{"id":"node_modules/elliptic/lib/elliptic/curve/short.js","dependencies":[{"name":"/www/ml-classifier/example/package.json","includedInParent":true,"mtime":1551949031632},{"name":"/www/ml-classifier/example/.babelrc","includedInParent":true,"mtime":1551703756168},{"name":"/www/ml-classifier/example/node_modules/elliptic/package.json","includedInParent":true,"mtime":1542583799903},{"name":"../curve","loc":{"line":3,"column":20},"parent":"/www/ml-classifier/example/node_modules/elliptic/lib/elliptic/curve/short.js","resolved":"/www/ml-classifier/example/node_modules/elliptic/lib/elliptic/curve/index.js"},{"name":"../../elliptic","loc":{"line":4,"column":23},"parent":"/www/ml-classifier/example/node_modules/elliptic/lib/elliptic/curve/short.js","resolved":"/www/ml-classifier/example/node_modules/elliptic/lib/elliptic.js"},{"name":"bn.js","loc":{"line":5,"column":17},"parent":"/www/ml-classifier/example/node_modules/elliptic/lib/elliptic/curve/short.js","resolved":"/www/ml-classifier/example/node_modules/bn.js/lib/bn.js"},{"name":"inherits","loc":{"line":6,"column":23},"parent":"/www/ml-classifier/example/node_modules/elliptic/lib/elliptic/curve/short.js","resolved":"/www/ml-classifier/example/node_modules/inherits/inherits_browser.js"}],"generated":{"js":"'use strict';\n\nvar curve = require('../curve');\nvar elliptic = require('../../elliptic');\nvar BN = require('bn.js');\nvar inherits = require('inherits');\nvar Base = curve.base;\n\nvar assert = elliptic.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 '';\n return '';\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\n 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 if (this.curve.zeroA || this.curve.threeA) {\n var r = this;\n for (var 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 (var 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 '';\n return 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strict';\n\nvar curve = require('../curve');\nvar elliptic = require('../../elliptic');\nvar BN = require('bn.js');\nvar inherits = require('inherits');\nvar Base = curve.base;\n\nvar assert = elliptic.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 '';\n return '';\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\n 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 if (this.curve.zeroA || this.curve.threeA) {\n var r = this;\n for (var 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 (var 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 '';\n return '';\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"},"lineCount":938}},"hash":"693d2ca111f9e95d39397244bb8b440c","cacheData":{"env":{}}}