytes', function pubBytes() {\n return this.eddsa.encodePoint(this.pub());\n});\n\ncachedProperty(KeyPair, 'pub', function pub() {\n if (this._pubBytes)\n return this.eddsa.decodePoint(this._pubBytes);\n return this.eddsa.g.mul(this.priv());\n});\n\ncachedProperty(KeyPair, 'privBytes', function privBytes() {\n var eddsa = this.eddsa;\n var hash = this.hash();\n var lastIx = eddsa.encodingLength - 1;\n\n var a = hash.slice(0, eddsa.encodingLength);\n a[0] &= 248;\n a[lastIx] &= 127;\n a[lastIx] |= 64;\n\n return a;\n});\n\ncachedProperty(KeyPair, 'priv', function priv() {\n return this.eddsa.decodeInt(this.privBytes());\n});\n\ncachedProperty(KeyPair, 'hash', function hash() {\n return this.eddsa.hash().update(this.secret()).digest();\n});\n\ncachedProperty(KeyPair, 'messagePrefix', function messagePrefix() {\n return this.hash().slice(this.eddsa.encodingLength);\n});\n\nKeyPair.prototype.sign = function sign(message) {\n assert(this._secret, 'KeyPair can only verify');\n return this.eddsa.sign(message, this);\n};\n\nKeyPair.prototype.verify = function verify(message, sig) {\n return this.eddsa.verify(message, sig, this);\n};\n\nKeyPair.prototype.getSecret = function getSecret(enc) {\n assert(this._secret, 'KeyPair is public only');\n return utils.encode(this.secret(), enc);\n};\n\nKeyPair.prototype.getPublic = function getPublic(enc) {\n return utils.encode(this.pubBytes(), enc);\n};\n\nmodule.exports = KeyPair;\n","'use strict';\n\nvar utils = exports;\nvar BN = require('bn.js');\nvar minAssert = require('minimalistic-assert');\nvar minUtils = require('minimalistic-crypto-utils');\n\nutils.assert = minAssert;\nutils.toArray = minUtils.toArray;\nutils.zero2 = minUtils.zero2;\nutils.toHex = minUtils.toHex;\nutils.encode = minUtils.encode;\n\n// Represent num in a w-NAF form\nfunction getNAF(num, w, bits) {\n var naf = new Array(Math.max(num.bitLength(), bits) + 1);\n naf.fill(0);\n\n var ws = 1 << (w + 1);\n var k = num.clone();\n\n for (var i = 0; i < naf.length; i++) {\n var z;\n var mod = k.andln(ws - 1);\n if (k.isOdd()) {\n if (mod > (ws >> 1) - 1)\n z = (ws >> 1) - mod;\n else\n z = mod;\n k.isubn(z);\n } else {\n z = 0;\n }\n\n naf[i] = z;\n k.iushrn(1);\n }\n\n return naf;\n}\nutils.getNAF = getNAF;\n\n// Represent k1, k2 in a Joint Sparse Form\nfunction getJSF(k1, k2) {\n var jsf = [\n [],\n [],\n ];\n\n k1 = k1.clone();\n k2 = k2.clone();\n var d1 = 0;\n var d2 = 0;\n var m8;\n while (k1.cmpn(-d1) > 0 || k2.cmpn(-d2) > 0) {\n // First phase\n var m14 = (k1.andln(3) + d1) & 3;\n var m24 = (k2.andln(3) + d2) & 3;\n if (m14 === 3)\n m14 = -1;\n if (m24 === 3)\n m24 = -1;\n var u1;\n if ((m14 & 1) === 0) {\n u1 = 0;\n } else {\n m8 = (k1.andln(7) + d1) & 7;\n if ((m8 === 3 || m8 === 5) && m24 === 2)\n u1 = -m14;\n else\n u1 = m14;\n }\n jsf[0].push(u1);\n\n var u2;\n if ((m24 & 1) === 0) {\n u2 = 0;\n } else {\n m8 = (k2.andln(7) + d2) & 7;\n if ((m8 === 3 || m8 === 5) && m14 === 2)\n u2 = -m24;\n else\n u2 = m24;\n }\n jsf[1].push(u2);\n\n // Second phase\n if (2 * d1 === u1 + 1)\n d1 = 1 - d1;\n if (2 * d2 === u2 + 1)\n d2 = 1 - d2;\n k1.iushrn(1);\n k2.iushrn(1);\n }\n\n return jsf;\n}\nutils.getJSF = getJSF;\n\nfunction cachedProperty(obj, name, computer) {\n var key = '_' + name;\n obj.prototype[name] = function cachedProperty() {\n return this[key] !== undefined ? this[key] :\n this[key] = computer.call(this);\n };\n}\nutils.cachedProperty = cachedProperty;\n\nfunction parseBytes(bytes) {\n return typeof bytes === 'string' ? utils.toArray(bytes, 'hex') :\n bytes;\n}\nutils.parseBytes = parseBytes;\n\nfunction intFromLE(bytes) {\n return new BN(bytes, 'hex', 'le');\n}\nutils.intFromLE = intFromLE;\n\n","'use strict';\n\nvar BN = require('bn.js');\nvar HmacDRBG = require('hmac-drbg');\nvar utils = require('../utils');\nvar curves = require('../curves');\nvar rand = require('brorand');\nvar assert = utils.assert;\n\nvar KeyPair = require('./key');\nvar Signature = require('./signature');\n\nfunction EC(options) {\n if (!(this instanceof EC))\n return new EC(options);\n\n // Shortcut `elliptic.ec(curve-name)`\n if (typeof options === 'string') {\n assert(Object.prototype.hasOwnProperty.call(curves, options),\n 'Unknown curve ' + options);\n\n options = curves[options];\n }\n\n // Shortcut for `elliptic.ec(elliptic.curves.curveName)`\n if (options instanceof curves.PresetCurve)\n options = { curve: options };\n\n this.curve = options.curve.curve;\n this.n = this.curve.n;\n this.nh = this.n.ushrn(1);\n this.g = this.curve.g;\n\n // Point on curve\n this.g = options.curve.g;\n this.g.precompute(options.curve.n.bitLength() + 1);\n\n // Hash for function for DRBG\n this.hash = options.hash || options.curve.hash;\n}\nmodule.exports = EC;\n\nEC.prototype.keyPair = function keyPair(options) {\n return new KeyPair(this, options);\n};\n\nEC.prototype.keyFromPrivate = function keyFromPrivate(priv, enc) {\n return KeyPair.fromPrivate(this, priv, enc);\n};\n\nEC.prototype.keyFromPublic = function keyFromPublic(pub, enc) {\n return KeyPair.fromPublic(this, pub, enc);\n};\n\nEC.prototype.genKeyPair = function genKeyPair(options) {\n if (!options)\n options = {};\n\n // Instantiate Hmac_DRBG\n var drbg = new HmacDRBG({\n hash: this.hash,\n pers: options.pers,\n persEnc: options.persEnc || 'utf8',\n entropy: options.entropy || rand(this.hash.hmacStrength),\n entropyEnc: options.entropy && options.entropyEnc || 'utf8',\n nonce: this.n.toArray(),\n });\n\n var bytes = this.n.byteLength();\n var ns2 = this.n.sub(new BN(2));\n for (;;) {\n var priv = new BN(drbg.generate(bytes));\n if (priv.cmp(ns2) > 0)\n continue;\n\n priv.iaddn(1);\n return this.keyFromPrivate(priv);\n }\n};\n\nEC.prototype._truncateToN = function _truncateToN(msg, truncOnly) {\n var delta = msg.byteLength() * 8 - this.n.bitLength();\n if (delta > 0)\n msg = msg.ushrn(delta);\n if (!truncOnly && msg.cmp(this.n) >= 0)\n return msg.sub(this.n);\n else\n return msg;\n};\n\nEC.prototype.sign = function sign(msg, key, enc, options) {\n if (typeof enc === 'object') {\n options = enc;\n enc = null;\n }\n if (!options)\n options = {};\n\n key = this.keyFromPrivate(key, enc);\n msg = this._truncateToN(new BN(msg, 16));\n\n // Zero-extend key to provide enough entropy\n var bytes = this.n.byteLength();\n var bkey = key.getPrivate().toArray('be', bytes);\n\n // Zero-extend nonce to have the same byte size as N\n var nonce = msg.toArray('be', bytes);\n\n // Instantiate Hmac_DRBG\n var drbg = new HmacDRBG({\n hash: this.hash,\n entropy: bkey,\n nonce: nonce,\n pers: options.pers,\n persEnc: options.persEnc || 'utf8',\n });\n\n // Number of bytes to generate\n var ns1 = this.n.sub(new BN(1));\n\n for (var iter = 0; ; iter++) {\n var k = options.k ?\n options.k(iter) :\n new BN(drbg.generate(this.n.byteLength()));\n k = this._truncateToN(k, true);\n if (k.cmpn(1) <= 0 || k.cmp(ns1) >= 0)\n continue;\n\n var kp = this.g.mul(k);\n if (kp.isInfinity())\n continue;\n\n var kpX = kp.getX();\n var r = kpX.umod(this.n);\n if (r.cmpn(0) === 0)\n continue;\n\n var s = k.invm(this.n).mul(r.mul(key.getPrivate()).iadd(msg));\n s = s.umod(this.n);\n if (s.cmpn(0) === 0)\n continue;\n\n var recoveryParam = (kp.getY().isOdd() ? 1 : 0) |\n (kpX.cmp(r) !== 0 ? 2 : 0);\n\n // Use complement of `s`, if it is > `n / 2`\n if (options.canonical && s.cmp(this.nh) > 0) {\n s = this.n.sub(s);\n recoveryParam ^= 1;\n }\n\n return new Signature({ r: r, s: s, recoveryParam: recoveryParam });\n }\n};\n\nEC.prototype.verify = function verify(msg, signature, key, enc) {\n msg = this._truncateToN(new BN(msg, 16));\n key = this.keyFromPublic(key, enc);\n signature = new Signature(signature, 'hex');\n\n // Perform primitive values validation\n var r = signature.r;\n var s = signature.s;\n if (r.cmpn(1) < 0 || r.cmp(this.n) >= 0)\n return false;\n if (s.cmpn(1) < 0 || s.cmp(this.n) >= 0)\n return false;\n\n // Validate signature\n var sinv = s.invm(this.n);\n var u1 = sinv.mul(msg).umod(this.n);\n var u2 = sinv.mul(r).umod(this.n);\n var p;\n\n if (!this.curve._maxwellTrick) {\n p = this.g.mulAdd(u1, key.getPublic(), u2);\n if (p.isInfinity())\n return false;\n\n return p.getX().umod(this.n).cmp(r) === 0;\n }\n\n // NOTE: Greg Maxwell's trick, inspired by:\n // https://git.io/vad3K\n\n p = this.g.jmulAdd(u1, key.getPublic(), u2);\n if (p.isInfinity())\n return false;\n\n // Compare `p.x` of Jacobian point with `r`,\n // this will do `p.x == r * p.z^2` instead of multiplying `p.x` by the\n // inverse of `p.z^2`\n return p.eqXToP(r);\n};\n\nEC.prototype.recoverPubKey = function(msg, signature, j, enc) {\n assert((3 & j) === j, 'The recovery param is more than two bits');\n signature = new Signature(signature, enc);\n\n var n = this.n;\n var e = new BN(msg);\n var r = signature.r;\n var s = signature.s;\n\n // A set LSB signifies that the y-coordinate is odd\n var isYOdd = j & 1;\n var isSecondKey = j >> 1;\n if (r.cmp(this.curve.p.umod(this.curve.n)) >= 0 && isSecondKey)\n throw new Error('Unable to find sencond key candinate');\n\n // 1.1. Let x = r + jn.\n if (isSecondKey)\n r = this.curve.pointFromX(r.add(this.curve.n), isYOdd);\n else\n r = this.curve.pointFromX(r, isYOdd);\n\n var rInv = signature.r.invm(n);\n var s1 = n.sub(e).mul(rInv).umod(n);\n var s2 = s.mul(rInv).umod(n);\n\n // 1.6.1 Compute Q = r^-1 (sR - eG)\n // Q = r^-1 (sR + -eG)\n return this.g.mulAdd(s1, r, s2);\n};\n\nEC.prototype.getKeyRecoveryParam = function(e, signature, Q, enc) {\n signature = new Signature(signature, enc);\n if (signature.recoveryParam !== null)\n return signature.recoveryParam;\n\n for (var i = 0; i < 4; i++) {\n var Qprime;\n try {\n Qprime = this.recoverPubKey(e, signature, i);\n } catch (e) {\n continue;\n }\n\n if (Qprime.eq(Q))\n return i;\n }\n throw new Error('Unable to find valid recovery factor');\n};\n","'use strict';\n\nvar curves = exports;\n\nvar hash = require('hash.js');\nvar curve = require('./curve');\nvar utils = require('./utils');\n\nvar assert = utils.assert;\n\nfunction PresetCurve(options) {\n if (options.type === 'short')\n this.curve = new curve.short(options);\n else if (options.type === 'edwards')\n this.curve = new curve.edwards(options);\n else\n this.curve = new curve.mont(options);\n this.g = this.curve.g;\n this.n = this.curve.n;\n this.hash = options.hash;\n\n assert(this.g.validate(), 'Invalid curve');\n assert(this.g.mul(this.n).isInfinity(), 'Invalid curve, G*N != O');\n}\ncurves.PresetCurve = PresetCurve;\n\nfunction defineCurve(name, options) {\n Object.defineProperty(curves, name, {\n configurable: true,\n enumerable: true,\n get: function() {\n var curve = new PresetCurve(options);\n Object.defineProperty(curves, name, {\n configurable: true,\n enumerable: true,\n value: curve,\n });\n return curve;\n },\n });\n}\n\ndefineCurve('p192', {\n type: 'short',\n prime: 'p192',\n p: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff',\n a: 'ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc',\n b: '64210519 e59c80e7 0fa7e9ab 72243049 feb8deec c146b9b1',\n n: 'ffffffff ffffffff ffffffff 99def836 146bc9b1 b4d22831',\n hash: hash.sha256,\n gRed: false,\n g: [\n '188da80e b03090f6 7cbf20eb 43a18800 f4ff0afd 82ff1012',\n '07192b95 ffc8da78 631011ed 6b24cdd5 73f977a1 1e794811',\n ],\n});\n\ndefineCurve('p224', {\n type: 'short',\n prime: 'p224',\n p: 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001',\n a: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe',\n b: 'b4050a85 0c04b3ab f5413256 5044b0b7 d7bfd8ba 270b3943 2355ffb4',\n n: 'ffffffff ffffffff ffffffff ffff16a2 e0b8f03e 13dd2945 5c5c2a3d',\n hash: hash.sha256,\n gRed: false,\n g: [\n 'b70e0cbd 6bb4bf7f 321390b9 4a03c1d3 56c21122 343280d6 115c1d21',\n 'bd376388 b5f723fb 4c22dfe6 cd4375a0 5a074764 44d58199 85007e34',\n ],\n});\n\ndefineCurve('p256', {\n type: 'short',\n prime: null,\n p: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff',\n a: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff fffffffc',\n b: '5ac635d8 aa3a93e7 b3ebbd55 769886bc 651d06b0 cc53b0f6 3bce3c3e 27d2604b',\n n: 'ffffffff 00000000 ffffffff ffffffff bce6faad a7179e84 f3b9cac2 fc632551',\n hash: hash.sha256,\n gRed: false,\n g: [\n '6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296',\n '4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5',\n ],\n});\n\ndefineCurve('p384', {\n type: 'short',\n prime: null,\n p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'fffffffe ffffffff 00000000 00000000 ffffffff',\n a: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'fffffffe ffffffff 00000000 00000000 fffffffc',\n b: 'b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112 0314088f ' +\n '5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef',\n n: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff c7634d81 ' +\n 'f4372ddf 581a0db2 48b0a77a ecec196a ccc52973',\n hash: hash.sha384,\n gRed: false,\n g: [\n 'aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98 59f741e0 82542a38 ' +\n '5502f25d bf55296c 3a545e38 72760ab7',\n '3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c e9da3113 b5f0b8c0 ' +\n '0a60b1ce 1d7e819d 7a431d7c 90ea0e5f',\n ],\n});\n\ndefineCurve('p521', {\n type: 'short',\n prime: null,\n p: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'ffffffff ffffffff ffffffff ffffffff ffffffff',\n a: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'ffffffff ffffffff ffffffff ffffffff fffffffc',\n b: '00000051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b ' +\n '99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd ' +\n '3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00',\n n: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +\n 'ffffffff ffffffff fffffffa 51868783 bf2f966b 7fcc0148 ' +\n 'f709a5d0 3bb5c9b8 899c47ae bb6fb71e 91386409',\n hash: hash.sha512,\n gRed: false,\n g: [\n '000000c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 ' +\n '053fb521 f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 ' +\n 'a2ffa8de 3348b3c1 856a429b f97e7e31 c2e5bd66',\n '00000118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 ' +\n '579b4468 17afbd17 273e662c 97ee7299 5ef42640 c550b901 ' +\n '3fad0761 353c7086 a272c240 88be9476 9fd16650',\n ],\n});\n\ndefineCurve('curve25519', {\n type: 'mont',\n prime: 'p25519',\n p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',\n a: '76d06',\n b: '1',\n n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',\n hash: hash.sha256,\n gRed: false,\n g: [\n '9',\n ],\n});\n\ndefineCurve('ed25519', {\n type: 'edwards',\n prime: 'p25519',\n p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',\n a: '-1',\n c: '1',\n // -121665 * (121666^(-1)) (mod P)\n d: '52036cee2b6ffe73 8cc740797779e898 00700a4d4141d8ab 75eb4dca135978a3',\n n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',\n hash: hash.sha256,\n gRed: false,\n g: [\n '216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a',\n\n // 4/5\n '6666666666666666666666666666666666666666666666666666666666666658',\n ],\n});\n\nvar pre;\ntry {\n pre = require('./precomputed/secp256k1');\n} catch (e) {\n pre = undefined;\n}\n\ndefineCurve('secp256k1', {\n type: 'short',\n prime: 'k256',\n p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f',\n a: '0',\n b: '7',\n n: 'ffffffff ffffffff ffffffff fffffffe baaedce6 af48a03b bfd25e8c d0364141',\n h: '1',\n hash: hash.sha256,\n\n // Precomputed endomorphism\n beta: '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee',\n lambda: '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72',\n basis: [\n {\n a: '3086d221a7d46bcde86c90e49284eb15',\n b: '-e4437ed6010e88286f547fa90abfe4c3',\n },\n {\n a: '114ca50f7a8e2f3f657c1108d9d44cfd8',\n b: '3086d221a7d46bcde86c90e49284eb15',\n },\n ],\n\n gRed: false,\n g: [\n '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',\n '483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8',\n pre,\n ],\n});\n","'use strict';\n\nvar BN = require('bn.js');\nvar utils = require('../utils');\nvar assert = utils.assert;\n\nfunction KeyPair(ec, options) {\n this.ec = ec;\n this.priv = null;\n this.pub = null;\n\n // KeyPair(ec, { priv: ..., pub: ... })\n if (options.priv)\n this._importPrivate(options.priv, options.privEnc);\n if (options.pub)\n this._importPublic(options.pub, options.pubEnc);\n}\nmodule.exports = KeyPair;\n\nKeyPair.fromPublic = function fromPublic(ec, pub, enc) {\n if (pub instanceof KeyPair)\n return pub;\n\n return new KeyPair(ec, {\n pub: pub,\n pubEnc: enc,\n });\n};\n\nKeyPair.fromPrivate = function fromPrivate(ec, priv, enc) {\n if (priv instanceof KeyPair)\n return priv;\n\n return new KeyPair(ec, {\n priv: priv,\n privEnc: enc,\n });\n};\n\nKeyPair.prototype.validate = function validate() {\n var pub = this.getPublic();\n\n if (pub.isInfinity())\n return { result: false, reason: 'Invalid public key' };\n if (!pub.validate())\n return { result: false, reason: 'Public key is not a point' };\n if (!pub.mul(this.ec.curve.n).isInfinity())\n return { result: false, reason: 'Public key * N != O' };\n\n return { result: true, reason: null };\n};\n\nKeyPair.prototype.getPublic = function getPublic(compact, enc) {\n // compact is optional argument\n if (typeof compact === 'string') {\n enc = compact;\n compact = null;\n }\n\n if (!this.pub)\n this.pub = this.ec.g.mul(this.priv);\n\n if (!enc)\n return this.pub;\n\n return this.pub.encode(enc, compact);\n};\n\nKeyPair.prototype.getPrivate = function getPrivate(enc) {\n if (enc === 'hex')\n return this.priv.toString(16, 2);\n else\n return this.priv;\n};\n\nKeyPair.prototype._importPrivate = function _importPrivate(key, enc) {\n this.priv = new BN(key, enc || 16);\n\n // Ensure that the priv won't be bigger than n, otherwise we may fail\n // in fixed multiplication method\n this.priv = this.priv.umod(this.ec.curve.n);\n};\n\nKeyPair.prototype._importPublic = function _importPublic(key, enc) {\n if (key.x || key.y) {\n // Montgomery points only have an `x` coordinate.\n // Weierstrass/Edwards points on the other hand have both `x` and\n // `y` coordinates.\n if (this.ec.curve.type === 'mont') {\n assert(key.x, 'Need x coordinate');\n } else if (this.ec.curve.type === 'short' ||\n this.ec.curve.type === 'edwards') {\n assert(key.x && key.y, 'Need both x and y coordinate');\n }\n this.pub = this.ec.curve.point(key.x, key.y);\n return;\n }\n this.pub = this.ec.curve.decodePoint(key, enc);\n};\n\n// ECDH\nKeyPair.prototype.derive = function derive(pub) {\n if(!pub.validate()) {\n assert(pub.validate(), 'public point not validated');\n }\n return pub.mul(this.priv).getX();\n};\n\n// ECDSA\nKeyPair.prototype.sign = function sign(msg, enc, options) {\n return this.ec.sign(msg, this, enc, options);\n};\n\nKeyPair.prototype.verify = 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require('../package.json').version;\nelliptic.utils = require('./elliptic/utils');\nelliptic.rand = require('brorand');\nelliptic.curve = require('./elliptic/curve');\nelliptic.curves = require('./elliptic/curves');\n\n// Protocols\nelliptic.ec = require('./elliptic/ec');\nelliptic.eddsa = require('./elliptic/eddsa');\n","'use strict';\n\nvar BN = require('bn.js');\nvar utils = require('../utils');\nvar assert = utils.assert;\nvar cachedProperty = utils.cachedProperty;\nvar parseBytes = utils.parseBytes;\n\n/**\n* @param {EDDSA} eddsa - eddsa instance\n* @param {Array<Bytes>|Object} sig -\n* @param {Array<Bytes>|Point} [sig.R] - R point as Point or bytes\n* @param {Array<Bytes>|bn} [sig.S] - S scalar as bn or bytes\n* @param {Array<Bytes>} [sig.Rencoded] - R point encoded\n* @param {Array<Bytes>} [sig.Sencoded] - S scalar encoded\n*/\nfunction Signature(eddsa, sig) {\n this.eddsa = eddsa;\n\n if (typeof sig !== 'object')\n sig = parseBytes(sig);\n\n if (Array.isArray(sig)) {\n sig = {\n R: sig.slice(0, eddsa.encodingLength),\n S: sig.slice(eddsa.encodingLength),\n };\n }\n\n assert(sig.R && sig.S, 'Signature without R or S');\n\n if (eddsa.isPoint(sig.R))\n this._R = sig.R;\n if (sig.S instanceof BN)\n this._S = sig.S;\n\n this._Rencoded = Array.isArray(sig.R) ? sig.R : sig.Rencoded;\n this._Sencoded = Array.isArray(sig.S) ? sig.S : sig.Sencoded;\n}\n\ncachedProperty(Signature, 'S', function S() {\n return this.eddsa.decodeInt(this.Sencoded());\n});\n\ncachedProperty(Signature, 'R', function R() {\n return this.eddsa.decodePoint(this.Rencoded());\n});\n\ncachedProperty(Signature, 'Rencoded', function Rencoded() {\n return this.eddsa.encodePoint(this.R());\n});\n\ncachedProperty(Signature, 'Sencoded', function Sencoded() {\n return this.eddsa.encodeInt(this.S());\n});\n\nSignature.prototype.toBytes = function toBytes() {\n return this.Rencoded().concat(this.Sencoded());\n};\n\nSignature.prototype.toHex = function toHex() {\n return utils.encode(this.toBytes(), 'hex').toUpperCase();\n};\n\nmodule.exports = Signature;\n"],"names":[],"sourceRoot":""}