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BigInteger = require('bigi')\n\nvar curves = require('./curves.json')\nvar Curve = require('./curve')\n\nfunction getCurveByName (name) {\n  var curve = curves[name]\n  if (!curve) return null\n\n  var p = new BigInteger(curve.p, 16)\n  var a = new BigInteger(curve.a, 16)\n  var b = new BigInteger(curve.b, 16)\n  var n = new BigInteger(curve.n, 16)\n  var h = new BigInteger(curve.h, 16)\n  var Gx = new BigInteger(curve.Gx, 16)\n  var Gy = new BigInteger(curve.Gy, 16)\n\n  return new Curve(p, a, b, Gx, Gy, n, h)\n}\n\nmodule.exports = getCurveByName\n","var assert = require('assert')\nvar Buffer = require('safe-buffer').Buffer\nvar BigInteger = require('bigi')\n\nvar THREE = BigInteger.valueOf(3)\n\nfunction Point (curve, x, y, z) {\n  assert.notStrictEqual(z, undefined, 'Missing Z coordinate')\n\n  this.curve = curve\n  this.x = x\n  this.y = y\n  this.z = z\n  this._zInv = null\n\n  this.compressed = true\n}\n\nObject.defineProperty(Point.prototype, 'zInv', {\n  get: function () {\n    if (this._zInv === null) {\n      this._zInv = this.z.modInverse(this.curve.p)\n    }\n\n    return this._zInv\n  }\n})\n\nObject.defineProperty(Point.prototype, 'affineX', {\n  get: function () {\n    return this.x.multiply(this.zInv).mod(this.curve.p)\n  }\n})\n\nObject.defineProperty(Point.prototype, 'affineY', {\n  get: function () {\n    return this.y.multiply(this.zInv).mod(this.curve.p)\n  }\n})\n\nPoint.fromAffine = function (curve, x, y) {\n  return new Point(curve, x, y, BigInteger.ONE)\n}\n\nPoint.prototype.equals = function (other) {\n  if (other === this) return true\n  if (this.curve.isInfinity(this)) return this.curve.isInfinity(other)\n  if (this.curve.isInfinity(other)) return this.curve.isInfinity(this)\n\n  // u = Y2 * Z1 - Y1 * Z2\n  var u = other.y.multiply(this.z).subtract(this.y.multiply(other.z)).mod(this.curve.p)\n\n  if (u.signum() !== 0) return false\n\n  // v = X2 * Z1 - X1 * Z2\n  var v = other.x.multiply(this.z).subtract(this.x.multiply(other.z)).mod(this.curve.p)\n\n  return v.signum() === 0\n}\n\nPoint.prototype.negate = function () {\n  var y = this.curve.p.subtract(this.y)\n\n  return new Point(this.curve, this.x, y, this.z)\n}\n\nPoint.prototype.add = function (b) {\n  if (this.curve.isInfinity(this)) return b\n  if (this.curve.isInfinity(b)) return this\n\n  var x1 = this.x\n  var y1 = this.y\n  var x2 = b.x\n  var y2 = b.y\n\n  // u = Y2 * Z1 - Y1 * Z2\n  var u = y2.multiply(this.z).subtract(y1.multiply(b.z)).mod(this.curve.p)\n  // v = X2 * Z1 - X1 * Z2\n  var v = x2.multiply(this.z).subtract(x1.multiply(b.z)).mod(this.curve.p)\n\n  if (v.signum() === 0) {\n    if (u.signum() === 0) {\n      return this.twice() // this == b, so double\n    }\n\n    return this.curve.infinity // this = -b, so infinity\n  }\n\n  var v2 = v.square()\n  var v3 = v2.multiply(v)\n  var x1v2 = x1.multiply(v2)\n  var zu2 = u.square().multiply(this.z)\n\n  // x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)\n  var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.p)\n  // y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3\n  var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.p)\n  // z3 = v^3 * z1 * z2\n  var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.p)\n\n  return new Point(this.curve, x3, y3, z3)\n}\n\nPoint.prototype.twice = function () {\n  if (this.curve.isInfinity(this)) return this\n  if (this.y.signum() === 0) return this.curve.infinity\n\n  var x1 = this.x\n  var y1 = this.y\n\n  var y1z1 = y1.multiply(this.z).mod(this.curve.p)\n  var y1sqz1 = y1z1.multiply(y1).mod(this.curve.p)\n  var a = this.curve.a\n\n  // w = 3 * x1^2 + a * z1^2\n  var w = x1.square().multiply(THREE)\n\n  if (a.signum() !== 0) {\n    w = w.add(this.z.square().multiply(a))\n  }\n\n  w = w.mod(this.curve.p)\n  // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)\n  var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.p)\n  // y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3\n  var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.p)\n  // z3 = 8 * (y1 * z1)^3\n  var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.p)\n\n  return new Point(this.curve, x3, y3, z3)\n}\n\n// Simple NAF (Non-Adjacent Form) multiplication algorithm\n// TODO: modularize the multiplication algorithm\nPoint.prototype.multiply = function (k) {\n  if (this.curve.isInfinity(this)) return this\n  if (k.signum() === 0) return this.curve.infinity\n\n  var e = k\n  var h = e.multiply(THREE)\n\n  var neg = this.negate()\n  var R = this\n\n  for (var i = h.bitLength() - 2; i > 0; --i) {\n    var hBit = h.testBit(i)\n    var eBit = e.testBit(i)\n\n    R = R.twice()\n\n    if (hBit !== eBit) {\n      R = R.add(hBit ? this : neg)\n    }\n  }\n\n  return R\n}\n\n// Compute this*j + x*k (simultaneous multiplication)\nPoint.prototype.multiplyTwo = function (j, x, k) {\n  var i = Math.max(j.bitLength(), k.bitLength()) - 1\n  var R = this.curve.infinity\n  var both = this.add(x)\n\n  while (i >= 0) {\n    var jBit = j.testBit(i)\n    var kBit = k.testBit(i)\n\n    R = R.twice()\n\n    if (jBit) {\n      if (kBit) {\n        R = R.add(both)\n      } else {\n        R = R.add(this)\n      }\n    } else if (kBit) {\n      R = R.add(x)\n    }\n    --i\n  }\n\n  return R\n}\n\nPoint.prototype.getEncoded = function (compressed) {\n  if (compressed == null) compressed = this.compressed\n  if (this.curve.isInfinity(this)) return Buffer.alloc(1, 0) // Infinity point encoded is simply '00'\n\n  var x = this.affineX\n  var y = this.affineY\n  var byteLength = this.curve.pLength\n  var buffer\n\n  // 0x02/0x03 | X\n  if (compressed) {\n    buffer = Buffer.allocUnsafe(1 + byteLength)\n    buffer.writeUInt8(y.isEven() ? 0x02 : 0x03, 0)\n\n  // 0x04 | X | Y\n  } else {\n    buffer = Buffer.allocUnsafe(1 + byteLength + byteLength)\n    buffer.writeUInt8(0x04, 0)\n\n    y.toBuffer(byteLength).copy(buffer, 1 + byteLength)\n  }\n\n  x.toBuffer(byteLength).copy(buffer, 1)\n\n  return buffer\n}\n\nPoint.decodeFrom = function (curve, buffer) {\n  var type = buffer.readUInt8(0)\n  var compressed = (type !== 4)\n\n  var byteLength = Math.floor((curve.p.bitLength() + 7) / 8)\n  var x = BigInteger.fromBuffer(buffer.slice(1, 1 + byteLength))\n\n  var Q\n  if (compressed) {\n    assert.equal(buffer.length, byteLength + 1, 'Invalid sequence length')\n    assert(type === 0x02 || type === 0x03, 'Invalid sequence tag')\n\n    var isOdd = (type === 0x03)\n    Q = curve.pointFromX(isOdd, x)\n  } else {\n    assert.equal(buffer.length, 1 + byteLength + byteLength, 'Invalid sequence length')\n\n    var y = BigInteger.fromBuffer(buffer.slice(1 + byteLength))\n    Q = Point.fromAffine(curve, x, y)\n  }\n\n  Q.compressed = compressed\n  return Q\n}\n\nPoint.prototype.toString = function () {\n  if (this.curve.isInfinity(this)) return '(INFINITY)'\n\n  return '(' + this.affineX.toString() + ',' + this.affineY.toString() + ')'\n}\n\nmodule.exports = Point\n","var assert = require('assert')\nvar BigInteger = require('bigi')\n\nvar Point = require('./point')\n\nfunction Curve (p, a, b, Gx, Gy, n, h) {\n  this.p = p\n  this.a = a\n  this.b = b\n  this.G = Point.fromAffine(this, Gx, Gy)\n  this.n = n\n  this.h = h\n\n  this.infinity = new Point(this, null, null, BigInteger.ZERO)\n\n  // result caching\n  this.pOverFour = p.add(BigInteger.ONE).shiftRight(2)\n\n  // determine size of p in bytes\n  this.pLength = Math.floor((this.p.bitLength() + 7) / 8)\n}\n\nCurve.prototype.pointFromX = function (isOdd, x) {\n  var alpha = x.pow(3).add(this.a.multiply(x)).add(this.b).mod(this.p)\n  var beta = alpha.modPow(this.pOverFour, this.p) // XXX: not compatible with all curves\n\n  var y = beta\n  if (beta.isEven() ^ !isOdd) {\n    y = this.p.subtract(y) // -y % p\n  }\n\n  return Point.fromAffine(this, x, y)\n}\n\nCurve.prototype.isInfinity = function (Q) {\n  if (Q === this.infinity) return true\n\n  return Q.z.signum() === 0 && Q.y.signum() !== 0\n}\n\nCurve.prototype.isOnCurve = function (Q) {\n  if (this.isInfinity(Q)) return true\n\n  var x = Q.affineX\n  var y = Q.affineY\n  var a = this.a\n  var b = this.b\n  var p = this.p\n\n  // Check that xQ and yQ are integers in the interval [0, p - 1]\n  if (x.signum() < 0 || x.compareTo(p) >= 0) return false\n  if (y.signum() < 0 || y.compareTo(p) >= 0) return false\n\n  // and check that y^2 = x^3 + ax + b (mod p)\n  var lhs = y.square().mod(p)\n  var rhs = x.pow(3).add(a.multiply(x)).add(b).mod(p)\n  return lhs.equals(rhs)\n}\n\n/**\n * Validate an elliptic curve point.\n *\n * See SEC 1, section 3.2.2.1: Elliptic Curve Public Key Validation Primitive\n */\nCurve.prototype.validate = function (Q) {\n  // Check Q != O\n  assert(!this.isInfinity(Q), 'Point is at infinity')\n  assert(this.isOnCurve(Q), 'Point is not on the curve')\n\n  // Check nQ = O (where Q is a scalar multiple of G)\n  var nQ = Q.multiply(this.n)\n  assert(this.isInfinity(nQ), 'Point is not a scalar multiple of G')\n\n  return true\n}\n\nmodule.exports = Curve\n","var Point = require('./point')\nvar Curve = require('./curve')\n\nvar getCurveByName = require('./names')\n\nmodule.exports = {\n  Curve: Curve,\n  Point: Point,\n  getCurveByName: getCurveByName\n}\n"],"sourceRoot":""}