elliptic/dist/elliptic.js

(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.ellipticjs = f()}})(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
'use strict';

var elliptic = exports;

elliptic.version = require('../package.json').version;
elliptic.utils = require('./elliptic/utils');
elliptic.rand = require('brorand');
elliptic.hmacDRBG = require('./elliptic/hmac-drbg');
elliptic.curve = require('./elliptic/curve');
elliptic.curves = require('./elliptic/curves');

// Protocols
elliptic.ec = require('./elliptic/ec');

},{"../package.json":23,"./elliptic/curve":4,"./elliptic/curves":7,"./elliptic/ec":8,"./elliptic/hmac-drbg":11,"./elliptic/utils":13,"brorand":15}],2:[function(require,module,exports){
'use strict';

var bn = require('bn.js');
var elliptic = require('../../elliptic');

var getNAF = elliptic.utils.getNAF;
var getJSF = elliptic.utils.getJSF;
var assert = elliptic.utils.assert;

function BaseCurve(type, conf) {
  this.type = type;
  this.p = new bn(conf.p, 16);

  // Use Montgomery, when there is no fast reduction for the prime
  this.red = conf.prime ? bn.red(conf.prime) : bn.mont(this.p);

  // Useful for many curves
  this.zero = new bn(0).toRed(this.red);
  this.one = new bn(1).toRed(this.red);
  this.two = new bn(2).toRed(this.red);

  // Curve configuration, optional
  this.n = conf.n && new bn(conf.n, 16);
  this.g = conf.g && this.pointFromJSON(conf.g, conf.gRed);

  // Temporary arrays
  this._wnafT1 = new Array(4);
  this._wnafT2 = new Array(4);
  this._wnafT3 = new Array(4);
  this._wnafT4 = new Array(4);
}
module.exports = BaseCurve;

BaseCurve.prototype.point = function point() {
  throw new Error('Not implemented');
};

BaseCurve.prototype.validate = function validate() {
  throw new Error('Not implemented');
};

BaseCurve.prototype._fixedNafMul = function _fixedNafMul(p, k) {
  var doubles = p._getDoubles();

  var naf = getNAF(k, 1);
  var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1);
  I /= 3;

  // Translate into more windowed form
  var repr = [];
  for (var j = 0; j < naf.length; j += doubles.step) {
    var nafW = 0;
    for (var k = j + doubles.step - 1; k >= j; k--)
      nafW = (nafW << 1) + naf[k];
    repr.push(nafW);
  }

  var a = this.jpoint(null, null, null);
  var b = this.jpoint(null, null, null);
  for (var i = I; i > 0; i--) {
    for (var j = 0; j < repr.length; j++) {
      var nafW = repr[j];
      if (nafW === i)
        b = b.mixedAdd(doubles.points[j]);
      else if (nafW === -i)
        b = b.mixedAdd(doubles.points[j].neg());
    }
    a = a.add(b);
  }
  return a.toP();
};

BaseCurve.prototype._wnafMul = function _wnafMul(p, k) {
  var w = 4;

  // Precompute window
  var nafPoints = p._getNAFPoints(w);
  w = nafPoints.wnd;
  var wnd = nafPoints.points;

  // Get NAF form
  var naf = getNAF(k, w);

  // Add `this`*(N+1) for every w-NAF index
  var acc = this.jpoint(null, null, null);
  for (var i = naf.length - 1; i >= 0; i--) {
    // Count zeroes
    for (var k = 0; i >= 0 && naf[i] === 0; i--)
      k++;
    if (i >= 0)
      k++;
    acc = acc.dblp(k);

    if (i < 0)
      break;
    var z = naf[i];
    assert(z !== 0);
    if (p.type === 'affine') {
      // J +- P
      if (z > 0)
        acc = acc.mixedAdd(wnd[(z - 1) >> 1]);
      else
        acc = acc.mixedAdd(wnd[(-z - 1) >> 1].neg());
    } else {
      // J +- J
      if (z > 0)
        acc = acc.add(wnd[(z - 1) >> 1]);
      else
        acc = acc.add(wnd[(-z - 1) >> 1].neg());
    }
  }
  return p.type === 'affine' ? acc.toP() : acc;
};

BaseCurve.prototype._wnafMulAdd = function _wnafMulAdd(defW,
                                                       points,
                                                       coeffs,
                                                       len) {
  var wndWidth = this._wnafT1;
  var wnd = this._wnafT2;
  var naf = this._wnafT3;

  // Fill all arrays
  var max = 0;
  for (var i = 0; i < len; i++) {
    var p = points[i];
    var nafPoints = p._getNAFPoints(defW);
    wndWidth[i] = nafPoints.wnd;
    wnd[i] = nafPoints.points;
  }

  // Comb small window NAFs
  for (var i = len - 1; i >= 1; i -= 2) {
    var a = i - 1;
    var b = i;
    if (wndWidth[a] !== 1 || wndWidth[b] !== 1) {
      naf[a] = getNAF(coeffs[a], wndWidth[a]);
      naf[b] = getNAF(coeffs[b], wndWidth[b]);
      max = Math.max(naf[a].length, max);
      max = Math.max(naf[b].length, max);
      continue;
    }

    var comb = [
      points[a], /* 1 */
      null, /* 3 */
      null, /* 5 */
      points[b] /* 7 */
    ];

    // Try to avoid Projective points, if possible
    if (points[a].y.cmp(points[b].y) === 0) {
      comb[1] = points[a].add(points[b]);
      comb[2] = points[a].toJ().mixedAdd(points[b].neg());
    } else if (points[a].y.cmp(points[b].y.redNeg()) === 0) {
      comb[1] = points[a].toJ().mixedAdd(points[b]);
      comb[2] = points[a].add(points[b].neg());
    } else {
      comb[1] = points[a].toJ().mixedAdd(points[b]);
      comb[2] = points[a].toJ().mixedAdd(points[b].neg());
    }

    var index = [
      -3, /* -1 -1 */
      -1, /* -1 0 */
      -5, /* -1 1 */
      -7, /* 0 -1 */
      0, /* 0 0 */
      7, /* 0 1 */
      5, /* 1 -1 */
      1, /* 1 0 */
      3  /* 1 1 */
    ];

    var jsf = getJSF(coeffs[a], coeffs[b]);
    max = Math.max(jsf[0].length, max);
    naf[a] = new Array(max);
    naf[b] = new Array(max);
    for (var j = 0; j < max; j++) {
      var ja = jsf[0][j] | 0;
      var jb = jsf[1][j] | 0;

      naf[a][j] = index[(ja + 1) * 3 + (jb + 1)];
      naf[b][j] = 0;
      wnd[a] = comb;
    }
  }

  var acc = this.jpoint(null, null, null);
  var tmp = this._wnafT4;
  for (var i = max; i >= 0; i--) {
    var k = 0;

    while (i >= 0) {
      var zero = true;
      for (var j = 0; j < len; j++) {
        tmp[j] = naf[j][i] | 0;
        if (tmp[j] !== 0)
          zero = false;
      }
      if (!zero)
        break;
      k++;
      i--;
    }
    if (i >= 0)
      k++;
    acc = acc.dblp(k);
    if (i < 0)
      break;

    for (var j = 0; j < len; j++) {
      var z = tmp[j];
      var p;
      if (z === 0)
        continue;
      else if (z > 0)
        p = wnd[j][(z - 1) >> 1];
      else if (z < 0)
        p = wnd[j][(-z - 1) >> 1].neg();

      if (p.type === 'affine')
        acc = acc.mixedAdd(p);
      else
        acc = acc.add(p);
    }
  }
  // Zeroify references
  for (var i = 0; i < len; i++)
    wnd[i] = null;
  return acc.toP();
};

function BasePoint(curve, type) {
  this.curve = curve;
  this.type = type;
  this.precomputed = null;
}
BaseCurve.BasePoint = BasePoint;

BasePoint.prototype.validate = function validate() {
  return this.curve.validate(this);
};

BasePoint.prototype.precompute = function precompute(power) {
  if (this.precomputed)
    return this;

  var precomputed = {
    doubles: null,
    naf: null,
    beta: null
  };
  precomputed.naf = this._getNAFPoints(8);
  precomputed.doubles = this._getDoubles(4, power);
  precomputed.beta = this._getBeta();
  this.precomputed = precomputed;

  return this;
};

BasePoint.prototype._getDoubles = function _getDoubles(step, power) {
  if (this.precomputed && this.precomputed.doubles)
    return this.precomputed.doubles;

  var doubles = [ this ];
  var acc = this;
  for (var i = 0; i < power; i += step) {
    for (var j = 0; j < step; j++)
      acc = acc.dbl();
    doubles.push(acc);
  }
  return {
    step: step,
    points: doubles
  };
};

BasePoint.prototype._getNAFPoints = function _getNAFPoints(wnd) {
  if (this.precomputed && this.precomputed.naf)
    return this.precomputed.naf;

  var res = [ this ];
  var max = (1 << wnd) - 1;
  var dbl = max === 1 ? null : this.dbl();
  for (var i = 1; i < max; i++)
    res[i] = res[i - 1].add(dbl);
  return {
    wnd: wnd,
    points: res
  };
};

BasePoint.prototype._getBeta = function _getBeta() {
  return null;
};

BasePoint.prototype.dblp = function dblp(k) {
  var r = this;
  for (var i = 0; i < k; i++)
    r = r.dbl();
  return r;
};

},{"../../elliptic":1,"bn.js":14}],3:[function(require,module,exports){
'use strict';

var curve = require('../curve');
var elliptic = require('../../elliptic');
var bn = require('bn.js');
var inherits = require('inherits');
var Base = curve.base;

var assert = elliptic.utils.assert;

function EdwardsCurve(conf) {
  // NOTE: Important as we are creating point in Base.call()
  this.twisted = (conf.a | 0) !== 1;
  this.mOneA = this.twisted && (conf.a | 0) === -1;
  this.extended = this.mOneA;

  Base.call(this, 'edwards', conf);

  this.a = new bn(conf.a, 16).mod(this.red.m).toRed(this.red);
  this.c = new bn(conf.c, 16).toRed(this.red);
  this.c2 = this.c.redSqr();
  this.d = new bn(conf.d, 16).toRed(this.red);
  this.dd = this.d.redAdd(this.d);

  assert(!this.twisted || this.c.fromRed().cmpn(1) === 0);
  this.oneC = (conf.c | 0) === 1;
}
inherits(EdwardsCurve, Base);
module.exports = EdwardsCurve;

EdwardsCurve.prototype._mulA = function _mulA(num) {
  if (this.mOneA)
    return num.redNeg();
  else
    return this.a.redMul(num);
};

EdwardsCurve.prototype._mulC = function _mulC(num) {
  if (this.oneC)
    return num;
  else
    return this.c.redMul(num);
};

// Just for compatibility with Short curve
EdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {
  return this.point(x, y, z, t);
};

EdwardsCurve.prototype.pointFromX = function pointFromX(odd, x) {
  x = new bn(x, 16);
  if (!x.red)
    x = x.toRed(this.red);

  var x2 = x.redSqr();
  var rhs = this.c2.redSub(this.a.redMul(x2));
  var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));

  var y = rhs.redMul(lhs.redInvm()).redSqrt();
  var isOdd = y.fromRed().isOdd();
  if (odd && !isOdd || !odd && isOdd)
    y = y.redNeg();

  return this.point(x, y, curve.one);
};

EdwardsCurve.prototype.validate = function validate(point) {
  if (point.isInfinity())
    return true;

  // Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)
  point.normalize();

  var x2 = point.x.redSqr();
  var y2 = point.y.redSqr();
  var lhs = x2.redMul(this.a).redAdd(y2);
  var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));

  return lhs.cmp(rhs) === 0;
};

function Point(curve, x, y, z, t) {
  Base.BasePoint.call(this, curve, 'projective');
  if (x === null && y === null && z === null) {
    this.x = this.curve.zero;
    this.y = this.curve.one;
    this.z = this.curve.one;
    this.t = this.curve.zero;
    this.zOne = true;
  } else {
    this.x = new bn(x, 16);
    this.y = new bn(y, 16);
    this.z = z ? new bn(z, 16) : this.curve.one;
    this.t = t && new bn(t, 16);
    if (!this.x.red)
      this.x = this.x.toRed(this.curve.red);
    if (!this.y.red)
      this.y = this.y.toRed(this.curve.red);
    if (!this.z.red)
      this.z = this.z.toRed(this.curve.red);
    if (this.t && !this.t.red)
      this.t = this.t.toRed(this.curve.red);
    this.zOne = this.z === this.curve.one;

    // Use extended coordinates
    if (this.curve.extended && !this.t) {
      this.t = this.x.redMul(this.y);
      if (!this.zOne)
        this.t = this.t.redMul(this.z.redInvm());
    }
  }
}
inherits(Point, Base.BasePoint);

EdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
  return Point.fromJSON(this, obj);
};

EdwardsCurve.prototype.point = function point(x, y, z, t) {
  return new Point(this, x, y, z, t);
};

Point.fromJSON = function fromJSON(curve, obj) {
  return new Point(curve, obj[0], obj[1], obj[2]);
};

Point.prototype.inspect = function inspect() {
  if (this.isInfinity())
    return '<EC Point Infinity>';
  return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
      ' y: ' + this.y.fromRed().toString(16, 2) +
      ' z: ' + this.z.fromRed().toString(16, 2) + '>';
};

Point.prototype.isInfinity = function isInfinity() {
  // XXX This code assumes that zero is always zero in red
  return this.x.cmpn(0) === 0 &&
         this.y.cmp(this.z) === 0;
};

Point.prototype._extDbl = function _extDbl() {
  // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
  //     #doubling-dbl-2008-hwcd
  // 4M + 4S

  // A = X1^2
  var a = this.x.redSqr();
  // B = Y1^2
  var b = this.y.redSqr();
  // C = 2 * Z1^2
  var c = this.z.redSqr();
  c = c.redIAdd(c);
  // D = a * A
  var d = this.curve._mulA(a);
  // E = (X1 + Y1)^2 - A - B
  var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);
  // G = D + B
  var g = d.redAdd(b);
  // F = G - C
  var f = g.redSub(c);
  // H = D - B
  var h = d.redSub(b);
  // X3 = E * F
  var nx = e.redMul(f);
  // Y3 = G * H
  var ny = g.redMul(h);
  // T3 = E * H
  var nt = e.redMul(h);
  // Z3 = F * G
  var nz = f.redMul(g);
  return this.curve.point(nx, ny, nz, nt);
};

Point.prototype._projDbl = function _projDbl() {
  // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
  //     #doubling-dbl-2008-bbjlp
  //     #doubling-dbl-2007-bl
  // and others
  // Generally 3M + 4S or 2M + 4S

  // B = (X1 + Y1)^2
  var b = this.x.redAdd(this.y).redSqr();
  // C = X1^2
  var c = this.x.redSqr();
  // D = Y1^2
  var d = this.y.redSqr();

  var nx;
  var ny;
  var nz;
  if (this.curve.twisted) {
    // E = a * C
    var e = this.curve._mulA(c);
    // F = E + D
    var f = e.redAdd(d);
    if (this.zOne) {
      // X3 = (B - C - D) * (F - 2)
      nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));
      // Y3 = F * (E - D)
      ny = f.redMul(e.redSub(d));
      // Z3 = F^2 - 2 * F
      nz = f.redSqr().redSub(f).redSub(f);
    } else {
      // H = Z1^2
      var h = this.z.redSqr();
      // J = F - 2 * H
      var j = f.redSub(h).redISub(h);
      // X3 = (B-C-D)*J
      nx = b.redSub(c).redISub(d).redMul(j);
      // Y3 = F * (E - D)
      ny = f.redMul(e.redSub(d));
      // Z3 = F * J
      nz = f.redMul(j);
    }
  } else {
    // E = C + D
    var e = c.redAdd(d);
    // H = (c * Z1)^2
    var h = this.curve._mulC(this.c.redMul(this.z)).redSqr();
    // J = E - 2 * H
    var j = e.redSub(h).redSub(h);
    // X3 = c * (B - E) * J
    nx = this.curve._mulC(b.redISub(e)).redMul(j);
    // Y3 = c * E * (C - D)
    ny = this.curve._mulC(e).redMul(c.redISub(d));
    // Z3 = E * J
    nz = e.redMul(j);
  }
  return this.curve.point(nx, ny, nz);
};

Point.prototype.dbl = function dbl() {
  if (this.isInfinity())
    return this;

  // Double in extended coordinates
  if (this.curve.extended)
    return this._extDbl();
  else
    return this._projDbl();
};

Point.prototype._extAdd = function _extAdd(p) {
  // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
  //     #addition-add-2008-hwcd-3
  // 8M

  // A = (Y1 - X1) * (Y2 - X2)
  var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));
  // B = (Y1 + X1) * (Y2 + X2)
  var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));
  // C = T1 * k * T2
  var c = this.t.redMul(this.curve.dd).redMul(p.t);
  // D = Z1 * 2 * Z2
  var d = this.z.redMul(p.z.redAdd(p.z));
  // E = B - A
  var e = b.redSub(a);
  // F = D - C
  var f = d.redSub(c);
  // G = D + C
  var g = d.redAdd(c);
  // H = B + A
  var h = b.redAdd(a);
  // X3 = E * F
  var nx = e.redMul(f);
  // Y3 = G * H
  var ny = g.redMul(h);
  // T3 = E * H
  var nt = e.redMul(h);
  // Z3 = F * G
  var nz = f.redMul(g);
  return this.curve.point(nx, ny, nz, nt);
};

Point.prototype._projAdd = function _projAdd(p) {
  // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
  //     #addition-add-2008-bbjlp
  //     #addition-add-2007-bl
  // 10M + 1S

  // A = Z1 * Z2
  var a = this.z.redMul(p.z);
  // B = A^2
  var b = a.redSqr();
  // C = X1 * X2
  var c = this.x.redMul(p.x);
  // D = Y1 * Y2
  var d = this.y.redMul(p.y);
  // E = d * C * D
  var e = this.curve.d.redMul(c).redMul(d);
  // F = B - E
  var f = b.redSub(e);
  // G = B + E
  var g = b.redAdd(e);
  // X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)
  var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);
  var nx = a.redMul(f).redMul(tmp);
  var ny;
  var nz;
  if (this.curve.twisted) {
    // Y3 = A * G * (D - a * C)
    ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));
    // Z3 = F * G
    nz = f.redMul(g);
  } else {
    // Y3 = A * G * (D - C)
    ny = a.redMul(g).redMul(d.redSub(c));
    // Z3 = c * F * G
    nz = this.curve._mulC(f).redMul(g);
  }
  return this.curve.point(nx, ny, nz);
};

Point.prototype.add = function add(p) {
  if (this.isInfinity())
    return p;
  if (p.isInfinity())
    return this;

  if (this.curve.extended)
    return this._extAdd(p);
  else
    return this._projAdd(p);
};

Point.prototype.mul = function mul(k) {
  if (this.precomputed && this.precomputed.doubles)
    return this.curve._fixedNafMul(this, k);
  else
    return this.curve._wnafMul(this, k);
};

Point.prototype.mulAdd = function mulAdd(k1, p, k2) {
  return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2);
};

Point.prototype.normalize = function normalize() {
  if (this.zOne)
    return this;

  // Normalize coordinates
  var zi = this.z.redInvm();
  this.x = this.x.redMul(zi);
  this.y = this.y.redMul(zi);
  if (this.t)
    this.t = this.t.redMul(zi);
  this.z = this.curve.one;
  this.zOne = true;
  return this;
};

Point.prototype.neg = function neg() {
  return this.curve.point(this.x.redNeg(),
                          this.y,
                          this.z,
                          this.t && this.t.redNeg());
};

Point.prototype.getX = function getX() {
  this.normalize();
  return this.x.fromRed();
};

Point.prototype.getY = function getY() {
  this.normalize();
  return this.y.fromRed();
};

// Compatibility with BaseCurve
Point.prototype.toP = Point.prototype.normalize;
Point.prototype.mixedAdd = Point.prototype.add;

},{"../../elliptic":1,"../curve":4,"bn.js":14,"inherits":22}],4:[function(require,module,exports){
'use strict';

var curve = exports;

curve.base = require('./base');
curve.short = require('./short');
curve.mont = require('./mont');
curve.edwards = require('./edwards');

},{"./base":2,"./edwards":3,"./mont":5,"./short":6}],5:[function(require,module,exports){
'use strict';

var curve = require('../curve');
var bn = require('bn.js');
var inherits = require('inherits');
var Base = curve.base;

function MontCurve(conf) {
  Base.call(this, 'mont', conf);

  this.a = new bn(conf.a, 16).toRed(this.red);
  this.b = new bn(conf.b, 16).toRed(this.red);
  this.i4 = new bn(4).toRed(this.red).redInvm();
  this.two = new bn(2).toRed(this.red);
  this.a24 = this.i4.redMul(this.a.redAdd(this.two));
}
inherits(MontCurve, Base);
module.exports = MontCurve;

MontCurve.prototype.validate = function validate(point) {
  var x = point.normalize().x;
  var x2 = x.redSqr();
  var rhs = x2.redMul(x).redAdd(x2.redMul(this.a)).redAdd(x);
  var y = rhs.redSqrt();

  return y.redSqr().cmp(rhs) === 0;
};

function Point(curve, x, z) {
  Base.BasePoint.call(this, curve, 'projective');
  if (x === null && z === null) {
    this.x = this.curve.one;
    this.z = this.curve.zero;
  } else {
    this.x = new bn(x, 16);
    this.z = new bn(z, 16);
    if (!this.x.red)
      this.x = this.x.toRed(this.curve.red);
    if (!this.z.red)
      this.z = this.z.toRed(this.curve.red);
  }
}
inherits(Point, Base.BasePoint);

MontCurve.prototype.point = function point(x, z) {
  return new Point(this, x, z);
};

MontCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
  return Point.fromJSON(this, obj);
};

Point.prototype.precompute = function precompute() {
  // No-op
};

Point.fromJSON = function fromJSON(curve, obj) {
  return new Point(curve, obj[0], obj[1] || curve.one);
};

Point.prototype.inspect = function inspect() {
  if (this.isInfinity())
    return '<EC Point Infinity>';
  return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
      ' z: ' + this.z.fromRed().toString(16, 2) + '>';
};

Point.prototype.isInfinity = function isInfinity() {
  // XXX This code assumes that zero is always zero in red
  return this.z.cmpn(0) === 0;
};

Point.prototype.dbl = function dbl() {
  // http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#doubling-dbl-1987-m-3
  // 2M + 2S + 4A

  // A = X1 + Z1
  var a = this.x.redAdd(this.z);
  // AA = A^2
  var aa = a.redSqr();
  // B = X1 - Z1
  var b = this.x.redSub(this.z);
  // BB = B^2
  var bb = b.redSqr();
  // C = AA - BB
  var c = aa.redSub(bb);
  // X3 = AA * BB
  var nx = aa.redMul(bb);
  // Z3 = C * (BB + A24 * C)
  var nz = c.redMul(bb.redAdd(this.curve.a24.redMul(c)));
  return this.curve.point(nx, nz);
};

Point.prototype.add = function add() {
  throw new Error('Not supported on Montgomery curve');
};

Point.prototype.diffAdd = function diffAdd(p, diff) {
  // http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#diffadd-dadd-1987-m-3
  // 4M + 2S + 6A

  // A = X2 + Z2
  var a = this.x.redAdd(this.z);
  // B = X2 - Z2
  var b = this.x.redSub(this.z);
  // C = X3 + Z3
  var c = p.x.redAdd(p.z);
  // D = X3 - Z3
  var d = p.x.redSub(p.z);
  // DA = D * A
  var da = d.redMul(a);
  // CB = C * B
  var cb = c.redMul(b);
  // X5 = Z1 * (DA + CB)^2
  var nx = diff.z.redMul(da.redAdd(cb).redSqr());
  // Z5 = X1 * (DA - CB)^2
  var nz = diff.x.redMul(da.redISub(cb).redSqr());
  return this.curve.point(nx, nz);
};

Point.prototype.mul = function mul(k) {
  var t = k.clone();
  var a = this; // (N / 2) * Q + Q
  var b = this.curve.point(null, null); // (N / 2) * Q
  var c = this; // Q

  for (var bits = []; t.cmpn(0) !== 0; t.ishrn(1))
    bits.push(t.andln(1));

  for (var i = bits.length - 1; i >= 0; i--) {
    if (bits[i] === 0) {
      // N * Q + Q = ((N / 2) * Q + Q)) + (N / 2) * Q
      a = a.diffAdd(b, c);
      // N * Q = 2 * ((N / 2) * Q + Q))
      b = b.dbl();
    } else {
      // N * Q = ((N / 2) * Q + Q) + ((N / 2) * Q)
      b = a.diffAdd(b, c);
      // N * Q + Q = 2 * ((N / 2) * Q + Q)
      a = a.dbl();
    }
  }
  return b;
};

Point.prototype.mulAdd = function mulAdd() {
  throw new Error('Not supported on Montgomery curve');
};

Point.prototype.normalize = function normalize() {
  this.x = this.x.redMul(this.z.redInvm());
  this.z = this.curve.one;
  return this;
};

Point.prototype.getX = function getX() {
  // Normalize coordinates
  this.normalize();

  return this.x.fromRed();
};

},{"../curve":4,"bn.js":14,"inherits":22}],6:[function(require,module,exports){
'use strict';

var curve = require('../curve');
var elliptic = require('../../elliptic');
var bn = require('bn.js');
var inherits = require('inherits');
var Base = curve.base;

var assert = elliptic.utils.assert;

function ShortCurve(conf) {
  Base.call(this, 'short', conf);

  this.a = new bn(conf.a, 16).toRed(this.red);
  this.b = new bn(conf.b, 16).toRed(this.red);
  this.tinv = this.two.redInvm();

  this.zeroA = this.a.fromRed().cmpn(0) === 0;
  this.threeA = this.a.fromRed().sub(this.p).cmpn(-3) === 0;

  // If the curve is endomorphic, precalculate beta and lambda
  this.endo = this._getEndomorphism(conf);
  this._endoWnafT1 = new Array(4);
  this._endoWnafT2 = new Array(4);
}
inherits(ShortCurve, Base);
module.exports = ShortCurve;

ShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {
  // No efficient endomorphism
  if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)
    return;

  // Compute beta and lambda, that lambda * P = (beta * Px; Py)
  var beta;
  var lambda;
  if (conf.beta) {
    beta = new bn(conf.beta, 16).toRed(this.red);
  } else {
    var betas = this._getEndoRoots(this.p);
    // Choose the smallest beta
    beta = betas[0].cmp(betas[1]) < 0 ? betas[0] : betas[1];
    beta = beta.toRed(this.red);
  }
  if (conf.lambda) {
    lambda = new bn(conf.lambda, 16);
  } else {
    // Choose the lambda that is matching selected beta
    var lambdas = this._getEndoRoots(this.n);
    if (this.g.mul(lambdas[0]).x.cmp(this.g.x.redMul(beta)) === 0) {
      lambda = lambdas[0];
    } else {
      lambda = lambdas[1];
      assert(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);
    }
  }

  // Get basis vectors, used for balanced length-two representation
  var basis;
  if (conf.basis) {
    basis = conf.basis.map(function(vec) {
      return {
        a: new bn(vec.a, 16),
        b: new bn(vec.b, 16)
      };
    });
  } else {
    basis = this._getEndoBasis(lambda);
  }

  return {
    beta: beta,
    lambda: lambda,
    basis: basis
  };
};

ShortCurve.prototype._getEndoRoots = function _getEndoRoots(num) {
  // Find roots of for x^2 + x + 1 in F
  // Root = (-1 +- Sqrt(-3)) / 2
  //
  var red = num === this.p ? this.red : bn.mont(num);
  var tinv = new bn(2).toRed(red).redInvm();
  var ntinv = tinv.redNeg();

  var s = new bn(3).toRed(red).redNeg().redSqrt().redMul(tinv);

  var l1 = ntinv.redAdd(s).fromRed();
  var l2 = ntinv.redSub(s).fromRed();
  return [ l1, l2 ];
};

ShortCurve.prototype._getEndoBasis = function _getEndoBasis(lambda) {
  // aprxSqrt >= sqrt(this.n)
  var aprxSqrt = this.n.shrn(Math.floor(this.n.bitLength() / 2));

  // 3.74
  // Run EGCD, until r(L + 1) < aprxSqrt
  var u = lambda;
  var v = this.n.clone();
  var x1 = new bn(1);
  var y1 = new bn(0);
  var x2 = new bn(0);
  var y2 = new bn(1);

  // NOTE: all vectors are roots of: a + b * lambda = 0 (mod n)
  var a0;
  var b0;
  // First vector
  var a1;
  var b1;
  // Second vector
  var a2;
  var b2;

  var prevR;
  var i = 0;
  var r;
  var x;
  while (u.cmpn(0) !== 0) {
    var q = v.div(u);
    r = v.sub(q.mul(u));
    x = x2.sub(q.mul(x1));
    var y = y2.sub(q.mul(y1));

    if (!a1 && r.cmp(aprxSqrt) < 0) {
      a0 = prevR.neg();
      b0 = x1;
      a1 = r.neg();
      b1 = x;
    } else if (a1 && ++i === 2) {
      break;
    }
    prevR = r;

    v = u;
    u = r;
    x2 = x1;
    x1 = x;
    y2 = y1;
    y1 = y;
  }
  a2 = r.neg();
  b2 = x;

  var len1 = a1.sqr().add(b1.sqr());
  var len2 = a2.sqr().add(b2.sqr());
  if (len2.cmp(len1) >= 0) {
    a2 = a0;
    b2 = b0;
  }

  // Normalize signs
  if (a1.sign) {
    a1 = a1.neg();
    b1 = b1.neg();
  }
  if (a2.sign) {
    a2 = a2.neg();
    b2 = b2.neg();
  }

  return [
    { a: a1, b: b1 },
    { a: a2, b: b2 }
  ];
};

ShortCurve.prototype._endoSplit = function _endoSplit(k) {
  var basis = this.endo.basis;
  var v1 = basis[0];
  var v2 = basis[1];

  var c1 = v2.b.mul(k).divRound(this.n);
  var c2 = v1.b.neg().mul(k).divRound(this.n);

  var p1 = c1.mul(v1.a);
  var p2 = c2.mul(v2.a);
  var q1 = c1.mul(v1.b);
  var q2 = c2.mul(v2.b);

  // Calculate answer
  var k1 = k.sub(p1).sub(p2);
  var k2 = q1.add(q2).neg();
  return { k1: k1, k2: k2 };
};

ShortCurve.prototype.pointFromX = function pointFromX(odd, x) {
  x = new bn(x, 16);
  if (!x.red)
    x = x.toRed(this.red);

  var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);
  var y = y2.redSqrt();

  // XXX Is there any way to tell if the number is odd without converting it
  // to non-red form?
  var isOdd = y.fromRed().isOdd();
  if (odd && !isOdd || !odd && isOdd)
    y = y.redNeg();

  return this.point(x, y);
};

ShortCurve.prototype.validate = function validate(point) {
  if (point.inf)
    return true;

  var x = point.x;
  var y = point.y;

  var ax = this.a.redMul(x);
  var rhs = x.redSqr().redMul(x).redIAdd(ax).redIAdd(this.b);
  return y.redSqr().redISub(rhs).cmpn(0) === 0;
};

ShortCurve.prototype._endoWnafMulAdd =
    function _endoWnafMulAdd(points, coeffs) {
  var npoints = this._endoWnafT1;
  var ncoeffs = this._endoWnafT2;
  for (var i = 0; i < points.length; i++) {
    var split = this._endoSplit(coeffs[i]);
    var p = points[i];
    var beta = p._getBeta();

    if (split.k1.sign) {
      split.k1.sign = !split.k1.sign;
      p = p.neg(true);
    }
    if (split.k2.sign) {
      split.k2.sign = !split.k2.sign;
      beta = beta.neg(true);
    }

    npoints[i * 2] = p;
    npoints[i * 2 + 1] = beta;
    ncoeffs[i * 2] = split.k1;
    ncoeffs[i * 2 + 1] = split.k2;
  }
  var res = this._wnafMulAdd(1, npoints, ncoeffs, i * 2);

  // Clean-up references to points and coefficients
  for (var j = 0; j < i * 2; j++) {
    npoints[j] = null;
    ncoeffs[j] = null;
  }
  return res;
};

function Point(curve, x, y, isRed) {
  Base.BasePoint.call(this, curve, 'affine');
  if (x === null && y === null) {
    this.x = null;
    this.y = null;
    this.inf = true;
  } else {
    this.x = new bn(x, 16);
    this.y = new bn(y, 16);
    // Force redgomery representation when loading from JSON
    if (isRed) {
      this.x.forceRed(this.curve.red);
      this.y.forceRed(this.curve.red);
    }
    if (!this.x.red)
      this.x = this.x.toRed(this.curve.red);
    if (!this.y.red)
      this.y = this.y.toRed(this.curve.red);
    this.inf = false;
  }
}
inherits(Point, Base.BasePoint);

ShortCurve.prototype.point = function point(x, y, isRed) {
  return new Point(this, x, y, isRed);
};

ShortCurve.prototype.pointFromJSON = function pointFromJSON(obj, red) {
  return Point.fromJSON(this, obj, red);
};

Point.prototype._getBeta = function _getBeta() {
  if (!this.curve.endo)
    return;

  var pre = this.precomputed;
  if (pre && pre.beta)
    return pre.beta;

  var beta = this.curve.point(this.x.redMul(this.curve.endo.beta), this.y);
  if (pre) {
    var curve = this.curve;
    var endoMul = function(p) {
      return curve.point(p.x.redMul(curve.endo.beta), p.y);
    };
    pre.beta = beta;
    beta.precomputed = {
      beta: null,
      naf: pre.naf && {
        wnd: pre.naf.wnd,
        points: pre.naf.points.map(endoMul)
      },
      doubles: pre.doubles && {
        step: pre.doubles.step,
        points: pre.doubles.points.map(endoMul)
      }
    };
  }
  return beta;
};

Point.prototype.toJSON = function toJSON() {
  if (!this.precomputed)
    return [ this.x, this.y ];

  return [ this.x, this.y, this.precomputed && {
    doubles: this.precomputed.doubles && {
      step: this.precomputed.doubles.step,
      points: this.precomputed.doubles.points.slice(1)
    },
    naf: this.precomputed.naf && {
      wnd: this.precomputed.naf.wnd,
      points: this.precomputed.naf.points.slice(1)
    }
  } ];
};

Point.fromJSON = function fromJSON(curve, obj, red) {
  if (typeof obj === 'string')
    obj = JSON.parse(obj);
  var res = curve.point(obj[0], obj[1], red);
  if (!obj[2])
    return res;

  function obj2point(obj) {
    return curve.point(obj[0], obj[1], red);
  }

  var pre = obj[2];
  res.precomputed = {
    beta: null,
    doubles: pre.doubles && {
      step: pre.doubles.step,
      points: [ res ].concat(pre.doubles.points.map(obj2point))
    },
    naf: pre.naf && {
      wnd: pre.naf.wnd,
      points: [ res ].concat(pre.naf.points.map(obj2point))
    }
  };
  return res;
};

Point.prototype.inspect = function inspect() {
  if (this.isInfinity())
    return '<EC Point Infinity>';
  return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
      ' y: ' + this.y.fromRed().toString(16, 2) + '>';
};

Point.prototype.isInfinity = function isInfinity() {
  return this.inf;
};

Point.prototype.add = function add(p) {
  // O + P = P
  if (this.inf)
    return p;

  // P + O = P
  if (p.inf)
    return this;

  // P + P = 2P
  if (this.eq(p))
    return this.dbl();

  // P + (-P) = O
  if (this.neg().eq(p))
    return this.curve.point(null, null);

  // P + Q = O
  if (this.x.cmp(p.x) === 0)
    return this.curve.point(null, null);

  var c = this.y.redSub(p.y);
  if (c.cmpn(0) !== 0)
    c = c.redMul(this.x.redSub(p.x).redInvm());
  var nx = c.redSqr().redISub(this.x).redISub(p.x);
  var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
  return this.curve.point(nx, ny);
};

Point.prototype.dbl = function dbl() {
  if (this.inf)
    return this;

  // 2P = O
  var ys1 = this.y.redAdd(this.y);
  if (ys1.cmpn(0) === 0)
    return this.curve.point(null, null);

  var a = this.curve.a;

  var x2 = this.x.redSqr();
  var dyinv = ys1.redInvm();
  var c = x2.redAdd(x2).redIAdd(x2).redIAdd(a).redMul(dyinv);

  var nx = c.redSqr().redISub(this.x.redAdd(this.x));
  var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
  return this.curve.point(nx, ny);
};

Point.prototype.getX = function getX() {
  return this.x.fromRed();
};

Point.prototype.getY = function getY() {
  return this.y.fromRed();
};

Point.prototype.mul = function mul(k) {
  k = new bn(k, 16);

  if (this.precomputed && this.precomputed.doubles)
    return this.curve._fixedNafMul(this, k);
  else if (this.curve.endo)
    return this.curve._endoWnafMulAdd([ this ], [ k ]);
  else
    return this.curve._wnafMul(this, k);
};

Point.prototype.mulAdd = function mulAdd(k1, p2, k2) {
  var points = [ this, p2 ];
  var coeffs = [ k1, k2 ];
  if (this.curve.endo)
    return this.curve._endoWnafMulAdd(points, coeffs);
  else
    return this.curve._wnafMulAdd(1, points, coeffs, 2);
};

Point.prototype.eq = function eq(p) {
  return this === p ||
         this.inf === p.inf &&
             (this.inf || this.x.cmp(p.x) === 0 && this.y.cmp(p.y) === 0);
};

Point.prototype.neg = function neg(_precompute) {
  if (this.inf)
    return this;

  var res = this.curve.point(this.x, this.y.redNeg());
  if (_precompute && this.precomputed) {
    var pre = this.precomputed;
    var negate = function(p) {
      return p.neg();
    };
    res.precomputed = {
      naf: pre.naf && {
        wnd: pre.naf.wnd,
        points: pre.naf.points.map(negate)
      },
      doubles: pre.doubles && {
        step: pre.doubles.step,
        points: pre.doubles.points.map(negate)
      }
    };
  }
  return res;
};

Point.prototype.toJ = function toJ() {
  if (this.inf)
    return this.curve.jpoint(null, null, null);

  var res = this.curve.jpoint(this.x, this.y, this.curve.one);
  return res;
};

function JPoint(curve, x, y, z) {
  Base.BasePoint.call(this, curve, 'jacobian');
  if (x === null && y === null && z === null) {
    this.x = this.curve.one;
    this.y = this.curve.one;
    this.z = new bn(0);
  } else {
    this.x = new bn(x, 16);
    this.y = new bn(y, 16);
    this.z = new bn(z, 16);
  }
  if (!this.x.red)
    this.x = this.x.toRed(this.curve.red);
  if (!this.y.red)
    this.y = this.y.toRed(this.curve.red);
  if (!this.z.red)
    this.z = this.z.toRed(this.curve.red);

  this.zOne = this.z === this.curve.one;
}
inherits(JPoint, Base.BasePoint);

ShortCurve.prototype.jpoint = function jpoint(x, y, z) {
  return new JPoint(this, x, y, z);
};

JPoint.prototype.toP = function toP() {
  if (this.isInfinity())
    return this.curve.point(null, null);

  var zinv = this.z.redInvm();
  var zinv2 = zinv.redSqr();
  var ax = this.x.redMul(zinv2);
  var ay = this.y.redMul(zinv2).redMul(zinv);

  return this.curve.point(ax, ay);
};

JPoint.prototype.neg = function neg() {
  return this.curve.jpoint(this.x, this.y.redNeg(), this.z);
};

JPoint.prototype.add = function add(p) {
  // O + P = P
  if (this.isInfinity())
    return p;

  // P + O = P
  if (p.isInfinity())
    return this;

  // 12M + 4S + 7A
  var pz2 = p.z.redSqr();
  var z2 = this.z.redSqr();
  var u1 = this.x.redMul(pz2);
  var u2 = p.x.redMul(z2);
  var s1 = this.y.redMul(pz2.redMul(p.z));
  var s2 = p.y.redMul(z2.redMul(this.z));

  var h = u1.redSub(u2);
  var r = s1.redSub(s2);
  if (h.cmpn(0) === 0) {
    if (r.cmpn(0) !== 0)
      return this.curve.jpoint(null, null, null);
    else
      return this.dbl();
  }

  var h2 = h.redSqr();
  var h3 = h2.redMul(h);
  var v = u1.redMul(h2);

  var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
  var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
  var nz = this.z.redMul(p.z).redMul(h);

  return this.curve.jpoint(nx, ny, nz);
};

JPoint.prototype.mixedAdd = function mixedAdd(p) {
  // O + P = P
  if (this.isInfinity())
    return p.toJ();

  // P + O = P
  if (p.isInfinity())
    return this;

  // 8M + 3S + 7A
  var z2 = this.z.redSqr();
  var u1 = this.x;
  var u2 = p.x.redMul(z2);
  var s1 = this.y;
  var s2 = p.y.redMul(z2).redMul(this.z);

  var h = u1.redSub(u2);
  var r = s1.redSub(s2);
  if (h.cmpn(0) === 0) {
    if (r.cmpn(0) !== 0)
      return this.curve.jpoint(null, null, null);
    else
      return this.dbl();
  }

  var h2 = h.redSqr();
  var h3 = h2.redMul(h);
  var v = u1.redMul(h2);

  var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
  var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
  var nz = this.z.redMul(h);

  return this.curve.jpoint(nx, ny, nz);
};

JPoint.prototype.dblp = function dblp(pow) {
  if (pow === 0)
    return this;
  if (this.isInfinity())
    return this;
  if (!pow)
    return this.dbl();

  if (this.curve.zeroA || this.curve.threeA) {
    var r = this;
    for (var i = 0; i < pow; i++)
      r = r.dbl();
    return r;
  }

  // 1M + 2S + 1A + N * (4S + 5M + 8A)
  // N = 1 => 6M + 6S + 9A
  var a = this.curve.a;
  var tinv = this.curve.tinv;

  var jx = this.x;
  var jy = this.y;
  var jz = this.z;
  var jz4 = jz.redSqr().redSqr();

  // Reuse results
  var jyd = jy.redAdd(jy);
  for (var i = 0; i < pow; i++) {
    var jx2 = jx.redSqr();
    var jyd2 = jyd.redSqr();
    var jyd4 = jyd2.redSqr();
    var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));

    var t1 = jx.redMul(jyd2);
    var nx = c.redSqr().redISub(t1.redAdd(t1));
    var t2 = t1.redISub(nx);
    var dny = c.redMul(t2);
    dny = dny.redIAdd(dny).redISub(jyd4);
    var nz = jyd.redMul(jz);
    if (i + 1 < pow)
      jz4 = jz4.redMul(jyd4);

    jx = nx;
    jz = nz;
    jyd = dny;
  }

  return this.curve.jpoint(jx, jyd.redMul(tinv), jz);
};

JPoint.prototype.dbl = function dbl() {
  if (this.isInfinity())
    return this;

  if (this.curve.zeroA)
    return this._zeroDbl();
  else if (this.curve.threeA)
    return this._threeDbl();
  else
    return this._dbl();
};

JPoint.prototype._zeroDbl = function _zeroDbl() {
  var nx;
  var ny;
  var nz;
  // Z = 1
  if (this.zOne) {
    // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
    //     #doubling-mdbl-2007-bl
    // 1M + 5S + 14A

    // XX = X1^2
    var xx = this.x.redSqr();
    // YY = Y1^2
    var yy = this.y.redSqr();
    // YYYY = YY^2
    var yyyy = yy.redSqr();
    // S = 2 * ((X1 + YY)^2 - XX - YYYY)
    var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
    s = s.redIAdd(s);
    // M = 3 * XX + a; a = 0
    var m = xx.redAdd(xx).redIAdd(xx);
    // T = M ^ 2 - 2*S
    var t = m.redSqr().redISub(s).redISub(s);

    // 8 * YYYY
    var yyyy8 = yyyy.redIAdd(yyyy);
    yyyy8 = yyyy8.redIAdd(yyyy8);
    yyyy8 = yyyy8.redIAdd(yyyy8);

    // X3 = T
    nx = t;
    // Y3 = M * (S - T) - 8 * YYYY
    ny = m.redMul(s.redISub(t)).redISub(yyyy8);
    // Z3 = 2*Y1
    nz = this.y.redAdd(this.y);
  } else {
    // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
    //     #doubling-dbl-2009-l
    // 2M + 5S + 13A

    // A = X1^2
    var a = this.x.redSqr();
    // B = Y1^2
    var b = this.y.redSqr();
    // C = B^2
    var c = b.redSqr();
    // D = 2 * ((X1 + B)^2 - A - C)
    var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);
    d = d.redIAdd(d);
    // E = 3 * A
    var e = a.redAdd(a).redIAdd(a);
    // F = E^2
    var f = e.redSqr();

    // 8 * C
    var c8 = c.redIAdd(c);
    c8 = c8.redIAdd(c8);
    c8 = c8.redIAdd(c8);

    // X3 = F - 2 * D
    nx = f.redISub(d).redISub(d);
    // Y3 = E * (D - X3) - 8 * C
    ny = e.redMul(d.redISub(nx)).redISub(c8);
    // Z3 = 2 * Y1 * Z1
    nz = this.y.redMul(this.z);
    nz = nz.redIAdd(nz);
  }

  return this.curve.jpoint(nx, ny, nz);
};

JPoint.prototype._threeDbl = function _threeDbl() {
  var nx;
  var ny;
  var nz;
  // Z = 1
  if (this.zOne) {
    // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html
    //     #doubling-mdbl-2007-bl
    // 1M + 5S + 15A

    // XX = X1^2
    var xx = this.x.redSqr();
    // YY = Y1^2
    var yy = this.y.redSqr();
    // YYYY = YY^2
    var yyyy = yy.redSqr();
    // S = 2 * ((X1 + YY)^2 - XX - YYYY)
    var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
    s = s.redIAdd(s);
    // M = 3 * XX + a
    var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);
    // T = M^2 - 2 * S
    var t = m.redSqr().redISub(s).redISub(s);
    // X3 = T
    nx = t;
    // Y3 = M * (S - T) - 8 * YYYY
    var yyyy8 = yyyy.redIAdd(yyyy);
    yyyy8 = yyyy8.redIAdd(yyyy8);
    yyyy8 = yyyy8.redIAdd(yyyy8);
    ny = m.redMul(s.redISub(t)).redISub(yyyy8);
    // Z3 = 2 * Y1
    nz = this.y.redAdd(this.y);
  } else {
    // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
    // 3M + 5S

    // delta = Z1^2
    var delta = this.z.redSqr();
    // gamma = Y1^2
    var gamma = this.y.redSqr();
    // beta = X1 * gamma
    var beta = this.x.redMul(gamma);
    // alpha = 3 * (X1 - delta) * (X1 + delta)
    var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));
    alpha = alpha.redAdd(alpha).redIAdd(alpha);
    // X3 = alpha^2 - 8 * beta
    var beta4 = beta.redIAdd(beta);
    beta4 = beta4.redIAdd(beta4);
    var beta8 = beta4.redAdd(beta4);
    nx = alpha.redSqr().redISub(beta8);
    // Z3 = (Y1 + Z1)^2 - gamma - delta
    nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);
    // Y3 = alpha * (4 * beta - X3) - 8 * gamma^2
    var ggamma8 = gamma.redSqr();
    ggamma8 = ggamma8.redIAdd(ggamma8);
    ggamma8 = ggamma8.redIAdd(ggamma8);
    ggamma8 = ggamma8.redIAdd(ggamma8);
    ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);
  }

  return this.curve.jpoint(nx, ny, nz);
};

JPoint.prototype._dbl = function _dbl() {
  var a = this.curve.a;

  // 4M + 6S + 10A
  var jx = this.x;
  var jy = this.y;
  var jz = this.z;
  var jz4 = jz.redSqr().redSqr();

  var jx2 = jx.redSqr();
  var jy2 = jy.redSqr();

  var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));

  var jxd4 = jx.redAdd(jx);
  jxd4 = jxd4.redIAdd(jxd4);
  var t1 = jxd4.redMul(jy2);
  var nx = c.redSqr().redISub(t1.redAdd(t1));
  var t2 = t1.redISub(nx);

  var jyd8 = jy2.redSqr();
  jyd8 = jyd8.redIAdd(jyd8);
  jyd8 = jyd8.redIAdd(jyd8);
  jyd8 = jyd8.redIAdd(jyd8);
  var ny = c.redMul(t2).redISub(jyd8);
  var nz = jy.redAdd(jy).redMul(jz);

  return this.curve.jpoint(nx, ny, nz);
};

JPoint.prototype.trpl = function trpl() {
  if (!this.curve.zeroA)
    return this.dbl().add(this);

  // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#tripling-tpl-2007-bl
  // 5M + 10S + ...

  // XX = X1^2
  var xx = this.x.redSqr();
  // YY = Y1^2
  var yy = this.y.redSqr();
  // ZZ = Z1^2
  var zz = this.z.redSqr();
  // YYYY = YY^2
  var yyyy = yy.redSqr();
  // M = 3 * XX + a * ZZ2; a = 0
  var m = xx.redAdd(xx).redIAdd(xx);
  // MM = M^2
  var mm = m.redSqr();
  // E = 6 * ((X1 + YY)^2 - XX - YYYY) - MM
  var e = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
  e = e.redIAdd(e);
  e = e.redAdd(e).redIAdd(e);
  e = e.redISub(mm);
  // EE = E^2
  var ee = e.redSqr();
  // T = 16*YYYY
  var t = yyyy.redIAdd(yyyy);
  t = t.redIAdd(t);
  t = t.redIAdd(t);
  t = t.redIAdd(t);
  // U = (M + E)^2 - MM - EE - T
  var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);
  // X3 = 4 * (X1 * EE - 4 * YY * U)
  var yyu4 = yy.redMul(u);
  yyu4 = yyu4.redIAdd(yyu4);
  yyu4 = yyu4.redIAdd(yyu4);
  var nx = this.x.redMul(ee).redISub(yyu4);
  nx = nx.redIAdd(nx);
  nx = nx.redIAdd(nx);
  // Y3 = 8 * Y1 * (U * (T - U) - E * EE)
  var ny = this.y.redMul(u.redMul(t.redISub(u)).redISub(e.redMul(ee)));
  ny = ny.redIAdd(ny);
  ny = ny.redIAdd(ny);
  ny = ny.redIAdd(ny);
  // Z3 = (Z1 + E)^2 - ZZ - EE
  var nz = this.z.redAdd(e).redSqr().redISub(zz).redISub(ee);

  return this.curve.jpoint(nx, ny, nz);
};

JPoint.prototype.mul = function mul(k, kbase) {
  k = new bn(k, kbase);

  return this.curve._wnafMul(this, k);
};

JPoint.prototype.eq = function eq(p) {
  if (p.type === 'affine')
    return this.eq(p.toJ());

  if (this === p)
    return true;

  // x1 * z2^2 == x2 * z1^2
  var z2 = this.z.redSqr();
  var pz2 = p.z.redSqr();
  if (this.x.redMul(pz2).redISub(p.x.redMul(z2)).cmpn(0) !== 0)
    return false;

  // y1 * z2^3 == y2 * z1^3
  var z3 = z2.redMul(this.z);
  var pz3 = pz2.redMul(p.z);
  return this.y.redMul(pz3).redISub(p.y.redMul(z3)).cmpn(0) === 0;
};

JPoint.prototype.inspect = function inspect() {
  if (this.isInfinity())
    return '<EC JPoint Infinity>';
  return '<EC JPoint x: ' + this.x.toString(16, 2) +
      ' y: ' + this.y.toString(16, 2) +
      ' z: ' + this.z.toString(16, 2) + '>';
};

JPoint.prototype.isInfinity = function isInfinity() {
  // XXX This code assumes that zero is always zero in red
  return this.z.cmpn(0) === 0;
};

},{"../../elliptic":1,"../curve":4,"bn.js":14,"inherits":22}],7:[function(require,module,exports){
'use strict';

var curves = exports;

var hash = require('hash.js');
var elliptic = require('../elliptic');

var assert = elliptic.utils.assert;

function PresetCurve(options) {
  if (options.type === 'short')
    this.curve = new elliptic.curve.short(options);
  else if (options.type === 'edwards')
    this.curve = new elliptic.curve.edwards(options);
  else
    this.curve = new elliptic.curve.mont(options);
  this.g = this.curve.g;
  this.n = this.curve.n;
  this.hash = options.hash;

  assert(this.g.validate(), 'Invalid curve');
  assert(this.g.mul(this.n).isInfinity(), 'Invalid curve, G*N != O');
}
curves.PresetCurve = PresetCurve;

function defineCurve(name, options) {
  Object.defineProperty(curves, name, {
    configurable: true,
    enumerable: true,
    get: function() {
      var curve = new PresetCurve(options);
      Object.defineProperty(curves, name, {
        configurable: true,
        enumerable: true,
        value: curve
      });
      return curve;
    }
  });
}

defineCurve('p192', {
  type: 'short',
  prime: 'p192',
  p: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff',
  a: 'ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc',
  b: '64210519 e59c80e7 0fa7e9ab 72243049 feb8deec c146b9b1',
  n: 'ffffffff ffffffff ffffffff 99def836 146bc9b1 b4d22831',
  hash: hash.sha256,
  gRed: false,
  g: [
    '188da80e b03090f6 7cbf20eb 43a18800 f4ff0afd 82ff1012',
    '07192b95 ffc8da78 631011ed 6b24cdd5 73f977a1 1e794811'
  ]
});

defineCurve('p224', {
  type: 'short',
  prime: 'p224',
  p: 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001',
  a: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe',
  b: 'b4050a85 0c04b3ab f5413256 5044b0b7 d7bfd8ba 270b3943 2355ffb4',
  n: 'ffffffff ffffffff ffffffff ffff16a2 e0b8f03e 13dd2945 5c5c2a3d',
  hash: hash.sha256,
  gRed: false,
  g: [
    'b70e0cbd 6bb4bf7f 321390b9 4a03c1d3 56c21122 343280d6 115c1d21',
    'bd376388 b5f723fb 4c22dfe6 cd4375a0 5a074764 44d58199 85007e34'
  ]
});

defineCurve('p256', {
  type: 'short',
  prime: null,
  p: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff',
  a: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff fffffffc',
  b: '5ac635d8 aa3a93e7 b3ebbd55 769886bc 651d06b0 cc53b0f6 3bce3c3e 27d2604b',
  n: 'ffffffff 00000000 ffffffff ffffffff bce6faad a7179e84 f3b9cac2 fc632551',
  hash: hash.sha256,
  gRed: false,
  g: [
    '6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296',
    '4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5'
  ]
});

defineCurve('curve25519', {
  type: 'mont',
  prime: 'p25519',
  p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
  a: '76d06',
  b: '0',
  n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
  hash: hash.sha256,
  gRed: false,
  g: [
    '9'
  ]
});

defineCurve('ed25519', {
  type: 'edwards',
  prime: 'p25519',
  p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
  a: '-1',
  c: '1',
  // -121665 * (121666^(-1)) (mod P)
  d: '52036cee2b6ffe73 8cc740797779e898 00700a4d4141d8ab 75eb4dca135978a3',
  n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
  hash: hash.sha256,
  gRed: false,
  g: [
    '216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a',

    // 4/5
    '6666666666666666666666666666666666666666666666666666666666666658'
  ]
});

var pre;
try {
  pre = require('./precomputed/secp256k1');
} catch (e) {
  pre = undefined;
}

defineCurve('secp256k1', {
  type: 'short',
  prime: 'k256',
  p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f',
  a: '0',
  b: '7',
  n: 'ffffffff ffffffff ffffffff fffffffe baaedce6 af48a03b bfd25e8c d0364141',
  h: '1',
  hash: hash.sha256,

  // Precomputed endomorphism
  beta: '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee',
  lambda: '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72',
  basis: [
    {
      a: '3086d221a7d46bcde86c90e49284eb15',
      b: '-e4437ed6010e88286f547fa90abfe4c3'
    },
    {
      a: '114ca50f7a8e2f3f657c1108d9d44cfd8',
      b: '3086d221a7d46bcde86c90e49284eb15'
    }
  ],

  gRed: false,
  g: [
    '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
    '483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8',
    pre
  ]
});

},{"../elliptic":1,"./precomputed/secp256k1":12,"hash.js":16}],8:[function(require,module,exports){
'use strict';

var bn = require('bn.js');
var elliptic = require('../../elliptic');
var utils = elliptic.utils;
var assert = utils.assert;

var KeyPair = require('./key');
var Signature = require('./signature');

function EC(options) {
  if (!(this instanceof EC))
    return new EC(options);

  // Shortcut `elliptic.ec(curve-name)`
  if (typeof options === 'string') {
    assert(elliptic.curves.hasOwnProperty(options), 'Unknown curve ' + options);

    options = elliptic.curves[options];
  }

  // Shortcut for `elliptic.ec(elliptic.curves.curveName)`
  if (options instanceof elliptic.curves.PresetCurve)
    options = { curve: options };

  this.curve = options.curve.curve;
  this.n = this.curve.n;
  this.nh = this.n.shrn(1);
  this.g = this.curve.g;

  // Point on curve
  this.g = options.curve.g;
  this.g.precompute(options.curve.n.bitLength() + 1);

  // Hash for function for DRBG
  this.hash = options.hash || options.curve.hash;
}
module.exports = EC;

EC.prototype.keyPair = function keyPair(options) {
  return new KeyPair(this, options);
};

EC.prototype.keyFromPrivate = function keyFromPrivate(priv, enc) {
  return KeyPair.fromPrivate(this, priv, enc);
};

EC.prototype.keyFromPublic = function keyFromPublic(pub, enc) {
  return KeyPair.fromPublic(this, pub, enc);
};

EC.prototype.genKeyPair = function genKeyPair(options) {
  if (!options)
    options = {};

  // Instantiate Hmac_DRBG
  var drbg = new elliptic.hmacDRBG({
    hash: this.hash,
    pers: options.pers,
    entropy: options.entropy || elliptic.rand(this.hash.hmacStrength),
    nonce: this.n.toArray()
  });

  var bytes = this.n.byteLength();
  var ns2 = this.n.sub(new bn(2));
  do {
    var priv = new bn(drbg.generate(bytes));
    if (priv.cmp(ns2) > 0)
      continue;

    priv.iaddn(1);
    return this.keyFromPrivate(priv);
  } while (true);
};

EC.prototype._truncateToN = function truncateToN(msg, truncOnly) {
  var delta = msg.byteLength() * 8 - this.n.bitLength();
  if (delta > 0)
    msg = msg.shrn(delta);
  if (!truncOnly && msg.cmp(this.n) >= 0)
    return msg.sub(this.n);
  else
    return msg;
};

EC.prototype.sign = function sign(msg, key, enc, options) {
  if (typeof enc === 'object') {
    options = enc;
    enc = null;
  }
  if (!options)
    options = {};

  key = this.keyFromPrivate(key, enc);
  msg = this._truncateToN(new bn(msg, 16));

  // Zero-extend key to provide enough entropy
  var bytes = this.n.byteLength();
  var bkey = key.getPrivate().toArray();
  for (var i = bkey.length; i < 21; i++)
    bkey.unshift(0);

  // Zero-extend nonce to have the same byte size as N
  var nonce = msg.toArray();
  for (var i = nonce.length; i < bytes; i++)
    nonce.unshift(0);

  // Instantiate Hmac_DRBG
  var drbg = new elliptic.hmacDRBG({
    hash: this.hash,
    entropy: bkey,
    nonce: nonce
  });

  // Number of bytes to generate
  var ns1 = this.n.sub(new bn(1));
  do {
    var k = new bn(drbg.generate(this.n.byteLength()));
    k = this._truncateToN(k, true);
    if (k.cmpn(1) <= 0 || k.cmp(ns1) >= 0)
      continue;

    var kp = this.g.mul(k);
    if (kp.isInfinity())
      continue;

    var r = kp.getX().mod(this.n);
    if (r.cmpn(0) === 0)
      continue;

    var s = k.invm(this.n).mul(r.mul(key.getPrivate()).iadd(msg)).mod(this.n);
    if (s.cmpn(0) === 0)
      continue;

    // Use complement of `s`, if it is > `n / 2`
    if (options.canonical && s.cmp(this.nh) > 0)
      s = this.n.sub(s);

    return new Signature({ r: r, s: s });
  } while (true);
};

EC.prototype.verify = function verify(msg, signature, key, enc) {
  msg = this._truncateToN(new bn(msg, 16));
  key = this.keyFromPublic(key, enc);
  signature = new Signature(signature, 'hex');

  // Perform primitive values validation
  var r = signature.r;
  var s = signature.s;
  if (r.cmpn(1) < 0 || r.cmp(this.n) >= 0)
    return false;
  if (s.cmpn(1) < 0 || s.cmp(this.n) >= 0)
    return false;

  // Validate signature
  var sinv = s.invm(this.n);
  var u1 = sinv.mul(msg).mod(this.n);
  var u2 = sinv.mul(r).mod(this.n);

  var p = this.g.mulAdd(u1, key.getPublic(), u2);
  if (p.isInfinity())
    return false;

  return p.getX().mod(this.n).cmp(r) === 0;
};

},{"../../elliptic":1,"./key":9,"./signature":10,"bn.js":14}],9:[function(require,module,exports){
'use strict';

var bn = require('bn.js');

var elliptic = require('../../elliptic');
var utils = elliptic.utils;

function KeyPair(ec, options) {
  this.ec = ec;
  this.priv = null;
  this.pub = null;

  // KeyPair(ec, { priv: ..., pub: ... })
  if (options.priv)
    this._importPrivate(options.priv, options.privEnc);
  if (options.pub)
    this._importPublic(options.pub, options.pubEnc);
}
module.exports = KeyPair;

KeyPair.fromPublic = function fromPublic(ec, pub, enc) {
  if (pub instanceof KeyPair)
    return pub;

  return new KeyPair(ec, {
    pub: pub,
    pubEnc: enc
  });
};

KeyPair.fromPrivate = function fromPrivate(ec, priv, enc) {
  if (priv instanceof KeyPair)
    return priv;

  return new KeyPair(ec, {
    priv: priv,
    privEnc: enc
  });
};

KeyPair.prototype.validate = function validate() {
  var pub = this.getPublic();

  if (pub.isInfinity())
    return { result: false, reason: 'Invalid public key' };
  if (!pub.validate())
    return { result: false, reason: 'Public key is not a point' };
  if (!pub.mul(this.ec.curve.n).isInfinity())
    return { result: false, reason: 'Public key * N != O' };

  return { result: true, reason: null };
};

KeyPair.prototype.getPublic = function getPublic(compact, enc) {
  if (!this.pub)
    this.pub = this.ec.g.mul(this.priv);

  // compact is optional argument
  if (typeof compact === 'string') {
    enc = compact;
    compact = null;
  }

  if (!enc)
    return this.pub;

  var len = this.ec.curve.p.byteLength();
  var x = this.pub.getX().toArray();

  for (var i = x.length; i < len; i++)
    x.unshift(0);

  var res;
  if (this.ec.curve.type !== 'mont') {
    if (compact) {
      res = [ this.pub.getY().isEven() ? 0x02 : 0x03 ].concat(x);
    } else {
      var y = this.pub.getY().toArray();
      for (var i = y.length; i < len; i++)
        y.unshift(0);
      var res = [ 0x04 ].concat(x, y);
    }
  } else {
    res = x;
  }

  return utils.encode(res, enc);
};

KeyPair.prototype.getPrivate = function getPrivate(enc) {
  if (enc === 'hex')
    return this.priv.toString(16, 2);
  else
    return this.priv;
};

KeyPair.prototype._importPrivate = function _importPrivate(key, enc) {
  this.priv = new bn(key, enc || 16);

  // Ensure that the priv won't be bigger than n, otherwise we may fail
  // in fixed multiplication method
  this.priv = this.priv.mod(this.ec.curve.n);
};

KeyPair.prototype._importPublic = function _importPublic(key, enc) {
  if (key.x || key.y) {
    this.pub = this.ec.curve.point(key.x, key.y);
    return;
  }

  key = utils.toArray(key, enc);
  if (this.ec.curve.type !== 'mont')
    return this._importPublicShort(key);
  else
    return this._importPublicMont(key);
};

KeyPair.prototype._importPublicShort = function _importPublicShort(key) {
  var len = this.ec.curve.p.byteLength();
  if (key[0] === 0x04 && key.length - 1 === 2 * len) {
    this.pub = this.ec.curve.point(
      key.slice(1, 1 + len),
      key.slice(1 + len, 1 + 2 * len));
  } else if ((key[0] === 0x02 || key[0] === 0x03) && key.length - 1 === len) {
    this.pub = this.ec.curve.pointFromX(key[0] === 0x03, key.slice(1, 1 + len));
  }
};

KeyPair.prototype._importPublicMont = function _importPublicMont(key) {
  this.pub = this.ec.curve.point(key, 1);
};

// ECDH
KeyPair.prototype.derive = function derive(pub) {
  return pub.mul(this.priv).getX();
};

// ECDSA
KeyPair.prototype.sign = function sign(msg) {
  return this.ec.sign(msg, this);
};

KeyPair.prototype.verify = function verify(msg, signature) {
  return this.ec.verify(msg, signature, this);
};

KeyPair.prototype.inspect = function inspect() {
  return '<Key priv: ' + (this.priv && this.priv.toString(16, 2)) +
         ' pub: ' + (this.pub && this.pub.inspect()) + ' >';
};

},{"../../elliptic":1,"bn.js":14}],10:[function(require,module,exports){
'use strict';

var bn = require('bn.js');

var elliptic = require('../../elliptic');
var utils = elliptic.utils;
var assert = utils.assert;

function Signature(options, enc) {
  if (options instanceof Signature)
    return options;

  if (this._importDER(options, enc))
    return;

  assert(options.r && options.s, 'Signature without r or s');
  this.r = new bn(options.r, 16);
  this.s = new bn(options.s, 16);
}
module.exports = Signature;

Signature.prototype._importDER = function _importDER(data, enc) {
  data = utils.toArray(data, enc);
  if (data.length < 6 || data[0] !== 0x30 || data[2] !== 0x02)
    return false;
  var total = data[1];
  if (1 + total > data.length)
    return false;
  var rlen = data[3];
  // Short length notation
  if (rlen >= 0x80)
    return false;
  if (4 + rlen + 2 >= data.length)
    return false;
  if (data[4 + rlen] !== 0x02)
    return false;
  var slen = data[5 + rlen];
  // Short length notation
  if (slen >= 0x80)
    return false;
  if (4 + rlen + 2 + slen > data.length)
    return false;

  this.r = new bn(data.slice(4, 4 + rlen));
  this.s = new bn(data.slice(4 + rlen + 2, 4 + rlen + 2 + slen));

  return true;
};

Signature.prototype.toDER = function toDER(enc) {
  var r = this.r.toArray();
  var s = this.s.toArray();

  // Pad values
  if (r[0] & 0x80)
    r = [ 0 ].concat(r);
  // Pad values
  if (s[0] & 0x80)
    s = [ 0 ].concat(s);

  var total = r.length + s.length + 4;
  var res = [ 0x30, total, 0x02, r.length ];
  res = res.concat(r, [ 0x02, s.length ], s);
  return utils.encode(res, enc);
};

},{"../../elliptic":1,"bn.js":14}],11:[function(require,module,exports){
'use strict';

var hash = require('hash.js');
var elliptic = require('../elliptic');
var utils = elliptic.utils;
var assert = utils.assert;

function HmacDRBG(options) {
  if (!(this instanceof HmacDRBG))
    return new HmacDRBG(options);
  this.hash = options.hash;
  this.predResist = !!options.predResist;

  this.outLen = this.hash.outSize;
  this.minEntropy = options.minEntropy || this.hash.hmacStrength;

  this.reseed = null;
  this.reseedInterval = null;
  this.K = null;
  this.V = null;

  var entropy = utils.toArray(options.entropy, options.entropyEnc);
  var nonce = utils.toArray(options.nonce, options.nonceEnc);
  var pers = utils.toArray(options.pers, options.persEnc);
  assert(entropy.length >= (this.minEntropy / 8),
         'Not enough entropy. Minimum is: ' + this.minEntropy + ' bits');
  this._init(entropy, nonce, pers);
}
module.exports = HmacDRBG;

HmacDRBG.prototype._init = function init(entropy, nonce, pers) {
  var seed = entropy.concat(nonce).concat(pers);

  this.K = new Array(this.outLen / 8);
  this.V = new Array(this.outLen / 8);
  for (var i = 0; i < this.V.length; i++) {
    this.K[i] = 0x00;
    this.V[i] = 0x01;
  }

  this._update(seed);
  this.reseed = 1;
  this.reseedInterval = 0x1000000000000;  // 2^48
};

HmacDRBG.prototype._hmac = function hmac() {
  return new hash.hmac(this.hash, this.K);
};

HmacDRBG.prototype._update = function update(seed) {
  var kmac = this._hmac()
                 .update(this.V)
                 .update([ 0x00 ]);
  if (seed)
    kmac = kmac.update(seed);
  this.K = kmac.digest();
  this.V = this._hmac().update(this.V).digest();
  if (!seed)
    return;

  this.K = this._hmac()
               .update(this.V)
               .update([ 0x01 ])
               .update(seed)
               .digest();
  this.V = this._hmac().update(this.V).digest();
};

HmacDRBG.prototype.reseed = function reseed(entropy, entropyEnc, add, addEnc) {
  // Optional entropy enc
  if (typeof entropyEnc !== 'string') {
    addEnc = add;
    add = entropyEnc;
    entropyEnc = null;
  }

  entropy = utils.toBuffer(entropy, entropyEnc);
  add = utils.toBuffer(add, addEnc);

  assert(entropy.length >= (this.minEntropy / 8),
         'Not enough entropy. Minimum is: ' + this.minEntropy + ' bits');

  this._update(entropy.concat(add || []));
  this.reseed = 1;
};

HmacDRBG.prototype.generate = function generate(len, enc, add, addEnc) {
  if (this.reseed > this.reseedInterval)
    throw new Error('Reseed is required');

  // Optional encoding
  if (typeof enc !== 'string') {
    addEnc = add;
    add = enc;
    enc = null;
  }

  // Optional additional data
  if (add) {
    add = utils.toArray(add, addEnc);
    this._update(add);
  }

  var temp = [];
  while (temp.length < len) {
    this.V = this._hmac().update(this.V).digest();
    temp = temp.concat(this.V);
  }

  var res = temp.slice(0, len);
  this._update(add);
  this.reseed++;
  return utils.encode(res, enc);
};

},{"../elliptic":1,"hash.js":16}],12:[function(require,module,exports){
module.exports = {
  doubles: {
    step: 4,
    points: [
      [
        'e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a',
        'f7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821'
      ],
      [
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        '11f8a8098557dfe45e8256e830b60ace62d613ac2f7b17bed31b6eaff6e26caf'
      ],
      [
        '175e159f728b865a72f99cc6c6fc846de0b93833fd2222ed73fce5b551e5b739',
        'd3506e0d9e3c79eba4ef97a51ff71f5eacb5955add24345c6efa6ffee9fed695'
      ],
      [
        '363d90d447b00c9c99ceac05b6262ee053441c7e55552ffe526bad8f83ff4640',
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      ],
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        '4aad0a6f68d308b4b3fbd7813ab0da04f9e336546162ee56b3eff0c65fd4fd36'
      ],
      [
        '723cbaa6e5db996d6bf771c00bd548c7b700dbffa6c0e77bcb6115925232fcda',
        '96e867b5595cc498a921137488824d6e2660a0653779494801dc069d9eb39f5f'
      ],
      [
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      [
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      [
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      ],
      [
        'ff2b0dce97eece97c1c9b6041798b85dfdfb6d8882da20308f5404824526087e',
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      ],
      [
        '827fbbe4b1e880ea9ed2b2e6301b212b57f1ee148cd6dd28780e5e2cf856e241',
        'c60f9c923c727b0b71bef2c67d1d12687ff7a63186903166d605b68baec293ec'
      ],
      [
        'eaa649f21f51bdbae7be4ae34ce6e5217a58fdce7f47f9aa7f3b58fa2120e2b3',
        'be3279ed5bbbb03ac69a80f89879aa5a01a6b965f13f7e59d47a5305ba5ad93d'
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        'ae434102edde0958ec4b19d917a6a28e6b72da1834aff0e650f049503a296cf2'
      ],
      [
        '4e8ceafb9b3e9a136dc7ff67e840295b499dfb3b2133e4ba113f2e4c0e121e5',
        'cf2174118c8b6d7a4b48f6d534ce5c79422c086a63460502b827ce62a326683c'
      ],
      [
        'd24a44e047e19b6f5afb81c7ca2f69080a5076689a010919f42725c2b789a33b',
        '6fb8d5591b466f8fc63db50f1c0f1c69013f996887b8244d2cdec417afea8fa3'
      ],
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        'ea01606a7a6c9cdd249fdfcfacb99584001edd28abbab77b5104e98e8e3b35d4',
        '322af4908c7312b0cfbfe369f7a7b3cdb7d4494bc2823700cfd652188a3ea98d'
      ],
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      ],
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      ],
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        'b0ea558a113c30bea60fc4775460c7901ff0b053d25ca2bdeee98f1a4be5d196'
      ],
      [
        '11396d55fda54c49f19aa97318d8da61fa8584e47b084945077cf03255b52984',
        '998c74a8cd45ac01289d5833a7beb4744ff536b01b257be4c5767bea93ea57a4'
      ],
      [
        '3c5d2a1ba39c5a1790000738c9e0c40b8dcdfd5468754b6405540157e017aa7a',
        'b2284279995a34e2f9d4de7396fc18b80f9b8b9fdd270f6661f79ca4c81bd257'
      ],
      [
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        'bdd46039feed17881d1e0862db347f8cf395b74fc4bcdc4e940b74e3ac1f1b13'
      ],
      [
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        '6f0a256bc5efdf429a2fb6242f1a43a2d9b925bb4a4b3a26bb8e0f45eb596096'
      ],
      [
        'c14f8f2ccb27d6f109f6d08d03cc96a69ba8c34eec07bbcf566d48e33da6593',
        'c359d6923bb398f7fd4473e16fe1c28475b740dd098075e6c0e8649113dc3a38'
      ],
      [
        'a6cbc3046bc6a450bac24789fa17115a4c9739ed75f8f21ce441f72e0b90e6ef',
        '21ae7f4680e889bb130619e2c0f95a360ceb573c70603139862afd617fa9b9f'
      ],
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        '60ea7f61a353524d1c987f6ecec92f086d565ab687870cb12689ff1e31c74448'
      ],
      [
        'da6545d2181db8d983f7dcb375ef5866d47c67b1bf31c8cf855ef7437b72656a',
        '49b96715ab6878a79e78f07ce5680c5d6673051b4935bd897fea824b77dc208a'
      ],
      [
        'c40747cc9d012cb1a13b8148309c6de7ec25d6945d657146b9d5994b8feb1111',
        '5ca560753be2a12fc6de6caf2cb489565db936156b9514e1bb5e83037e0fa2d4'
      ],
      [
        '4e42c8ec82c99798ccf3a610be870e78338c7f713348bd34c8203ef4037f3502',
        '7571d74ee5e0fb92a7a8b33a07783341a5492144cc54bcc40a94473693606437'
      ],
      [
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        'be52d107bcfa09d8bcb9736a828cfa7fac8db17bf7a76a2c42ad961409018cf7'
      ],
      [
        'cee31cbf7e34ec379d94fb814d3d775ad954595d1314ba8846959e3e82f74e26',
        '8fd64a14c06b589c26b947ae2bcf6bfa0149ef0be14ed4d80f448a01c43b1c6d'
      ],
      [
        'b4f9eaea09b6917619f6ea6a4eb5464efddb58fd45b1ebefcdc1a01d08b47986',
        '39e5c9925b5a54b07433a4f18c61726f8bb131c012ca542eb24a8ac07200682a'
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      [
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      [
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        'ecfb7056cf1de042f9420bab396793c0c390bde74b4bbdff16a83ae09a9a7517'
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      [
        '6d7ef6b17543f8373c573f44e1f389835d89bcbc6062ced36c82df83b8fae859',
        'cd450ec335438986dfefa10c57fea9bcc521a0959b2d80bbf74b190dca712d10'
      ],
      [
        'e75605d59102a5a2684500d3b991f2e3f3c88b93225547035af25af66e04541f',
        'f5c54754a8f71ee540b9b48728473e314f729ac5308b06938360990e2bfad125'
      ],
      [
        'eb98660f4c4dfaa06a2be453d5020bc99a0c2e60abe388457dd43fefb1ed620c',
        '6cb9a8876d9cb8520609af3add26cd20a0a7cd8a9411131ce85f44100099223e'
      ],
      [
        '13e87b027d8514d35939f2e6892b19922154596941888336dc3563e3b8dba942',
        'fef5a3c68059a6dec5d624114bf1e91aac2b9da568d6abeb2570d55646b8adf1'
      ],
      [
        'ee163026e9fd6fe017c38f06a5be6fc125424b371ce2708e7bf4491691e5764a',
        '1acb250f255dd61c43d94ccc670d0f58f49ae3fa15b96623e5430da0ad6c62b2'
      ],
      [
        'b268f5ef9ad51e4d78de3a750c2dc89b1e626d43505867999932e5db33af3d80',
        '5f310d4b3c99b9ebb19f77d41c1dee018cf0d34fd4191614003e945a1216e423'
      ],
      [
        'ff07f3118a9df035e9fad85eb6c7bfe42b02f01ca99ceea3bf7ffdba93c4750d',
        '438136d603e858a3a5c440c38eccbaddc1d2942114e2eddd4740d098ced1f0d8'
      ],
      [
        '8d8b9855c7c052a34146fd20ffb658bea4b9f69e0d825ebec16e8c3ce2b526a1',
        'cdb559eedc2d79f926baf44fb84ea4d44bcf50fee51d7ceb30e2e7f463036758'
      ],
      [
        '52db0b5384dfbf05bfa9d472d7ae26dfe4b851ceca91b1eba54263180da32b63',
        'c3b997d050ee5d423ebaf66a6db9f57b3180c902875679de924b69d84a7b375'
      ],
      [
        'e62f9490d3d51da6395efd24e80919cc7d0f29c3f3fa48c6fff543becbd43352',
        '6d89ad7ba4876b0b22c2ca280c682862f342c8591f1daf5170e07bfd9ccafa7d'
      ],
      [
        '7f30ea2476b399b4957509c88f77d0191afa2ff5cb7b14fd6d8e7d65aaab1193',
        'ca5ef7d4b231c94c3b15389a5f6311e9daff7bb67b103e9880ef4bff637acaec'
      ],
      [
        '5098ff1e1d9f14fb46a210fada6c903fef0fb7b4a1dd1d9ac60a0361800b7a00',
        '9731141d81fc8f8084d37c6e7542006b3ee1b40d60dfe5362a5b132fd17ddc0'
      ],
      [
        '32b78c7de9ee512a72895be6b9cbefa6e2f3c4ccce445c96b9f2c81e2778ad58',
        'ee1849f513df71e32efc3896ee28260c73bb80547ae2275ba497237794c8753c'
      ],
      [
        'e2cb74fddc8e9fbcd076eef2a7c72b0ce37d50f08269dfc074b581550547a4f7',
        'd3aa2ed71c9dd2247a62df062736eb0baddea9e36122d2be8641abcb005cc4a4'
      ],
      [
        '8438447566d4d7bedadc299496ab357426009a35f235cb141be0d99cd10ae3a8',
        'c4e1020916980a4da5d01ac5e6ad330734ef0d7906631c4f2390426b2edd791f'
      ],
      [
        '4162d488b89402039b584c6fc6c308870587d9c46f660b878ab65c82c711d67e',
        '67163e903236289f776f22c25fb8a3afc1732f2b84b4e95dbda47ae5a0852649'
      ],
      [
        '3fad3fa84caf0f34f0f89bfd2dcf54fc175d767aec3e50684f3ba4a4bf5f683d',
        'cd1bc7cb6cc407bb2f0ca647c718a730cf71872e7d0d2a53fa20efcdfe61826'
      ],
      [
        '674f2600a3007a00568c1a7ce05d0816c1fb84bf1370798f1c69532faeb1a86b',
        '299d21f9413f33b3edf43b257004580b70db57da0b182259e09eecc69e0d38a5'
      ],
      [
        'd32f4da54ade74abb81b815ad1fb3b263d82d6c692714bcff87d29bd5ee9f08f',
        'f9429e738b8e53b968e99016c059707782e14f4535359d582fc416910b3eea87'
      ],
      [
        '30e4e670435385556e593657135845d36fbb6931f72b08cb1ed954f1e3ce3ff6',
        '462f9bce619898638499350113bbc9b10a878d35da70740dc695a559eb88db7b'
      ],
      [
        'be2062003c51cc3004682904330e4dee7f3dcd10b01e580bf1971b04d4cad297',
        '62188bc49d61e5428573d48a74e1c655b1c61090905682a0d5558ed72dccb9bc'
      ],
      [
        '93144423ace3451ed29e0fb9ac2af211cb6e84a601df5993c419859fff5df04a',
        '7c10dfb164c3425f5c71a3f9d7992038f1065224f72bb9d1d902a6d13037b47c'
      ],
      [
        'b015f8044f5fcbdcf21ca26d6c34fb8197829205c7b7d2a7cb66418c157b112c',
        'ab8c1e086d04e813744a655b2df8d5f83b3cdc6faa3088c1d3aea1454e3a1d5f'
      ],
      [
        'd5e9e1da649d97d89e4868117a465a3a4f8a18de57a140d36b3f2af341a21b52',
        '4cb04437f391ed73111a13cc1d4dd0db1693465c2240480d8955e8592f27447a'
      ],
      [
        'd3ae41047dd7ca065dbf8ed77b992439983005cd72e16d6f996a5316d36966bb',
        'bd1aeb21ad22ebb22a10f0303417c6d964f8cdd7df0aca614b10dc14d125ac46'
      ],
      [
        '463e2763d885f958fc66cdd22800f0a487197d0a82e377b49f80af87c897b065',
        'bfefacdb0e5d0fd7df3a311a94de062b26b80c61fbc97508b79992671ef7ca7f'
      ],
      [
        '7985fdfd127c0567c6f53ec1bb63ec3158e597c40bfe747c83cddfc910641917',
        '603c12daf3d9862ef2b25fe1de289aed24ed291e0ec6708703a5bd567f32ed03'
      ],
      [
        '74a1ad6b5f76e39db2dd249410eac7f99e74c59cb83d2d0ed5ff1543da7703e9',
        'cc6157ef18c9c63cd6193d83631bbea0093e0968942e8c33d5737fd790e0db08'
      ],
      [
        '30682a50703375f602d416664ba19b7fc9bab42c72747463a71d0896b22f6da3',
        '553e04f6b018b4fa6c8f39e7f311d3176290d0e0f19ca73f17714d9977a22ff8'
      ],
      [
        '9e2158f0d7c0d5f26c3791efefa79597654e7a2b2464f52b1ee6c1347769ef57',
        '712fcdd1b9053f09003a3481fa7762e9ffd7c8ef35a38509e2fbf2629008373'
      ],
      [
        '176e26989a43c9cfeba4029c202538c28172e566e3c4fce7322857f3be327d66',
        'ed8cc9d04b29eb877d270b4878dc43c19aefd31f4eee09ee7b47834c1fa4b1c3'
      ],
      [
        '75d46efea3771e6e68abb89a13ad747ecf1892393dfc4f1b7004788c50374da8',
        '9852390a99507679fd0b86fd2b39a868d7efc22151346e1a3ca4726586a6bed8'
      ],
      [
        '809a20c67d64900ffb698c4c825f6d5f2310fb0451c869345b7319f645605721',
        '9e994980d9917e22b76b061927fa04143d096ccc54963e6a5ebfa5f3f8e286c1'
      ],
      [
        '1b38903a43f7f114ed4500b4eac7083fdefece1cf29c63528d563446f972c180',
        '4036edc931a60ae889353f77fd53de4a2708b26b6f5da72ad3394119daf408f9'
      ]
    ]
  }
};

},{}],13:[function(require,module,exports){
'use strict';

var utils = exports;

utils.assert = function assert(val, msg) {
  if (!val)
    throw new Error(msg || 'Assertion failed');
};

function toArray(msg, enc) {
  if (Array.isArray(msg))
    return msg.slice();
  if (!msg)
    return [];
  var res = [];
  if (typeof msg !== 'string') {
    for (var i = 0; i < msg.length; i++)
      res[i] = msg[i] | 0;
    return res;
  }
  if (!enc) {
    for (var i = 0; i < msg.length; i++) {
      var c = msg.charCodeAt(i);
      var hi = c >> 8;
      var lo = c & 0xff;
      if (hi)
        res.push(hi, lo);
      else
        res.push(lo);
    }
  } else if (enc === 'hex') {
    msg = msg.replace(/[^a-z0-9]+/ig, '');
    if (msg.length % 2 !== 0)
      msg = '0' + msg;
    for (var i = 0; i < msg.length; i += 2)
      res.push(parseInt(msg[i] + msg[i + 1], 16));
  }
  return res;
}
utils.toArray = toArray;

function zero2(word) {
  if (word.length === 1)
    return '0' + word;
  else
    return word;
}
utils.zero2 = zero2;

function toHex(msg) {
  var res = '';
  for (var i = 0; i < msg.length; i++)
    res += zero2(msg[i].toString(16));
  return res;
}
utils.toHex = toHex;

utils.encode = function encode(arr, enc) {
  if (enc === 'hex')
    return toHex(arr);
  else
    return arr;
};

// Represent num in a w-NAF form
function getNAF(num, w) {
  var naf = [];
  var ws = 1 << (w + 1);
  var k = num.clone();
  while (k.cmpn(1) >= 0) {
    var z;
    if (k.isOdd()) {
      var mod = k.andln(ws - 1);
      if (mod > (ws >> 1) - 1)
        z = (ws >> 1) - mod;
      else
        z = mod;
      k.isubn(z);
    } else {
      z = 0;
    }
    naf.push(z);

    // Optimization, shift by word if possible
    var shift = (k.cmpn(0) !== 0 && k.andln(ws - 1) === 0) ? (w + 1) : 1;
    for (var i = 1; i < shift; i++)
      naf.push(0);
    k.ishrn(shift);
  }

  return naf;
}
utils.getNAF = getNAF;

// Represent k1, k2 in a Joint Sparse Form
function getJSF(k1, k2) {
  var jsf = [
    [],
    []
  ];

  k1 = k1.clone();
  k2 = k2.clone();
  var d1 = 0;
  var d2 = 0;
  while (k1.cmpn(-d1) > 0 || k2.cmpn(-d2) > 0) {

    // First phase
    var m14 = (k1.andln(3) + d1) & 3;
    var m24 = (k2.andln(3) + d2) & 3;
    if (m14 === 3)
      m14 = -1;
    if (m24 === 3)
      m24 = -1;
    var u1;
    if ((m14 & 1) === 0) {
      u1 = 0;
    } else {
      var m8 = (k1.andln(7) + d1) & 7;
      if ((m8 === 3 || m8 === 5) && m24 === 2)
        u1 = -m14;
      else
        u1 = m14;
    }
    jsf[0].push(u1);

    var u2;
    if ((m24 & 1) === 0) {
      u2 = 0;
    } else {
      var m8 = (k2.andln(7) + d2) & 7;
      if ((m8 === 3 || m8 === 5) && m14 === 2)
        u2 = -m24;
      else
        u2 = m24;
    }
    jsf[1].push(u2);

    // Second phase
    if (2 * d1 === u1 + 1)
      d1 = 1 - d1;
    if (2 * d2 === u2 + 1)
      d2 = 1 - d2;
    k1.ishrn(1);
    k2.ishrn(1);
  }

  return jsf;
}
utils.getJSF = getJSF;

},{}],14:[function(require,module,exports){
(function (module, exports) {

'use strict';

// Utils

function assert(val, msg) {
  if (!val)
    throw new Error(msg || 'Assertion failed');
}

// Could use `inherits` module, but don't want to move from single file
// architecture yet.
function inherits(ctor, superCtor) {
  ctor.super_ = superCtor;
  var TempCtor = function () {};
  TempCtor.prototype = superCtor.prototype;
  ctor.prototype = new TempCtor();
  ctor.prototype.constructor = ctor;
}

// BN

function BN(number, base, endian) {
  // May be `new BN(bn)` ?
  if (number !== null &&
      typeof number === 'object' &&
      Array.isArray(number.words)) {
    return number;
  }

  this.sign = false;
  this.words = null;
  this.length = 0;

  // Reduction context
  this.red = null;

  if (base === 'le' || base === 'be') {
    endian = base;
    base = 10;
  }

  if (number !== null)
    this._init(number || 0, base || 10, endian || 'be');
}
if (typeof module === 'object')
  module.exports = BN;
else
  exports.BN = BN;

BN.BN = BN;
BN.wordSize = 26;

BN.prototype._init = function init(number, base, endian) {
  if (typeof number === 'number') {
    if (number < 0) {
      this.sign = true;
      number = -number;
    }
    if (number < 0x4000000) {
      this.words = [ number & 0x3ffffff ];
      this.length = 1;
    } else {
      this.words = [
        number & 0x3ffffff,
        (number / 0x4000000) & 0x3ffffff
      ];
      this.length = 2;
    }
    return;
  } else if (typeof number === 'object') {
    return this._initArray(number, base, endian);
  }
  if (base === 'hex')
    base = 16;
  assert(base === (base | 0) && base >= 2 && base <= 36);

  number = number.toString().replace(/\s+/g, '');
  var start = 0;
  if (number[0] === '-')
    start++;

  if (base === 16)
    this._parseHex(number, start);
  else
    this._parseBase(number, base, start);

  if (number[0] === '-')
    this.sign = true;

  this.strip();
};

BN.prototype._initArray = function _initArray(number, base, endian) {
  // Perhaps a Uint8Array
  assert(typeof number.length === 'number');
  this.length = Math.ceil(number.length / 3);
  this.words = new Array(this.length);
  for (var i = 0; i < this.length; i++)
    this.words[i] = 0;

  var off = 0;
  if (endian === 'be') {
    for (var i = number.length - 1, j = 0; i >= 0; i -= 3) {
      var w = number[i] | (number[i - 1] << 8) | (number[i - 2] << 16);
      this.words[j] |= (w << off) & 0x3ffffff;
      this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff;
      off += 24;
      if (off >= 26) {
        off -= 26;
        j++;
      }
    }
  } else if (endian === 'le') {
    for (var i = 0, j = 0; i < number.length; i += 3) {
      var w = number[i] | (number[i + 1] << 8) | (number[i + 2] << 16);
      this.words[j] |= (w << off) & 0x3ffffff;
      this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff;
      off += 24;
      if (off >= 26) {
        off -= 26;
        j++;
      }
    }
  }
  return this.strip();
};

function parseHex(str, start, end) {
  var r = 0;
  var len = Math.min(str.length, end);
  for (var i = start; i < len; i++) {
    var c = str.charCodeAt(i) - 48;

    r <<= 4;

    // 'a' - 'f'
    if (c >= 49 && c <= 54)
      r |= c - 49 + 0xa;

    // 'A' - 'F'
    else if (c >= 17 && c <= 22)
      r |= c - 17 + 0xa;

    // '0' - '9'
    else
      r |= c & 0xf;
  }
  return r;
}

BN.prototype._parseHex = function _parseHex(number, start) {
  // Create possibly bigger array to ensure that it fits the number
  this.length = Math.ceil((number.length - start) / 6);
  this.words = new Array(this.length);
  for (var i = 0; i < this.length; i++)
    this.words[i] = 0;

  // Scan 24-bit chunks and add them to the number
  var off = 0;
  for (var i = number.length - 6, j = 0; i >= start; i -= 6) {
    var w = parseHex(number, i, i + 6);
    this.words[j] |= (w << off) & 0x3ffffff;
    this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
    off += 24;
    if (off >= 26) {
      off -= 26;
      j++;
    }
  }
  if (i + 6 !== start) {
    var w = parseHex(number, start, i + 6);
    this.words[j] |= (w << off) & 0x3ffffff;
    this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
  }
  this.strip();
};

function parseBase(str, start, end, mul) {
  var r = 0;
  var len = Math.min(str.length, end);
  for (var i = start; i < len; i++) {
    var c = str.charCodeAt(i) - 48;

    r *= mul;

    // 'a'
    if (c >= 49)
      r += c - 49 + 0xa;

    // 'A'
    else if (c >= 17)
      r += c - 17 + 0xa;

    // '0' - '9'
    else
      r += c;
  }
  return r;
}

BN.prototype._parseBase = function _parseBase(number, base, start) {
  // Initialize as zero
  this.words = [ 0 ];
  this.length = 1;

  // Find length of limb in base
  for (var limbLen = 0, limbPow = 1; limbPow <= 0x3ffffff; limbPow *= base)
    limbLen++;
  limbLen--;
  limbPow = (limbPow / base) | 0;

  var total = number.length - start;
  var mod = total % limbLen;
  var end = Math.min(total, total - mod) + start;

  var word = 0;
  for (var i = start; i < end; i += limbLen) {
    word = parseBase(number, i, i + limbLen, base);

    this.imuln(limbPow);
    if (this.words[0] + word < 0x4000000)
      this.words[0] += word;
    else
      this._iaddn(word);
  }

  if (mod !== 0) {
    var pow = 1;
    var word = parseBase(number, i, number.length, base);

    for (var i = 0; i < mod; i++)
      pow *= base;
    this.imuln(pow);
    if (this.words[0] + word < 0x4000000)
      this.words[0] += word;
    else
      this._iaddn(word);
  }
};

BN.prototype.copy = function copy(dest) {
  dest.words = new Array(this.length);
  for (var i = 0; i < this.length; i++)
    dest.words[i] = this.words[i];
  dest.length = this.length;
  dest.sign = this.sign;
  dest.red = this.red;
};

BN.prototype.clone = function clone() {
  var r = new BN(null);
  this.copy(r);
  return r;
};

// Remove leading `0` from `this`
BN.prototype.strip = function strip() {
  while (this.length > 1 && this.words[this.length - 1] === 0)
    this.length--;
  return this._normSign();
};

BN.prototype._normSign = function _normSign() {
  // -0 = 0
  if (this.length === 1 && this.words[0] === 0)
    this.sign = false;
  return this;
};

BN.prototype.inspect = function inspect() {
  return (this.red ? '<BN-R: ' : '<BN: ') + this.toString(16) + '>';
};

/*

var zeros = [];
var groupSizes = [];
var groupBases = [];

var s = '';
var i = -1;
while (++i < BN.wordSize) {
  zeros[i] = s;
  s += '0';
}
groupSizes[0] = 0;
groupSizes[1] = 0;
groupBases[0] = 0;
groupBases[1] = 0;
var base = 2 - 1;
while (++base < 36 + 1) {
  var groupSize = 0;
  var groupBase = 1;
  while (groupBase < (1 << BN.wordSize) / base) {
    groupBase *= base;
    groupSize += 1;
  }
  groupSizes[base] = groupSize;
  groupBases[base] = groupBase;
}

*/

var zeros = [
  '',
  '0',
  '00',
  '000',
  '0000',
  '00000',
  '000000',
  '0000000',
  '00000000',
  '000000000',
  '0000000000',
  '00000000000',
  '000000000000',
  '0000000000000',
  '00000000000000',
  '000000000000000',
  '0000000000000000',
  '00000000000000000',
  '000000000000000000',
  '0000000000000000000',
  '00000000000000000000',
  '000000000000000000000',
  '0000000000000000000000',
  '00000000000000000000000',
  '000000000000000000000000',
  '0000000000000000000000000'
];

var groupSizes = [
  0, 0,
  25, 16, 12, 11, 10, 9, 8,
  8, 7, 7, 7, 7, 6, 6,
  6, 6, 6, 6, 6, 5, 5,
  5, 5, 5, 5, 5, 5, 5,
  5, 5, 5, 5, 5, 5, 5
];

var groupBases = [
  0, 0,
  33554432, 43046721, 16777216, 48828125, 60466176, 40353607, 16777216,
  43046721, 10000000, 19487171, 35831808, 62748517, 7529536, 11390625,
  16777216, 24137569, 34012224, 47045881, 64000000, 4084101, 5153632,
  6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149,
  24300000, 28629151, 33554432, 39135393, 45435424, 52521875, 60466176
];

BN.prototype.toString = function toString(base, padding) {
  base = base || 10;
  if (base === 16 || base === 'hex') {
    var out = '';
    var off = 0;
    var padding = padding | 0 || 1;
    var carry = 0;
    for (var i = 0; i < this.length; i++) {
      var w = this.words[i];
      var word = (((w << off) | carry) & 0xffffff).toString(16);
      carry = (w >>> (24 - off)) & 0xffffff;
      if (carry !== 0 || i !== this.length - 1)
        out = zeros[6 - word.length] + word + out;
      else
        out = word + out;
      off += 2;
      if (off >= 26) {
        off -= 26;
        i--;
      }
    }
    if (carry !== 0)
      out = carry.toString(16) + out;
    while (out.length % padding !== 0)
      out = '0' + out;
    if (this.sign)
      out = '-' + out;
    return out;
  } else if (base === (base | 0) && base >= 2 && base <= 36) {
    // var groupSize = Math.floor(BN.wordSize * Math.LN2 / Math.log(base));
    var groupSize = groupSizes[base];
    // var groupBase = Math.pow(base, groupSize);
    var groupBase = groupBases[base];
    var out = '';
    var c = this.clone();
    c.sign = false;
    while (c.cmpn(0) !== 0) {
      var r = c.modn(groupBase).toString(base);
      c = c.idivn(groupBase);

      if (c.cmpn(0) !== 0)
        out = zeros[groupSize - r.length] + r + out;
      else
        out = r + out;
    }
    if (this.cmpn(0) === 0)
      out = '0' + out;
    if (this.sign)
      out = '-' + out;
    return out;
  } else {
    assert(false, 'Base should be between 2 and 36');
  }
};

BN.prototype.toJSON = function toJSON() {
  return this.toString(16);
};

BN.prototype.toArray = function toArray() {
  this.strip();
  var res = new Array(this.byteLength());
  res[0] = 0;

  var q = this.clone();
  for (var i = 0; q.cmpn(0) !== 0; i++) {
    var b = q.andln(0xff);
    q.ishrn(8);

    // Assume big-endian
    res[res.length - i - 1] = b;
  }

  return res;
};

if (Math.clz32) {
  BN.prototype._countBits = function _countBits(w) {
    return 32 - Math.clz32(w);
  };
} else {
  BN.prototype._countBits = function _countBits(w) {
    var t = w;
    var r = 0;
    if (t >= 0x1000) {
      r += 13;
      t >>>= 13;
    }
    if (t >= 0x40) {
      r += 7;
      t >>>= 7;
    }
    if (t >= 0x8) {
      r += 4;
      t >>>= 4;
    }
    if (t >= 0x02) {
      r += 2;
      t >>>= 2;
    }
    return r + t;
  };
}

BN.prototype._zeroBits = function _zeroBits(w) {
  // Short-cut
  if (w === 0)
    return 26;

  var t = w;
  var r = 0;
  if ((t & 0x1fff) === 0) {
    r += 13;
    t >>>= 13;
  }
  if ((t & 0x7f) === 0) {
    r += 7;
    t >>>= 7;
  }
  if ((t & 0xf) === 0) {
    r += 4;
    t >>>= 4;
  }
  if ((t & 0x3) === 0) {
    r += 2;
    t >>>= 2;
  }
  if ((t & 0x1) === 0)
    r++;
  return r;
};

// Return number of used bits in a BN
BN.prototype.bitLength = function bitLength() {
  var hi = 0;
  var w = this.words[this.length - 1];
  var hi = this._countBits(w);
  return (this.length - 1) * 26 + hi;
};

// Number of trailing zero bits
BN.prototype.zeroBits = function zeroBits() {
  if (this.cmpn(0) === 0)
    return 0;

  var r = 0;
  for (var i = 0; i < this.length; i++) {
    var b = this._zeroBits(this.words[i]);
    r += b;
    if (b !== 26)
      break;
  }
  return r;
};

BN.prototype.byteLength = function byteLength() {
  return Math.ceil(this.bitLength() / 8);
};

// Return negative clone of `this`
BN.prototype.neg = function neg() {
  if (this.cmpn(0) === 0)
    return this.clone();

  var r = this.clone();
  r.sign = !this.sign;
  return r;
};


// Or `num` with `this` in-place
BN.prototype.ior = function ior(num) {
  this.sign = this.sign || num.sign;

  while (this.length < num.length)
    this.words[this.length++] = 0;

  for (var i = 0; i < num.length; i++)
    this.words[i] = this.words[i] | num.words[i];

  return this.strip();
};


// Or `num` with `this`
BN.prototype.or = function or(num) {
  if (this.length > num.length)
    return this.clone().ior(num);
  else
    return num.clone().ior(this);
};


// And `num` with `this` in-place
BN.prototype.iand = function iand(num) {
  this.sign = this.sign && num.sign;

  // b = min-length(num, this)
  var b;
  if (this.length > num.length)
    b = num;
  else
    b = this;

  for (var i = 0; i < b.length; i++)
    this.words[i] = this.words[i] & num.words[i];

  this.length = b.length;

  return this.strip();
};


// And `num` with `this`
BN.prototype.and = function and(num) {
  if (this.length > num.length)
    return this.clone().iand(num);
  else
    return num.clone().iand(this);
};


// Xor `num` with `this` in-place
BN.prototype.ixor = function ixor(num) {
  this.sign = this.sign || num.sign;

  // a.length > b.length
  var a;
  var b;
  if (this.length > num.length) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  for (var i = 0; i < b.length; i++)
    this.words[i] = a.words[i] ^ b.words[i];

  if (this !== a)
    for (; i < a.length; i++)
      this.words[i] = a.words[i];

  this.length = a.length;

  return this.strip();
};


// Xor `num` with `this`
BN.prototype.xor = function xor(num) {
  if (this.length > num.length)
    return this.clone().ixor(num);
  else
    return num.clone().ixor(this);
};


// Set `bit` of `this`
BN.prototype.setn = function setn(bit, val) {
  assert(typeof bit === 'number' && bit >= 0);

  var off = (bit / 26) | 0;
  var wbit = bit % 26;

  while (this.length <= off)
    this.words[this.length++] = 0;

  if (val)
    this.words[off] = this.words[off] | (1 << wbit);
  else
    this.words[off] = this.words[off] & ~(1 << wbit);

  return this.strip();
};


// Add `num` to `this` in-place
BN.prototype.iadd = function iadd(num) {
  // negative + positive
  if (this.sign && !num.sign) {
    this.sign = false;
    var r = this.isub(num);
    this.sign = !this.sign;
    return this._normSign();

  // positive + negative
  } else if (!this.sign && num.sign) {
    num.sign = false;
    var r = this.isub(num);
    num.sign = true;
    return r._normSign();
  }

  // a.length > b.length
  var a;
  var b;
  if (this.length > num.length) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  var carry = 0;
  for (var i = 0; i < b.length; i++) {
    var r = a.words[i] + b.words[i] + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }
  for (; carry !== 0 && i < a.length; i++) {
    var r = a.words[i] + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }

  this.length = a.length;
  if (carry !== 0) {
    this.words[this.length] = carry;
    this.length++;
  // Copy the rest of the words
  } else if (a !== this) {
    for (; i < a.length; i++)
      this.words[i] = a.words[i];
  }

  return this;
};

// Add `num` to `this`
BN.prototype.add = function add(num) {
  if (num.sign && !this.sign) {
    num.sign = false;
    var res = this.sub(num);
    num.sign = true;
    return res;
  } else if (!num.sign && this.sign) {
    this.sign = false;
    var res = num.sub(this);
    this.sign = true;
    return res;
  }

  if (this.length > num.length)
    return this.clone().iadd(num);
  else
    return num.clone().iadd(this);
};

// Subtract `num` from `this` in-place
BN.prototype.isub = function isub(num) {
  // this - (-num) = this + num
  if (num.sign) {
    num.sign = false;
    var r = this.iadd(num);
    num.sign = true;
    return r._normSign();

  // -this - num = -(this + num)
  } else if (this.sign) {
    this.sign = false;
    this.iadd(num);
    this.sign = true;
    return this._normSign();
  }

  // At this point both numbers are positive
  var cmp = this.cmp(num);

  // Optimization - zeroify
  if (cmp === 0) {
    this.sign = false;
    this.length = 1;
    this.words[0] = 0;
    return this;
  }

  // a > b
  var a;
  var b;
  if (cmp > 0) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  var carry = 0;
  for (var i = 0; i < b.length; i++) {
    var r = a.words[i] - b.words[i] + carry;
    carry = r >> 26;
    this.words[i] = r & 0x3ffffff;
  }
  for (; carry !== 0 && i < a.length; i++) {
    var r = a.words[i] + carry;
    carry = r >> 26;
    this.words[i] = r & 0x3ffffff;
  }

  // Copy rest of the words
  if (carry === 0 && i < a.length && a !== this)
    for (; i < a.length; i++)
      this.words[i] = a.words[i];
  this.length = Math.max(this.length, i);

  if (a !== this)
    this.sign = true;

  return this.strip();
};

// Subtract `num` from `this`
BN.prototype.sub = function sub(num) {
  return this.clone().isub(num);
};

/*
// NOTE: This could be potentionally used to generate loop-less multiplications
function _genCombMulTo(alen, blen) {
  var len = alen + blen - 1;
  var src = [
    'var a = this.words, b = num.words, o = out.words, c = 0, w, ' +
        'mask = 0x3ffffff, shift = 0x4000000;',
    'out.length = ' + len + ';'
  ];
  for (var k = 0; k < len; k++) {
    var minJ = Math.max(0, k - alen + 1);
    var maxJ = Math.min(k, blen - 1);

    for (var j = minJ; j <= maxJ; j++) {
      var i = k - j;
      var mul = 'a[' + i + '] * b[' + j + ']';

      if (j === minJ) {
        src.push('w = ' + mul + ' + c;');
        src.push('c = (w / shift) | 0;');
      } else {
        src.push('w += ' + mul + ';');
        src.push('c += (w / shift) | 0;');
      }
      src.push('w &= mask;');
    }
    src.push('o[' + k + '] = w;');
  }
  src.push('if (c !== 0) {',
           '  o[' + k + '] = c;',
           '  out.length++;',
           '}',
           'return out;');

  return src.join('\n');
}
*/

BN.prototype._smallMulTo = function _smallMulTo(num, out) {
  out.sign = num.sign !== this.sign;
  out.length = this.length + num.length;

  var carry = 0;
  for (var k = 0; k < out.length - 1; k++) {
    // Sum all words with the same `i + j = k` and accumulate `ncarry`,
    // note that ncarry could be >= 0x3ffffff
    var ncarry = carry >>> 26;
    var rword = carry & 0x3ffffff;
    var maxJ = Math.min(k, num.length - 1);
    for (var j = Math.max(0, k - this.length + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.words[i] | 0;
      var b = num.words[j] | 0;
      var r = a * b;

      var lo = r & 0x3ffffff;
      ncarry = (ncarry + ((r / 0x4000000) | 0)) | 0;
      lo = (lo + rword) | 0;
      rword = lo & 0x3ffffff;
      ncarry = (ncarry + (lo >>> 26)) | 0;
    }
    out.words[k] = rword;
    carry = ncarry;
  }
  if (carry !== 0) {
    out.words[k] = carry;
  } else {
    out.length--;
  }

  return out.strip();
};

BN.prototype._bigMulTo = function _bigMulTo(num, out) {
  out.sign = num.sign !== this.sign;
  out.length = this.length + num.length;

  var carry = 0;
  var hncarry = 0;
  for (var k = 0; k < out.length - 1; k++) {
    // Sum all words with the same `i + j = k` and accumulate `ncarry`,
    // note that ncarry could be >= 0x3ffffff
    var ncarry = hncarry;
    hncarry = 0;
    var rword = carry & 0x3ffffff;
    var maxJ = Math.min(k, num.length - 1);
    for (var j = Math.max(0, k - this.length + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.words[i] | 0;
      var b = num.words[j] | 0;
      var r = a * b;

      var lo = r & 0x3ffffff;
      ncarry = (ncarry + ((r / 0x4000000) | 0)) | 0;
      lo = (lo + rword) | 0;
      rword = lo & 0x3ffffff;
      ncarry = (ncarry + (lo >>> 26)) | 0;

      hncarry += ncarry >>> 26;
      ncarry &= 0x3ffffff;
    }
    out.words[k] = rword;
    carry = ncarry;
    ncarry = hncarry;
  }
  if (carry !== 0) {
    out.words[k] = carry;
  } else {
    out.length--;
  }

  return out.strip();
};

BN.prototype.mulTo = function mulTo(num, out) {
  var res;
  if (this.length + num.length < 63)
    res = this._smallMulTo(num, out);
  else
    res = this._bigMulTo(num, out);
  return res;
};

// Multiply `this` by `num`
BN.prototype.mul = function mul(num) {
  var out = new BN(null);
  out.words = new Array(this.length + num.length);
  return this.mulTo(num, out);
};

// In-place Multiplication
BN.prototype.imul = function imul(num) {
  if (this.cmpn(0) === 0 || num.cmpn(0) === 0) {
    this.words[0] = 0;
    this.length = 1;
    return this;
  }

  var tlen = this.length;
  var nlen = num.length;

  this.sign = num.sign !== this.sign;
  this.length = this.length + num.length;
  this.words[this.length - 1] = 0;

  for (var k = this.length - 2; k >= 0; k--) {
    // Sum all words with the same `i + j = k` and accumulate `carry`,
    // note that carry could be >= 0x3ffffff
    var carry = 0;
    var rword = 0;
    var maxJ = Math.min(k, nlen - 1);
    for (var j = Math.max(0, k - tlen + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.words[i];
      var b = num.words[j];
      var r = a * b;

      var lo = r & 0x3ffffff;
      carry += (r / 0x4000000) | 0;
      lo += rword;
      rword = lo & 0x3ffffff;
      carry += lo >>> 26;
    }
    this.words[k] = rword;
    this.words[k + 1] += carry;
    carry = 0;
  }

  // Propagate overflows
  var carry = 0;
  for (var i = 1; i < this.length; i++) {
    var w = this.words[i] + carry;
    this.words[i] = w & 0x3ffffff;
    carry = w >>> 26;
  }

  return this.strip();
};

BN.prototype.imuln = function imuln(num) {
  assert(typeof num === 'number');

  // Carry
  var carry = 0;
  for (var i = 0; i < this.length; i++) {
    var w = this.words[i] * num;
    var lo = (w & 0x3ffffff) + (carry & 0x3ffffff);
    carry >>= 26;
    carry += (w / 0x4000000) | 0;
    // NOTE: lo is 27bit maximum
    carry += lo >>> 26;
    this.words[i] = lo & 0x3ffffff;
  }

  if (carry !== 0) {
    this.words[i] = carry;
    this.length++;
  }

  return this;
};

// `this` * `this`
BN.prototype.sqr = function sqr() {
  return this.mul(this);
};

// `this` * `this` in-place
BN.prototype.isqr = function isqr() {
  return this.mul(this);
};

// Shift-left in-place
BN.prototype.ishln = function ishln(bits) {
  assert(typeof bits === 'number' && bits >= 0);
  var r = bits % 26;
  var s = (bits - r) / 26;
  var carryMask = (0x3ffffff >>> (26 - r)) << (26 - r);

  if (r !== 0) {
    var carry = 0;
    for (var i = 0; i < this.length; i++) {
      var newCarry = this.words[i] & carryMask;
      var c = (this.words[i] - newCarry) << r;
      this.words[i] = c | carry;
      carry = newCarry >>> (26 - r);
    }
    if (carry) {
      this.words[i] = carry;
      this.length++;
    }
  }

  if (s !== 0) {
    for (var i = this.length - 1; i >= 0; i--)
      this.words[i + s] = this.words[i];
    for (var i = 0; i < s; i++)
      this.words[i] = 0;
    this.length += s;
  }

  return this.strip();
};

// Shift-right in-place
// NOTE: `hint` is a lowest bit before trailing zeroes
// NOTE: if `extended` is present - it will be filled with destroyed bits
BN.prototype.ishrn = function ishrn(bits, hint, extended) {
  assert(typeof bits === 'number' && bits >= 0);
  var h;
  if (hint)
    h = (hint - (hint % 26)) / 26;
  else
    h = 0;

  var r = bits % 26;
  var s = Math.min((bits - r) / 26, this.length);
  var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
  var maskedWords = extended;

  h -= s;
  h = Math.max(0, h);

  // Extended mode, copy masked part
  if (maskedWords) {
    for (var i = 0; i < s; i++)
      maskedWords.words[i] = this.words[i];
    maskedWords.length = s;
  }

  if (s === 0) {
    // No-op, we should not move anything at all
  } else if (this.length > s) {
    this.length -= s;
    for (var i = 0; i < this.length; i++)
      this.words[i] = this.words[i + s];
  } else {
    this.words[0] = 0;
    this.length = 1;
  }

  var carry = 0;
  for (var i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) {
    var word = this.words[i];
    this.words[i] = (carry << (26 - r)) | (word >>> r);
    carry = word & mask;
  }

  // Push carried bits as a mask
  if (maskedWords && carry !== 0)
    maskedWords.words[maskedWords.length++] = carry;

  if (this.length === 0) {
    this.words[0] = 0;
    this.length = 1;
  }

  this.strip();

  return this;
};

// Shift-left
BN.prototype.shln = function shln(bits) {
  return this.clone().ishln(bits);
};

// Shift-right
BN.prototype.shrn = function shrn(bits) {
  return this.clone().ishrn(bits);
};

// Test if n bit is set
BN.prototype.testn = function testn(bit) {
  assert(typeof bit === 'number' && bit >= 0);
  var r = bit % 26;
  var s = (bit - r) / 26;
  var q = 1 << r;

  // Fast case: bit is much higher than all existing words
  if (this.length <= s) {
    return false;
  }

  // Check bit and return
  var w = this.words[s];

  return !!(w & q);
};

// Return only lowers bits of number (in-place)
BN.prototype.imaskn = function imaskn(bits) {
  assert(typeof bits === 'number' && bits >= 0);
  var r = bits % 26;
  var s = (bits - r) / 26;

  assert(!this.sign, 'imaskn works only with positive numbers');

  if (r !== 0)
    s++;
  this.length = Math.min(s, this.length);

  if (r !== 0) {
    var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
    this.words[this.length - 1] &= mask;
  }

  return this.strip();
};

// Return only lowers bits of number
BN.prototype.maskn = function maskn(bits) {
  return this.clone().imaskn(bits);
};

// Add plain number `num` to `this`
BN.prototype.iaddn = function iaddn(num) {
  assert(typeof num === 'number');
  if (num < 0)
    return this.isubn(-num);

  // Possible sign change
  if (this.sign) {
    if (this.length === 1 && this.words[0] < num) {
      this.words[0] = num - this.words[0];
      this.sign = false;
      return this;
    }

    this.sign = false;
    this.isubn(num);
    this.sign = true;
    return this;
  }

  // Add without checks
  return this._iaddn(num);
};

BN.prototype._iaddn = function _iaddn(num) {
  this.words[0] += num;

  // Carry
  for (var i = 0; i < this.length && this.words[i] >= 0x4000000; i++) {
    this.words[i] -= 0x4000000;
    if (i === this.length - 1)
      this.words[i + 1] = 1;
    else
      this.words[i + 1]++;
  }
  this.length = Math.max(this.length, i + 1);

  return this;
};

// Subtract plain number `num` from `this`
BN.prototype.isubn = function isubn(num) {
  assert(typeof num === 'number');
  if (num < 0)
    return this.iaddn(-num);

  if (this.sign) {
    this.sign = false;
    this.iaddn(num);
    this.sign = true;
    return this;
  }

  this.words[0] -= num;

  // Carry
  for (var i = 0; i < this.length && this.words[i] < 0; i++) {
    this.words[i] += 0x4000000;
    this.words[i + 1] -= 1;
  }

  return this.strip();
};

BN.prototype.addn = function addn(num) {
  return this.clone().iaddn(num);
};

BN.prototype.subn = function subn(num) {
  return this.clone().isubn(num);
};

BN.prototype.iabs = function iabs() {
  this.sign = false;

  return this;
};

BN.prototype.abs = function abs() {
  return this.clone().iabs();
};

BN.prototype._ishlnsubmul = function _ishlnsubmul(num, mul, shift) {
  // Bigger storage is needed
  var len = num.length + shift;
  var i;
  if (this.words.length < len) {
    var t = new Array(len);
    for (var i = 0; i < this.length; i++)
      t[i] = this.words[i];
    this.words = t;
  } else {
    i = this.length;
  }

  // Zeroify rest
  this.length = Math.max(this.length, len);
  for (; i < this.length; i++)
    this.words[i] = 0;

  var carry = 0;
  for (var i = 0; i < num.length; i++) {
    var w = this.words[i + shift] + carry;
    var right = num.words[i] * mul;
    w -= right & 0x3ffffff;
    carry = (w >> 26) - ((right / 0x4000000) | 0);
    this.words[i + shift] = w & 0x3ffffff;
  }
  for (; i < this.length - shift; i++) {
    var w = this.words[i + shift] + carry;
    carry = w >> 26;
    this.words[i + shift] = w & 0x3ffffff;
  }

  if (carry === 0)
    return this.strip();

  // Subtraction overflow
  assert(carry === -1);
  carry = 0;
  for (var i = 0; i < this.length; i++) {
    var w = -this.words[i] + carry;
    carry = w >> 26;
    this.words[i] = w & 0x3ffffff;
  }
  this.sign = true;

  return this.strip();
};

BN.prototype._wordDiv = function _wordDiv(num, mode) {
  var shift = this.length - num.length;

  var a = this.clone();
  var b = num;

  // Normalize
  var bhi = b.words[b.length - 1];
  var bhiBits = this._countBits(bhi);
  shift = 26 - bhiBits;
  if (shift !== 0) {
    b = b.shln(shift);
    a.ishln(shift);
    bhi = b.words[b.length - 1];
  }

  // Initialize quotient
  var m = a.length - b.length;
  var q;

  if (mode !== 'mod') {
    q = new BN(null);
    q.length = m + 1;
    q.words = new Array(q.length);
    for (var i = 0; i < q.length; i++)
      q.words[i] = 0;
  }

  var diff = a.clone()._ishlnsubmul(b, 1, m);
  if (!diff.sign) {
    a = diff;
    if (q)
      q.words[m] = 1;
  }

  for (var j = m - 1; j >= 0; j--) {
    var qj = a.words[b.length + j] * 0x4000000 + a.words[b.length + j - 1];

    // NOTE: (qj / bhi) is (0x3ffffff * 0x4000000 + 0x3ffffff) / 0x2000000 max
    // (0x7ffffff)
    qj = Math.min((qj / bhi) | 0, 0x3ffffff);

    a._ishlnsubmul(b, qj, j);
    while (a.sign) {
      qj--;
      a.sign = false;
      a._ishlnsubmul(b, 1, j);
      a.sign = !a.sign;
    }
    if (q)
      q.words[j] = qj;
  }
  if (q)
    q.strip();
  a.strip();

  // Denormalize
  if (mode !== 'div' && shift !== 0)
    a.ishrn(shift);
  return { div: q ? q : null, mod: a };
};

BN.prototype.divmod = function divmod(num, mode) {
  assert(num.cmpn(0) !== 0);

  if (this.sign && !num.sign) {
    var res = this.neg().divmod(num, mode);
    var div;
    var mod;
    if (mode !== 'mod')
      div = res.div.neg();
    if (mode !== 'div')
      mod = res.mod.cmpn(0) === 0 ? res.mod : num.sub(res.mod);
    return {
      div: div,
      mod: mod
    };
  } else if (!this.sign && num.sign) {
    var res = this.divmod(num.neg(), mode);
    var div;
    if (mode !== 'mod')
      div = res.div.neg();
    return { div: div, mod: res.mod };
  } else if (this.sign && num.sign) {
    return this.neg().divmod(num.neg(), mode);
  }

  // Both numbers are positive at this point

  // Strip both numbers to approximate shift value
  if (num.length > this.length || this.cmp(num) < 0)
    return { div: new BN(0), mod: this };

  // Very short reduction
  if (num.length === 1) {
    if (mode === 'div')
      return { div: this.divn(num.words[0]), mod: null };
    else if (mode === 'mod')
      return { div: null, mod: new BN(this.modn(num.words[0])) };
    return {
      div: this.divn(num.words[0]),
      mod: new BN(this.modn(num.words[0]))
    };
  }

  return this._wordDiv(num, mode);
};

// Find `this` / `num`
BN.prototype.div = function div(num) {
  return this.divmod(num, 'div').div;
};

// Find `this` % `num`
BN.prototype.mod = function mod(num) {
  return this.divmod(num, 'mod').mod;
};

// Find Round(`this` / `num`)
BN.prototype.divRound = function divRound(num) {
  var dm = this.divmod(num);

  // Fast case - exact division
  if (dm.mod.cmpn(0) === 0)
    return dm.div;

  var mod = dm.div.sign ? dm.mod.isub(num) : dm.mod;

  var half = num.shrn(1);
  var r2 = num.andln(1);
  var cmp = mod.cmp(half);

  // Round down
  if (cmp < 0 || r2 === 1 && cmp === 0)
    return dm.div;

  // Round up
  return dm.div.sign ? dm.div.isubn(1) : dm.div.iaddn(1);
};

BN.prototype.modn = function modn(num) {
  assert(num <= 0x3ffffff);
  var p = (1 << 26) % num;

  var acc = 0;
  for (var i = this.length - 1; i >= 0; i--)
    acc = (p * acc + this.words[i]) % num;

  return acc;
};

// In-place division by number
BN.prototype.idivn = function idivn(num) {
  assert(num <= 0x3ffffff);

  var carry = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    var w = this.words[i] + carry * 0x4000000;
    this.words[i] = (w / num) | 0;
    carry = w % num;
  }

  return this.strip();
};

BN.prototype.divn = function divn(num) {
  return this.clone().idivn(num);
};

BN.prototype.egcd = function egcd(p) {
  assert(!p.sign);
  assert(p.cmpn(0) !== 0);

  var x = this;
  var y = p.clone();

  if (x.sign)
    x = x.mod(p);
  else
    x = x.clone();

  // A * x + B * y = x
  var A = new BN(1);
  var B = new BN(0);

  // C * x + D * y = y
  var C = new BN(0);
  var D = new BN(1);

  var g = 0;

  while (x.isEven() && y.isEven()) {
    x.ishrn(1);
    y.ishrn(1);
    ++g;
  }

  var yp = y.clone();
  var xp = x.clone();

  while (x.cmpn(0) !== 0) {
    while (x.isEven()) {
      x.ishrn(1);
      if (A.isEven() && B.isEven()) {
        A.ishrn(1);
        B.ishrn(1);
      } else {
        A.iadd(yp).ishrn(1);
        B.isub(xp).ishrn(1);
      }
    }

    while (y.isEven()) {
      y.ishrn(1);
      if (C.isEven() && D.isEven()) {
        C.ishrn(1);
        D.ishrn(1);
      } else {
        C.iadd(yp).ishrn(1);
        D.isub(xp).ishrn(1);
      }
    }

    if (x.cmp(y) >= 0) {
      x.isub(y);
      A.isub(C);
      B.isub(D);
    } else {
      y.isub(x);
      C.isub(A);
      D.isub(B);
    }
  }

  return {
    a: C,
    b: D,
    gcd: y.ishln(g)
  };
};

// This is reduced incarnation of the binary EEA
// above, designated to invert members of the
// _prime_ fields F(p) at a maximal speed
BN.prototype._invmp = function _invmp(p) {
  assert(!p.sign);
  assert(p.cmpn(0) !== 0);

  var a = this;
  var b = p.clone();

  if (a.sign)
    a = a.mod(p);
  else
    a = a.clone();

  var x1 = new BN(1);
  var x2 = new BN(0);

  var delta = b.clone();

  while (a.cmpn(1) > 0 && b.cmpn(1) > 0) {
    while (a.isEven()) {
      a.ishrn(1);
      if (x1.isEven())
        x1.ishrn(1);
      else
        x1.iadd(delta).ishrn(1);
    }
    while (b.isEven()) {
      b.ishrn(1);
      if (x2.isEven())
        x2.ishrn(1);
      else
        x2.iadd(delta).ishrn(1);
    }
    if (a.cmp(b) >= 0) {
      a.isub(b);
      x1.isub(x2);
    } else {
      b.isub(a);
      x2.isub(x1);
    }
  }
  if (a.cmpn(1) === 0)
    return x1;
  else
    return x2;
};

BN.prototype.gcd = function gcd(num) {
  if (this.cmpn(0) === 0)
    return num.clone();
  if (num.cmpn(0) === 0)
    return this.clone();

  var a = this.clone();
  var b = num.clone();
  a.sign = false;
  b.sign = false;

  // Remove common factor of two
  for (var shift = 0; a.isEven() && b.isEven(); shift++) {
    a.ishrn(1);
    b.ishrn(1);
  }

  do {
    while (a.isEven())
      a.ishrn(1);
    while (b.isEven())
      b.ishrn(1);

    var r = a.cmp(b);
    if (r < 0) {
      // Swap `a` and `b` to make `a` always bigger than `b`
      var t = a;
      a = b;
      b = t;
    } else if (r === 0 || b.cmpn(1) === 0) {
      break;
    }

    a.isub(b);
  } while (true);

  return b.ishln(shift);
};

// Invert number in the field F(num)
BN.prototype.invm = function invm(num) {
  return this.egcd(num).a.mod(num);
};

BN.prototype.isEven = function isEven() {
  return (this.words[0] & 1) === 0;
};

BN.prototype.isOdd = function isOdd() {
  return (this.words[0] & 1) === 1;
};

// And first word and num
BN.prototype.andln = function andln(num) {
  return this.words[0] & num;
};

// Increment at the bit position in-line
BN.prototype.bincn = function bincn(bit) {
  assert(typeof bit === 'number');
  var r = bit % 26;
  var s = (bit - r) / 26;
  var q = 1 << r;

  // Fast case: bit is much higher than all existing words
  if (this.length <= s) {
    for (var i = this.length; i < s + 1; i++)
      this.words[i] = 0;
    this.words[s] |= q;
    this.length = s + 1;
    return this;
  }

  // Add bit and propagate, if needed
  var carry = q;
  for (var i = s; carry !== 0 && i < this.length; i++) {
    var w = this.words[i];
    w += carry;
    carry = w >>> 26;
    w &= 0x3ffffff;
    this.words[i] = w;
  }
  if (carry !== 0) {
    this.words[i] = carry;
    this.length++;
  }
  return this;
};

BN.prototype.cmpn = function cmpn(num) {
  var sign = num < 0;
  if (sign)
    num = -num;

  if (this.sign && !sign)
    return -1;
  else if (!this.sign && sign)
    return 1;

  num &= 0x3ffffff;
  this.strip();

  var res;
  if (this.length > 1) {
    res = 1;
  } else {
    var w = this.words[0];
    res = w === num ? 0 : w < num ? -1 : 1;
  }
  if (this.sign)
    res = -res;
  return res;
};

// Compare two numbers and return:
// 1 - if `this` > `num`
// 0 - if `this` == `num`
// -1 - if `this` < `num`
BN.prototype.cmp = function cmp(num) {
  if (this.sign && !num.sign)
    return -1;
  else if (!this.sign && num.sign)
    return 1;

  var res = this.ucmp(num);
  if (this.sign)
    return -res;
  else
    return res;
};

// Unsigned comparison
BN.prototype.ucmp = function ucmp(num) {
  // At this point both numbers have the same sign
  if (this.length > num.length)
    return 1;
  else if (this.length < num.length)
    return -1;

  var res = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    var a = this.words[i];
    var b = num.words[i];

    if (a === b)
      continue;
    if (a < b)
      res = -1;
    else if (a > b)
      res = 1;
    break;
  }
  return res;
};

//
// A reduce context, could be using montgomery or something better, depending
// on the `m` itself.
//
BN.red = function red(num) {
  return new Red(num);
};

BN.prototype.toRed = function toRed(ctx) {
  assert(!this.red, 'Already a number in reduction context');
  assert(!this.sign, 'red works only with positives');
  return ctx.convertTo(this)._forceRed(ctx);
};

BN.prototype.fromRed = function fromRed() {
  assert(this.red, 'fromRed works only with numbers in reduction context');
  return this.red.convertFrom(this);
};

BN.prototype._forceRed = function _forceRed(ctx) {
  this.red = ctx;
  return this;
};

BN.prototype.forceRed = function forceRed(ctx) {
  assert(!this.red, 'Already a number in reduction context');
  return this._forceRed(ctx);
};

BN.prototype.redAdd = function redAdd(num) {
  assert(this.red, 'redAdd works only with red numbers');
  return this.red.add(this, num);
};

BN.prototype.redIAdd = function redIAdd(num) {
  assert(this.red, 'redIAdd works only with red numbers');
  return this.red.iadd(this, num);
};

BN.prototype.redSub = function redSub(num) {
  assert(this.red, 'redSub works only with red numbers');
  return this.red.sub(this, num);
};

BN.prototype.redISub = function redISub(num) {
  assert(this.red, 'redISub works only with red numbers');
  return this.red.isub(this, num);
};

BN.prototype.redShl = function redShl(num) {
  assert(this.red, 'redShl works only with red numbers');
  return this.red.shl(this, num);
};

BN.prototype.redMul = function redMul(num) {
  assert(this.red, 'redMul works only with red numbers');
  this.red._verify2(this, num);
  return this.red.mul(this, num);
};

BN.prototype.redIMul = function redIMul(num) {
  assert(this.red, 'redMul works only with red numbers');
  this.red._verify2(this, num);
  return this.red.imul(this, num);
};

BN.prototype.redSqr = function redSqr() {
  assert(this.red, 'redSqr works only with red numbers');
  this.red._verify1(this);
  return this.red.sqr(this);
};

BN.prototype.redISqr = function redISqr() {
  assert(this.red, 'redISqr works only with red numbers');
  this.red._verify1(this);
  return this.red.isqr(this);
};

// Square root over p
BN.prototype.redSqrt = function redSqrt() {
  assert(this.red, 'redSqrt works only with red numbers');
  this.red._verify1(this);
  return this.red.sqrt(this);
};

BN.prototype.redInvm = function redInvm() {
  assert(this.red, 'redInvm works only with red numbers');
  this.red._verify1(this);
  return this.red.invm(this);
};

// Return negative clone of `this` % `red modulo`
BN.prototype.redNeg = function redNeg() {
  assert(this.red, 'redNeg works only with red numbers');
  this.red._verify1(this);
  return this.red.neg(this);
};

BN.prototype.redPow = function redPow(num) {
  assert(this.red && !num.red, 'redPow(normalNum)');
  this.red._verify1(this);
  return this.red.pow(this, num);
};

// Prime numbers with efficient reduction
var primes = {
  k256: null,
  p224: null,
  p192: null,
  p25519: null
};

// Pseudo-Mersenne prime
function MPrime(name, p) {
  // P = 2 ^ N - K
  this.name = name;
  this.p = new BN(p, 16);
  this.n = this.p.bitLength();
  this.k = new BN(1).ishln(this.n).isub(this.p);

  this.tmp = this._tmp();
}

MPrime.prototype._tmp = function _tmp() {
  var tmp = new BN(null);
  tmp.words = new Array(Math.ceil(this.n / 13));
  return tmp;
};

MPrime.prototype.ireduce = function ireduce(num) {
  // Assumes that `num` is less than `P^2`
  // num = HI * (2 ^ N - K) + HI * K + LO = HI * K + LO (mod P)
  var r = num;
  var rlen;

  do {
    this.split(r, this.tmp);
    r = this.imulK(r);
    r = r.iadd(this.tmp);
    rlen = r.bitLength();
  } while (rlen > this.n);

  var cmp = rlen < this.n ? -1 : r.ucmp(this.p);
  if (cmp === 0) {
    r.words[0] = 0;
    r.length = 1;
  } else if (cmp > 0) {
    r.isub(this.p);
  } else {
    r.strip();
  }

  return r;
};

MPrime.prototype.split = function split(input, out) {
  input.ishrn(this.n, 0, out);
};

MPrime.prototype.imulK = function imulK(num) {
  return num.imul(this.k);
};

function K256() {
  MPrime.call(
    this,
    'k256',
    'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f');
}
inherits(K256, MPrime);

K256.prototype.split = function split(input, output) {
  // 256 = 9 * 26 + 22
  var mask = 0x3fffff;

  var outLen = Math.min(input.length, 9);
  for (var i = 0; i < outLen; i++)
    output.words[i] = input.words[i];
  output.length = outLen;

  if (input.length <= 9) {
    input.words[0] = 0;
    input.length = 1;
    return;
  }

  // Shift by 9 limbs
  var prev = input.words[9];
  output.words[output.length++] = prev & mask;

  for (var i = 10; i < input.length; i++) {
    var next = input.words[i];
    input.words[i - 10] = ((next & mask) << 4) | (prev >>> 22);
    prev = next;
  }
  input.words[i - 10] = prev >>> 22;
  input.length -= 9;
};

K256.prototype.imulK = function imulK(num) {
  // K = 0x1000003d1 = [ 0x40, 0x3d1 ]
  num.words[num.length] = 0;
  num.words[num.length + 1] = 0;
  num.length += 2;

  // bounded at: 0x40 * 0x3ffffff + 0x3d0 = 0x100000390
  var hi;
  var lo = 0;
  for (var i = 0; i < num.length; i++) {
    var w = num.words[i];
    hi = w * 0x40;
    lo += w * 0x3d1;
    hi += (lo / 0x4000000) | 0;
    lo &= 0x3ffffff;

    num.words[i] = lo;

    lo = hi;
  }

  // Fast length reduction
  if (num.words[num.length - 1] === 0) {
    num.length--;
    if (num.words[num.length - 1] === 0)
      num.length--;
  }
  return num;
};

function P224() {
  MPrime.call(
    this,
    'p224',
    'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001');
}
inherits(P224, MPrime);

function P192() {
  MPrime.call(
    this,
    'p192',
    'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff');
}
inherits(P192, MPrime);

function P25519() {
  // 2 ^ 255 - 19
  MPrime.call(
    this,
    '25519',
    '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed');
}
inherits(P25519, MPrime);

P25519.prototype.imulK = function imulK(num) {
  // K = 0x13
  var carry = 0;
  for (var i = 0; i < num.length; i++) {
    var hi = num.words[i] * 0x13 + carry;
    var lo = hi & 0x3ffffff;
    hi >>>= 26;

    num.words[i] = lo;
    carry = hi;
  }
  if (carry !== 0)
    num.words[num.length++] = carry;
  return num;
};

// Exported mostly for testing purposes, use plain name instead
BN._prime = function prime(name) {
  // Cached version of prime
  if (primes[name])
    return primes[name];

  var prime;
  if (name === 'k256')
    prime = new K256();
  else if (name === 'p224')
    prime = new P224();
  else if (name === 'p192')
    prime = new P192();
  else if (name === 'p25519')
    prime = new P25519();
  else
    throw new Error('Unknown prime ' + name);
  primes[name] = prime;

  return prime;
};

//
// Base reduction engine
//
function Red(m) {
  if (typeof m === 'string') {
    var prime = BN._prime(m);
    this.m = prime.p;
    this.prime = prime;
  } else {
    this.m = m;
    this.prime = null;
  }
}

Red.prototype._verify1 = function _verify1(a) {
  assert(!a.sign, 'red works only with positives');
  assert(a.red, 'red works only with red numbers');
};

Red.prototype._verify2 = function _verify2(a, b) {
  assert(!a.sign && !b.sign, 'red works only with positives');
  assert(a.red && a.red === b.red,
         'red works only with red numbers');
};

Red.prototype.imod = function imod(a) {
  if (this.prime)
    return this.prime.ireduce(a)._forceRed(this);
  return a.mod(this.m)._forceRed(this);
};

Red.prototype.neg = function neg(a) {
  var r = a.clone();
  r.sign = !r.sign;
  return r.iadd(this.m)._forceRed(this);
};

Red.prototype.add = function add(a, b) {
  this._verify2(a, b);

  var res = a.add(b);
  if (res.cmp(this.m) >= 0)
    res.isub(this.m);
  return res._forceRed(this);
};

Red.prototype.iadd = function iadd(a, b) {
  this._verify2(a, b);

  var res = a.iadd(b);
  if (res.cmp(this.m) >= 0)
    res.isub(this.m);
  return res;
};

Red.prototype.sub = function sub(a, b) {
  this._verify2(a, b);

  var res = a.sub(b);
  if (res.cmpn(0) < 0)
    res.iadd(this.m);
  return res._forceRed(this);
};

Red.prototype.isub = function isub(a, b) {
  this._verify2(a, b);

  var res = a.isub(b);
  if (res.cmpn(0) < 0)
    res.iadd(this.m);
  return res;
};

Red.prototype.shl = function shl(a, num) {
  this._verify1(a);
  return this.imod(a.shln(num));
};

Red.prototype.imul = function imul(a, b) {
  this._verify2(a, b);
  return this.imod(a.imul(b));
};

Red.prototype.mul = function mul(a, b) {
  this._verify2(a, b);
  return this.imod(a.mul(b));
};

Red.prototype.isqr = function isqr(a) {
  return this.imul(a, a);
};

Red.prototype.sqr = function sqr(a) {
  return this.mul(a, a);
};

Red.prototype.sqrt = function sqrt(a) {
  if (a.cmpn(0) === 0)
    return a.clone();

  var mod3 = this.m.andln(3);
  assert(mod3 % 2 === 1);

  // Fast case
  if (mod3 === 3) {
    var pow = this.m.add(new BN(1)).ishrn(2);
    var r = this.pow(a, pow);
    return r;
  }

  // Tonelli-Shanks algorithm (Totally unoptimized and slow)
  //
  // Find Q and S, that Q * 2 ^ S = (P - 1)
  var q = this.m.subn(1);
  var s = 0;
  while (q.cmpn(0) !== 0 && q.andln(1) === 0) {
    s++;
    q.ishrn(1);
  }
  assert(q.cmpn(0) !== 0);

  var one = new BN(1).toRed(this);
  var nOne = one.redNeg();

  // Find quadratic non-residue
  // NOTE: Max is such because of generalized Riemann hypothesis.
  var lpow = this.m.subn(1).ishrn(1);
  var z = this.m.bitLength();
  z = new BN(2 * z * z).toRed(this);
  while (this.pow(z, lpow).cmp(nOne) !== 0)
    z.redIAdd(nOne);

  var c = this.pow(z, q);
  var r = this.pow(a, q.addn(1).ishrn(1));
  var t = this.pow(a, q);
  var m = s;
  while (t.cmp(one) !== 0) {
    var tmp = t;
    for (var i = 0; tmp.cmp(one) !== 0; i++)
      tmp = tmp.redSqr();
    assert(i < m);
    var b = this.pow(c, new BN(1).ishln(m - i - 1));

    r = r.redMul(b);
    c = b.redSqr();
    t = t.redMul(c);
    m = i;
  }

  return r;
};

Red.prototype.invm = function invm(a) {
  var inv = a._invmp(this.m);
  if (inv.sign) {
    inv.sign = false;
    return this.imod(inv).redNeg();
  } else {
    return this.imod(inv);
  }
};

Red.prototype.pow = function pow(a, num) {
  var w = [];
  var q = num.clone();
  while (q.cmpn(0) !== 0) {
    w.push(q.andln(1));
    q.ishrn(1);
  }

  // Skip leading zeroes
  var res = a;
  for (var i = 0; i < w.length; i++, res = this.sqr(res))
    if (w[i] !== 0)
      break;

  if (++i < w.length) {
    for (var q = this.sqr(res); i < w.length; i++, q = this.sqr(q)) {
      if (w[i] === 0)
        continue;
      res = this.mul(res, q);
    }
  }

  return res;
};

Red.prototype.convertTo = function convertTo(num) {
  return num.clone();
};

Red.prototype.convertFrom = function convertFrom(num) {
  var res = num.clone();
  res.red = null;
  return res;
};

//
// Montgomery method engine
//

BN.mont = function mont(num) {
  return new Mont(num);
};

function Mont(m) {
  Red.call(this, m);

  this.shift = this.m.bitLength();
  if (this.shift % 26 !== 0)
    this.shift += 26 - (this.shift % 26);
  this.r = new BN(1).ishln(this.shift);
  this.r2 = this.imod(this.r.sqr());
  this.rinv = this.r._invmp(this.m);

  this.minv = this.rinv.mul(this.r).isubn(1).div(this.m);
  this.minv.sign = true;
  this.minv = this.minv.mod(this.r);
}
inherits(Mont, Red);

Mont.prototype.convertTo = function convertTo(num) {
  return this.imod(num.shln(this.shift));
};

Mont.prototype.convertFrom = function convertFrom(num) {
  var r = this.imod(num.mul(this.rinv));
  r.red = null;
  return r;
};

Mont.prototype.imul = function imul(a, b) {
  if (a.cmpn(0) === 0 || b.cmpn(0) === 0) {
    a.words[0] = 0;
    a.length = 1;
    return a;
  }

  var t = a.imul(b);
  var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
  var u = t.isub(c).ishrn(this.shift);
  var res = u;
  if (u.cmp(this.m) >= 0)
    res = u.isub(this.m);
  else if (u.cmpn(0) < 0)
    res = u.iadd(this.m);

  return res._forceRed(this);
};

Mont.prototype.mul = function mul(a, b) {
  if (a.cmpn(0) === 0 || b.cmpn(0) === 0)
    return new BN(0)._forceRed(this);

  var t = a.mul(b);
  var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
  var u = t.isub(c).ishrn(this.shift);
  var res = u;
  if (u.cmp(this.m) >= 0)
    res = u.isub(this.m);
  else if (u.cmpn(0) < 0)
    res = u.iadd(this.m);

  return res._forceRed(this);
};

Mont.prototype.invm = function invm(a) {
  // (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R
  var res = this.imod(a._invmp(this.m).mul(this.r2));
  return res._forceRed(this);
};

})(typeof module === 'undefined' || module, this);

},{}],15:[function(require,module,exports){
var r;

module.exports = function rand(len) {
  if (!r)
    r = new Rand(null);

  return r.generate(len);
};

function Rand(rand) {
  this.rand = rand;
}
module.exports.Rand = Rand;

Rand.prototype.generate = function generate(len) {
  return this._rand(len);
};

if (typeof window === 'object') {
  if (window.crypto && window.crypto.getRandomValues) {
    // Modern browsers
    Rand.prototype._rand = function _rand(n) {
      var arr = new Uint8Array(n);
      window.crypto.getRandomValues(arr);
      return arr;
    };
  } else if (window.msCrypto && window.msCrypto.getRandomValues) {
    // IE
    Rand.prototype._rand = function _rand(n) {
      var arr = new Uint8Array(n);
      window.msCrypto.getRandomValues(arr);
      return arr;
    };
  } else {
    // Old junk
    Rand.prototype._rand = function() {
      throw new Error('Not implemented yet');
    };
  }
} else {
  // Node.js or Web worker
  try {
    var crypto = require('cry' + 'pto');

    Rand.prototype._rand = function _rand(n) {
      return crypto.randomBytes(n);
    };
  } catch (e) {
    // Emulate crypto API using randy
    Rand.prototype._rand = function _rand(n) {
      var res = new Uint8Array(n);
      for (var i = 0; i < res.length; i++)
        res[i] = this.rand.getByte();
      return res;
    };
  }
}

},{}],16:[function(require,module,exports){
var hash = exports;

hash.utils = require('./hash/utils');
hash.common = require('./hash/common');
hash.sha = require('./hash/sha');
hash.ripemd = require('./hash/ripemd');
hash.hmac = require('./hash/hmac');

// Proxy hash functions to the main object
hash.sha1 = hash.sha.sha1;
hash.sha256 = hash.sha.sha256;
hash.sha224 = hash.sha.sha224;
hash.sha384 = hash.sha.sha384;
hash.sha512 = hash.sha.sha512;
hash.ripemd160 = hash.ripemd.ripemd160;

},{"./hash/common":17,"./hash/hmac":18,"./hash/ripemd":19,"./hash/sha":20,"./hash/utils":21}],17:[function(require,module,exports){
var hash = require('../hash');
var utils = hash.utils;
var assert = utils.assert;

function BlockHash() {
  this.pending = null;
  this.pendingTotal = 0;
  this.blockSize = this.constructor.blockSize;
  this.outSize = this.constructor.outSize;
  this.hmacStrength = this.constructor.hmacStrength;
  this.padLength = this.constructor.padLength / 8;
  this.endian = 'big';

  this._delta8 = this.blockSize / 8;
  this._delta32 = this.blockSize / 32;
}
exports.BlockHash = BlockHash;

BlockHash.prototype.update = function update(msg, enc) {
  // Convert message to array, pad it, and join into 32bit blocks
  msg = utils.toArray(msg, enc);
  if (!this.pending)
    this.pending = msg;
  else
    this.pending = this.pending.concat(msg);
  this.pendingTotal += msg.length;

  // Enough data, try updating
  if (this.pending.length >= this._delta8) {
    msg = this.pending;

    // Process pending data in blocks
    var r = msg.length % this._delta8;
    this.pending = msg.slice(msg.length - r, msg.length);
    if (this.pending.length === 0)
      this.pending = null;

    msg = utils.join32(msg, 0, msg.length - r, this.endian);
    for (var i = 0; i < msg.length; i += this._delta32)
      this._update(msg, i, i + this._delta32);
  }

  return this;
};

BlockHash.prototype.digest = function digest(enc) {
  this.update(this._pad());
  assert(this.pending === null);

  return this._digest(enc);
};

BlockHash.prototype._pad = function pad() {
  var len = this.pendingTotal;
  var bytes = this._delta8;
  var k = bytes - ((len + this.padLength) % bytes);
  var res = new Array(k + this.padLength);
  res[0] = 0x80;
  for (var i = 1; i < k; i++)
    res[i] = 0;

  // Append length
  len <<= 3;
  if (this.endian === 'big') {
    for (var t = 8; t < this.padLength; t++)
      res[i++] = 0;

    res[i++] = 0;
    res[i++] = 0;
    res[i++] = 0;
    res[i++] = 0;
    res[i++] = (len >>> 24) & 0xff;
    res[i++] = (len >>> 16) & 0xff;
    res[i++] = (len >>> 8) & 0xff;
    res[i++] = len & 0xff;
  } else {
    res[i++] = len & 0xff;
    res[i++] = (len >>> 8) & 0xff;
    res[i++] = (len >>> 16) & 0xff;
    res[i++] = (len >>> 24) & 0xff;
    res[i++] = 0;
    res[i++] = 0;
    res[i++] = 0;
    res[i++] = 0;

    for (var t = 8; t < this.padLength; t++)
      res[i++] = 0;
  }

  return res;
};

},{"../hash":16}],18:[function(require,module,exports){
var hmac = exports;

var hash = require('../hash');
var utils = hash.utils;
var assert = utils.assert;

function Hmac(hash, key, enc) {
  if (!(this instanceof Hmac))
    return new Hmac(hash, key, enc);
  this.Hash = hash;
  this.blockSize = hash.blockSize / 8;
  this.outSize = hash.outSize / 8;
  this.inner = null;
  this.outer = null;

  this._init(utils.toArray(key, enc));
}
module.exports = Hmac;

Hmac.prototype._init = function init(key) {
  // Shorten key, if needed
  if (key.length > this.blockSize)
    key = new this.Hash().update(key).digest();
  assert(key.length <= this.blockSize);

  // Add padding to key
  for (var i = key.length; i < this.blockSize; i++)
    key.push(0);

  for (var i = 0; i < key.length; i++)
    key[i] ^= 0x36;
  this.inner = new this.Hash().update(key);

  // 0x36 ^ 0x5c = 0x6a
  for (var i = 0; i < key.length; i++)
    key[i] ^= 0x6a;
  this.outer = new this.Hash().update(key);
};

Hmac.prototype.update = function update(msg, enc) {
  this.inner.update(msg, enc);
  return this;
};

Hmac.prototype.digest = function digest(enc) {
  this.outer.update(this.inner.digest());
  return this.outer.digest(enc);
};

},{"../hash":16}],19:[function(require,module,exports){
var hash = require('../hash');
var utils = hash.utils;

var rotl32 = utils.rotl32;
var sum32 = utils.sum32;
var sum32_3 = utils.sum32_3;
var sum32_4 = utils.sum32_4;
var BlockHash = hash.common.BlockHash;

function RIPEMD160() {
  if (!(this instanceof RIPEMD160))
    return new RIPEMD160();

  BlockHash.call(this);

  this.h = [ 0x67452301, 0xefcdab89, 0x98badcfe, 0x10325476, 0xc3d2e1f0 ];
  this.endian = 'little';
}
utils.inherits(RIPEMD160, BlockHash);
exports.ripemd160 = RIPEMD160;

RIPEMD160.blockSize = 512;
RIPEMD160.outSize = 160;
RIPEMD160.hmacStrength = 192;
RIPEMD160.padLength = 64;

RIPEMD160.prototype._update = function update(msg, start) {
  var A = this.h[0];
  var B = this.h[1];
  var C = this.h[2];
  var D = this.h[3];
  var E = this.h[4];
  var Ah = A;
  var Bh = B;
  var Ch = C;
  var Dh = D;
  var Eh = E;
  for (var j = 0; j < 80; j++) {
    var T = sum32(
      rotl32(
        sum32_4(A, f(j, B, C, D), msg[r[j] + start], K(j)),
        s[j]),
      E);
    A = E;
    E = D;
    D = rotl32(C, 10);
    C = B;
    B = T;
    T = sum32(
      rotl32(
        sum32_4(Ah, f(79 - j, Bh, Ch, Dh), msg[rh[j] + start], Kh(j)),
        sh[j]),
      Eh);
    Ah = Eh;
    Eh = Dh;
    Dh = rotl32(Ch, 10);
    Ch = Bh;
    Bh = T;
  }
  T = sum32_3(this.h[1], C, Dh);
  this.h[1] = sum32_3(this.h[2], D, Eh);
  this.h[2] = sum32_3(this.h[3], E, Ah);
  this.h[3] = sum32_3(this.h[4], A, Bh);
  this.h[4] = sum32_3(this.h[0], B, Ch);
  this.h[0] = T;
};

RIPEMD160.prototype._digest = function digest(enc) {
  if (enc === 'hex')
    return utils.toHex32(this.h, 'little');
  else
    return utils.split32(this.h, 'little');
};

function f(j, x, y, z) {
  if (j <= 15)
    return x ^ y ^ z;
  else if (j <= 31)
    return (x & y) | ((~x) & z);
  else if (j <= 47)
    return (x | (~y)) ^ z;
  else if (j <= 63)
    return (x & z) | (y & (~z));
  else
    return x ^ (y | (~z));
}

function K(j) {
  if (j <= 15)
    return 0x00000000;
  else if (j <= 31)
    return 0x5a827999;
  else if (j <= 47)
    return 0x6ed9eba1;
  else if (j <= 63)
    return 0x8f1bbcdc;
  else
    return 0xa953fd4e;
}

function Kh(j) {
  if (j <= 15)
    return 0x50a28be6;
  else if (j <= 31)
    return 0x5c4dd124;
  else if (j <= 47)
    return 0x6d703ef3;
  else if (j <= 63)
    return 0x7a6d76e9;
  else
    return 0x00000000;
}

var r = [
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
  7, 4, 13, 1, 10, 6, 15, 3, 12, 0, 9, 5, 2, 14, 11, 8,
  3, 10, 14, 4, 9, 15, 8, 1, 2, 7, 0, 6, 13, 11, 5, 12,
  1, 9, 11, 10, 0, 8, 12, 4, 13, 3, 7, 15, 14, 5, 6, 2,
  4, 0, 5, 9, 7, 12, 2, 10, 14, 1, 3, 8, 11, 6, 15, 13,
];

var rh = [
  5, 14, 7, 0, 9, 2, 11, 4, 13, 6, 15, 8, 1, 10, 3, 12,
  6, 11, 3, 7, 0, 13, 5, 10, 14, 15, 8, 12, 4, 9, 1, 2,
  15, 5, 1, 3, 7, 14, 6, 9, 11, 8, 12, 2, 10, 0, 4, 13,
  8, 6, 4, 1, 3, 11, 15, 0, 5, 12, 2, 13, 9, 7, 10, 14,
  12, 15, 10, 4, 1, 5, 8, 7, 6, 2, 13, 14, 0, 3, 9, 11
];

var s = [
  11, 14, 15, 12, 5, 8, 7, 9, 11, 13, 14, 15, 6, 7, 9, 8,
  7, 6, 8, 13, 11, 9, 7, 15, 7, 12, 15, 9, 11, 7, 13, 12,
  11, 13, 6, 7, 14, 9, 13, 15, 14, 8, 13, 6, 5, 12, 7, 5,
  11, 12, 14, 15, 14, 15, 9, 8, 9, 14, 5, 6, 8, 6, 5, 12,
  9, 15, 5, 11, 6, 8, 13, 12, 5, 12, 13, 14, 11, 8, 5, 6,
];

var sh = [
  8, 9, 9, 11, 13, 15, 15, 5, 7, 7, 8, 11, 14, 14, 12, 6,
  9, 13, 15, 7, 12, 8, 9, 11, 7, 7, 12, 7, 6, 15, 13, 11,
  9, 7, 15, 11, 8, 6, 6, 14, 12, 13, 5, 14, 13, 13, 7, 5,
  15, 5, 8, 11, 14, 14, 6, 14, 6, 9, 12, 9, 12, 5, 15, 8,
  8, 5, 12, 9, 12, 5, 14, 6, 8, 13, 6, 5, 15, 13, 11, 11
];

},{"../hash":16}],20:[function(require,module,exports){
var hash = require('../hash');
var utils = hash.utils;
var assert = utils.assert;

var rotr32 = utils.rotr32;
var rotl32 = utils.rotl32;
var sum32 = utils.sum32;
var sum32_4 = utils.sum32_4;
var sum32_5 = utils.sum32_5;
var rotr64_hi = utils.rotr64_hi;
var rotr64_lo = utils.rotr64_lo;
var shr64_hi = utils.shr64_hi;
var shr64_lo = utils.shr64_lo;
var sum64 = utils.sum64;
var sum64_hi = utils.sum64_hi;
var sum64_lo = utils.sum64_lo;
var sum64_4_hi = utils.sum64_4_hi;
var sum64_4_lo = utils.sum64_4_lo;
var sum64_5_hi = utils.sum64_5_hi;
var sum64_5_lo = utils.sum64_5_lo;
var BlockHash = hash.common.BlockHash;

var sha256_K = [
  0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5,
  0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
  0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3,
  0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
  0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc,
  0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
  0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7,
  0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
  0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13,
  0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
  0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3,
  0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
  0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5,
  0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
  0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208,
  0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
];

var sha512_K = [
  0x428a2f98, 0xd728ae22, 0x71374491, 0x23ef65cd,
  0xb5c0fbcf, 0xec4d3b2f, 0xe9b5dba5, 0x8189dbbc,
  0x3956c25b, 0xf348b538, 0x59f111f1, 0xb605d019,
  0x923f82a4, 0xaf194f9b, 0xab1c5ed5, 0xda6d8118,
  0xd807aa98, 0xa3030242, 0x12835b01, 0x45706fbe,
  0x243185be, 0x4ee4b28c, 0x550c7dc3, 0xd5ffb4e2,
  0x72be5d74, 0xf27b896f, 0x80deb1fe, 0x3b1696b1,
  0x9bdc06a7, 0x25c71235, 0xc19bf174, 0xcf692694,
  0xe49b69c1, 0x9ef14ad2, 0xefbe4786, 0x384f25e3,
  0x0fc19dc6, 0x8b8cd5b5, 0x240ca1cc, 0x77ac9c65,
  0x2de92c6f, 0x592b0275, 0x4a7484aa, 0x6ea6e483,
  0x5cb0a9dc, 0xbd41fbd4, 0x76f988da, 0x831153b5,
  0x983e5152, 0xee66dfab, 0xa831c66d, 0x2db43210,
  0xb00327c8, 0x98fb213f, 0xbf597fc7, 0xbeef0ee4,
  0xc6e00bf3, 0x3da88fc2, 0xd5a79147, 0x930aa725,
  0x06ca6351, 0xe003826f, 0x14292967, 0x0a0e6e70,
  0x27b70a85, 0x46d22ffc, 0x2e1b2138, 0x5c26c926,
  0x4d2c6dfc, 0x5ac42aed, 0x53380d13, 0x9d95b3df,
  0x650a7354, 0x8baf63de, 0x766a0abb, 0x3c77b2a8,
  0x81c2c92e, 0x47edaee6, 0x92722c85, 0x1482353b,
  0xa2bfe8a1, 0x4cf10364, 0xa81a664b, 0xbc423001,
  0xc24b8b70, 0xd0f89791, 0xc76c51a3, 0x0654be30,
  0xd192e819, 0xd6ef5218, 0xd6990624, 0x5565a910,
  0xf40e3585, 0x5771202a, 0x106aa070, 0x32bbd1b8,
  0x19a4c116, 0xb8d2d0c8, 0x1e376c08, 0x5141ab53,
  0x2748774c, 0xdf8eeb99, 0x34b0bcb5, 0xe19b48a8,
  0x391c0cb3, 0xc5c95a63, 0x4ed8aa4a, 0xe3418acb,
  0x5b9cca4f, 0x7763e373, 0x682e6ff3, 0xd6b2b8a3,
  0x748f82ee, 0x5defb2fc, 0x78a5636f, 0x43172f60,
  0x84c87814, 0xa1f0ab72, 0x8cc70208, 0x1a6439ec,
  0x90befffa, 0x23631e28, 0xa4506ceb, 0xde82bde9,
  0xbef9a3f7, 0xb2c67915, 0xc67178f2, 0xe372532b,
  0xca273ece, 0xea26619c, 0xd186b8c7, 0x21c0c207,
  0xeada7dd6, 0xcde0eb1e, 0xf57d4f7f, 0xee6ed178,
  0x06f067aa, 0x72176fba, 0x0a637dc5, 0xa2c898a6,
  0x113f9804, 0xbef90dae, 0x1b710b35, 0x131c471b,
  0x28db77f5, 0x23047d84, 0x32caab7b, 0x40c72493,
  0x3c9ebe0a, 0x15c9bebc, 0x431d67c4, 0x9c100d4c,
  0x4cc5d4be, 0xcb3e42b6, 0x597f299c, 0xfc657e2a,
  0x5fcb6fab, 0x3ad6faec, 0x6c44198c, 0x4a475817
];

var sha1_K = [
  0x5A827999, 0x6ED9EBA1,
  0x8F1BBCDC, 0xCA62C1D6
];

function SHA256() {
  if (!(this instanceof SHA256))
    return new SHA256();

  BlockHash.call(this);
  this.h = [ 0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a,
             0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19 ];
  this.k = sha256_K;
  this.W = new Array(64);
}
utils.inherits(SHA256, BlockHash);
exports.sha256 = SHA256;

SHA256.blockSize = 512;
SHA256.outSize = 256;
SHA256.hmacStrength = 192;
SHA256.padLength = 64;

SHA256.prototype._update = function _update(msg, start) {
  var W = this.W;

  for (var i = 0; i < 16; i++)
    W[i] = msg[start + i];
  for (; i < W.length; i++)
    W[i] = sum32_4(g1_256(W[i - 2]), W[i - 7], g0_256(W[i - 15]), W[i - 16]);

  var a = this.h[0];
  var b = this.h[1];
  var c = this.h[2];
  var d = this.h[3];
  var e = this.h[4];
  var f = this.h[5];
  var g = this.h[6];
  var h = this.h[7];

  assert(this.k.length === W.length);
  for (var i = 0; i < W.length; i++) {
    var T1 = sum32_5(h, s1_256(e), ch32(e, f, g), this.k[i], W[i]);
    var T2 = sum32(s0_256(a), maj32(a, b, c));
    h = g;
    g = f;
    f = e;
    e = sum32(d, T1);
    d = c;
    c = b;
    b = a;
    a = sum32(T1, T2);
  }

  this.h[0] = sum32(this.h[0], a);
  this.h[1] = sum32(this.h[1], b);
  this.h[2] = sum32(this.h[2], c);
  this.h[3] = sum32(this.h[3], d);
  this.h[4] = sum32(this.h[4], e);
  this.h[5] = sum32(this.h[5], f);
  this.h[6] = sum32(this.h[6], g);
  this.h[7] = sum32(this.h[7], h);
};

SHA256.prototype._digest = function digest(enc) {
  if (enc === 'hex')
    return utils.toHex32(this.h, 'big');
  else
    return utils.split32(this.h, 'big');
};

function SHA224() {
  if (!(this instanceof SHA224))
    return new SHA224();

  SHA256.call(this);
  this.h = [ 0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939,
             0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4 ];
}
utils.inherits(SHA224, SHA256);
exports.sha224 = SHA224;

SHA224.blockSize = 512;
SHA224.outSize = 224;
SHA224.hmacStrength = 192;
SHA224.padLength = 64;

SHA224.prototype._digest = function digest(enc) {
  // Just truncate output
  if (enc === 'hex')
    return utils.toHex32(this.h.slice(0, 7), 'big');
  else
    return utils.split32(this.h.slice(0, 7), 'big');
};

function SHA512() {
  if (!(this instanceof SHA512))
    return new SHA512();

  BlockHash.call(this);
  this.h = [ 0x6a09e667, 0xf3bcc908,
             0xbb67ae85, 0x84caa73b,
             0x3c6ef372, 0xfe94f82b,
             0xa54ff53a, 0x5f1d36f1,
             0x510e527f, 0xade682d1,
             0x9b05688c, 0x2b3e6c1f,
             0x1f83d9ab, 0xfb41bd6b,
             0x5be0cd19, 0x137e2179 ];
  this.k = sha512_K;
  this.W = new Array(160);
}
utils.inherits(SHA512, BlockHash);
exports.sha512 = SHA512;

SHA512.blockSize = 1024;
SHA512.outSize = 512;
SHA512.hmacStrength = 192;
SHA512.padLength = 128;

SHA512.prototype._prepareBlock = function _prepareBlock(msg, start) {
  var W = this.W;

  // 32 x 32bit words
  for (var i = 0; i < 32; i++)
    W[i] = msg[start + i];
  for (; i < W.length; i += 2) {
    var c0_hi = g1_512_hi(W[i - 4], W[i - 3]);  // i - 2
    var c0_lo = g1_512_lo(W[i - 4], W[i - 3]);
    var c1_hi = W[i - 14];  // i - 7
    var c1_lo = W[i - 13];
    var c2_hi = g0_512_hi(W[i - 30], W[i - 29]);  // i - 15
    var c2_lo = g0_512_lo(W[i - 30], W[i - 29]);
    var c3_hi = W[i - 32];  // i - 16
    var c3_lo = W[i - 31];

    W[i] = sum64_4_hi(c0_hi, c0_lo,
                      c1_hi, c1_lo,
                      c2_hi, c2_lo,
                      c3_hi, c3_lo);
    W[i + 1] = sum64_4_lo(c0_hi, c0_lo,
                          c1_hi, c1_lo,
                          c2_hi, c2_lo,
                          c3_hi, c3_lo);
  }
};

SHA512.prototype._update = function _update(msg, start) {
  this._prepareBlock(msg, start);

  var W = this.W;

  var ah = this.h[0];
  var al = this.h[1];
  var bh = this.h[2];
  var bl = this.h[3];
  var ch = this.h[4];
  var cl = this.h[5];
  var dh = this.h[6];
  var dl = this.h[7];
  var eh = this.h[8];
  var el = this.h[9];
  var fh = this.h[10];
  var fl = this.h[11];
  var gh = this.h[12];
  var gl = this.h[13];
  var hh = this.h[14];
  var hl = this.h[15];

  assert(this.k.length === W.length);
  for (var i = 0; i < W.length; i += 2) {
    var c0_hi = hh;
    var c0_lo = hl;
    var c1_hi = s1_512_hi(eh, el);
    var c1_lo = s1_512_lo(eh, el);
    var c2_hi = ch64_hi(eh, el, fh, fl, gh, gl);
    var c2_lo = ch64_lo(eh, el, fh, fl, gh, gl);
    var c3_hi = this.k[i];
    var c3_lo = this.k[i + 1];
    var c4_hi = W[i];
    var c4_lo = W[i + 1];

    var T1_hi = sum64_5_hi(c0_hi, c0_lo,
                           c1_hi, c1_lo,
                           c2_hi, c2_lo,
                           c3_hi, c3_lo,
                           c4_hi, c4_lo);
    var T1_lo = sum64_5_lo(c0_hi, c0_lo,
                           c1_hi, c1_lo,
                           c2_hi, c2_lo,
                           c3_hi, c3_lo,
                           c4_hi, c4_lo);

    var c0_hi = s0_512_hi(ah, al);
    var c0_lo = s0_512_lo(ah, al);
    var c1_hi = maj64_hi(ah, al, bh, bl, ch, cl);
    var c1_lo = maj64_lo(ah, al, bh, bl, ch, cl);

    var T2_hi = sum64_hi(c0_hi, c0_lo, c1_hi, c1_lo);
    var T2_lo = sum64_lo(c0_hi, c0_lo, c1_hi, c1_lo);

    hh = gh;
    hl = gl;

    gh = fh;
    gl = fl;

    fh = eh;
    fl = el;

    eh = sum64_hi(dh, dl, T1_hi, T1_lo);
    el = sum64_lo(dl, dl, T1_hi, T1_lo);

    dh = ch;
    dl = cl;

    ch = bh;
    cl = bl;

    bh = ah;
    bl = al;

    ah = sum64_hi(T1_hi, T1_lo, T2_hi, T2_lo);
    al = sum64_lo(T1_hi, T1_lo, T2_hi, T2_lo);
  }

  sum64(this.h, 0, ah, al);
  sum64(this.h, 2, bh, bl);
  sum64(this.h, 4, ch, cl);
  sum64(this.h, 6, dh, dl);
  sum64(this.h, 8, eh, el);
  sum64(this.h, 10, fh, fl);
  sum64(this.h, 12, gh, gl);
  sum64(this.h, 14, hh, hl);
};

SHA512.prototype._digest = function digest(enc) {
  if (enc === 'hex')
    return utils.toHex32(this.h, 'big');
  else
    return utils.split32(this.h, 'big');
};

function SHA384() {
  if (!(this instanceof SHA384))
    return new SHA384();

  SHA512.call(this);
  this.h = [ 0xcbbb9d5d, 0xc1059ed8,
             0x629a292a, 0x367cd507,
             0x9159015a, 0x3070dd17,
             0x152fecd8, 0xf70e5939,
             0x67332667, 0xffc00b31,
             0x8eb44a87, 0x68581511,
             0xdb0c2e0d, 0x64f98fa7,
             0x47b5481d, 0xbefa4fa4 ];
}
utils.inherits(SHA384, SHA512);
exports.sha384 = SHA384;

SHA384.blockSize = 1024;
SHA384.outSize = 384;
SHA384.hmacStrength = 192;
SHA384.padLength = 128;

SHA384.prototype._digest = function digest(enc) {
  if (enc === 'hex')
    return utils.toHex32(this.h.slice(0, 12), 'big');
  else
    return utils.split32(this.h.slice(0, 12), 'big');
};

function SHA1() {
  if (!(this instanceof SHA1))
    return new SHA1();

  BlockHash.call(this);
  this.h = [ 0x67452301, 0xefcdab89, 0x98badcfe,
             0x10325476, 0xc3d2e1f0 ];
  this.W = new Array(80);
}

utils.inherits(SHA1, BlockHash);
exports.sha1 = SHA1;

SHA1.blockSize = 512;
SHA1.outSize = 160;
SHA1.hmacStrength = 80;
SHA1.padLength = 64;

SHA1.prototype._update = function _update(msg, start) {
  var W = this.W;

  for (var i = 0; i < 16; i++)
    W[i] = msg[start + i];

  for(; i < W.length; i++)
    W[i] = rotl32(W[i - 3] ^ W[i - 8] ^ W[i - 14] ^ W[i - 16], 1);

  var a = this.h[0];
  var b = this.h[1];
  var c = this.h[2];
  var d = this.h[3];
  var e = this.h[4];

  for (var i = 0; i < W.length; i++) {
    var s = ~~(i / 20);
    var t = sum32_5(rotl32(a, 5), ft_1(s, b, c, d), e, W[i], sha1_K[s]);
    e = d;
    d = c;
    c = rotl32(b, 30);
    b = a;
    a = t;
  }

  this.h[0] = sum32(this.h[0], a);
  this.h[1] = sum32(this.h[1], b);
  this.h[2] = sum32(this.h[2], c);
  this.h[3] = sum32(this.h[3], d);
  this.h[4] = sum32(this.h[4], e);
};

SHA1.prototype._digest = function digest(enc) {
  if (enc === 'hex')
    return utils.toHex32(this.h, 'big');
  else
    return utils.split32(this.h, 'big');
};

function ch32(x, y, z) {
  return (x & y) ^ ((~x) & z);
}

function maj32(x, y, z) {
  return (x & y) ^ (x & z) ^ (y & z);
}

function p32(x, y, z) {
  return x ^ y ^ z;
}

function s0_256(x) {
  return rotr32(x, 2) ^ rotr32(x, 13) ^ rotr32(x, 22);
}

function s1_256(x) {
  return rotr32(x, 6) ^ rotr32(x, 11) ^ rotr32(x, 25);
}

function g0_256(x) {
  return rotr32(x, 7) ^ rotr32(x, 18) ^ (x >>> 3);
}

function g1_256(x) {
  return rotr32(x, 17) ^ rotr32(x, 19) ^ (x >>> 10);
}

function ft_1(s, x, y, z) {
  if (s === 0)
    return ch32(x, y, z);
  if (s === 1 || s === 3)
    return p32(x, y, z);
  if (s === 2)
    return maj32(x, y, z);
}

function ch64_hi(xh, xl, yh, yl, zh, zl) {
  var r = (xh & yh) ^ ((~xh) & zh);
  if (r < 0)
    r += 0x100000000;
  return r;
}

function ch64_lo(xh, xl, yh, yl, zh, zl) {
  var r = (xl & yl) ^ ((~xl) & zl);
  if (r < 0)
    r += 0x100000000;
  return r;
}

function maj64_hi(xh, xl, yh, yl, zh, zl) {
  var r = (xh & yh) ^ (xh & zh) ^ (yh & zh);
  if (r < 0)
    r += 0x100000000;
  return r;
}

function maj64_lo(xh, xl, yh, yl, zh, zl) {
  var r = (xl & yl) ^ (xl & zl) ^ (yl & zl);
  if (r < 0)
    r += 0x100000000;
  return r;
}

function s0_512_hi(xh, xl) {
  var c0_hi = rotr64_hi(xh, xl, 28);
  var c1_hi = rotr64_hi(xl, xh, 2);  // 34
  var c2_hi = rotr64_hi(xl, xh, 7);  // 39

  var r = c0_hi ^ c1_hi ^ c2_hi;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function s0_512_lo(xh, xl) {
  var c0_lo = rotr64_lo(xh, xl, 28);
  var c1_lo = rotr64_lo(xl, xh, 2);  // 34
  var c2_lo = rotr64_lo(xl, xh, 7);  // 39

  var r = c0_lo ^ c1_lo ^ c2_lo;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function s1_512_hi(xh, xl) {
  var c0_hi = rotr64_hi(xh, xl, 14);
  var c1_hi = rotr64_hi(xh, xl, 18);
  var c2_hi = rotr64_hi(xl, xh, 9);  // 41

  var r = c0_hi ^ c1_hi ^ c2_hi;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function s1_512_lo(xh, xl) {
  var c0_lo = rotr64_lo(xh, xl, 14);
  var c1_lo = rotr64_lo(xh, xl, 18);
  var c2_lo = rotr64_lo(xl, xh, 9);  // 41

  var r = c0_lo ^ c1_lo ^ c2_lo;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function g0_512_hi(xh, xl) {
  var c0_hi = rotr64_hi(xh, xl, 1);
  var c1_hi = rotr64_hi(xh, xl, 8);
  var c2_hi = shr64_hi(xh, xl, 7);

  var r = c0_hi ^ c1_hi ^ c2_hi;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function g0_512_lo(xh, xl) {
  var c0_lo = rotr64_lo(xh, xl, 1);
  var c1_lo = rotr64_lo(xh, xl, 8);
  var c2_lo = shr64_lo(xh, xl, 7);

  var r = c0_lo ^ c1_lo ^ c2_lo;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function g1_512_hi(xh, xl) {
  var c0_hi = rotr64_hi(xh, xl, 19);
  var c1_hi = rotr64_hi(xl, xh, 29);  // 61
  var c2_hi = shr64_hi(xh, xl, 6);

  var r = c0_hi ^ c1_hi ^ c2_hi;
  if (r < 0)
    r += 0x100000000;
  return r;
}

function g1_512_lo(xh, xl) {
  var c0_lo = rotr64_lo(xh, xl, 19);
  var c1_lo = rotr64_lo(xl, xh, 29);  // 61
  var c2_lo = shr64_lo(xh, xl, 6);

  var r = c0_lo ^ c1_lo ^ c2_lo;
  if (r < 0)
    r += 0x100000000;
  return r;
}

},{"../hash":16}],21:[function(require,module,exports){
var utils = exports;
var inherits = require('inherits');

function toArray(msg, enc) {
  if (Array.isArray(msg))
    return msg.slice();
  if (!msg)
    return [];
  var res = [];
  if (typeof msg === 'string') {
    if (!enc) {
      for (var i = 0; i < msg.length; i++) {
        var c = msg.charCodeAt(i);
        var hi = c >> 8;
        var lo = c & 0xff;
        if (hi)
          res.push(hi, lo);
        else
          res.push(lo);
      }
    } else if (enc === 'hex') {
      msg = msg.replace(/[^a-z0-9]+/ig, '');
      if (msg.length % 2 !== 0)
        msg = '0' + msg;
      for (var i = 0; i < msg.length; i += 2)
        res.push(parseInt(msg[i] + msg[i + 1], 16));
    }
  } else {
    for (var i = 0; i < msg.length; i++)
      res[i] = msg[i] | 0;
  }
  return res;
}
utils.toArray = toArray;

function toHex(msg) {
  var res = '';
  for (var i = 0; i < msg.length; i++)
    res += zero2(msg[i].toString(16));
  return res;
}
utils.toHex = toHex;

function htonl(w) {
  var res = (w >>> 24) |
            ((w >>> 8) & 0xff00) |
            ((w << 8) & 0xff0000) |
            ((w & 0xff) << 24);
  return res >>> 0;
}
utils.htonl = htonl;

function toHex32(msg, endian) {
  var res = '';
  for (var i = 0; i < msg.length; i++) {
    var w = msg[i];
    if (endian === 'little')
      w = htonl(w);
    res += zero8(w.toString(16));
  }
  return res;
}
utils.toHex32 = toHex32;

function zero2(word) {
  if (word.length === 1)
    return '0' + word;
  else
    return word;
}
utils.zero2 = zero2;

function zero8(word) {
  if (word.length === 7)
    return '0' + word;
  else if (word.length === 6)
    return '00' + word;
  else if (word.length === 5)
    return '000' + word;
  else if (word.length === 4)
    return '0000' + word;
  else if (word.length === 3)
    return '00000' + word;
  else if (word.length === 2)
    return '000000' + word;
  else if (word.length === 1)
    return '0000000' + word;
  else
    return word;
}
utils.zero8 = zero8;

function join32(msg, start, end, endian) {
  var len = end - start;
  assert(len % 4 === 0);
  var res = new Array(len / 4);
  for (var i = 0, k = start; i < res.length; i++, k += 4) {
    var w;
    if (endian === 'big')
      w = (msg[k] << 24) | (msg[k + 1] << 16) | (msg[k + 2] << 8) | msg[k + 3];
    else
      w = (msg[k + 3] << 24) | (msg[k + 2] << 16) | (msg[k + 1] << 8) | msg[k];
    res[i] = w >>> 0;
  }
  return res;
}
utils.join32 = join32;

function split32(msg, endian) {
  var res = new Array(msg.length * 4);
  for (var i = 0, k = 0; i < msg.length; i++, k += 4) {
    var m = msg[i];
    if (endian === 'big') {
      res[k] = m >>> 24;
      res[k + 1] = (m >>> 16) & 0xff;
      res[k + 2] = (m >>> 8) & 0xff;
      res[k + 3] = m & 0xff;
    } else {
      res[k + 3] = m >>> 24;
      res[k + 2] = (m >>> 16) & 0xff;
      res[k + 1] = (m >>> 8) & 0xff;
      res[k] = m & 0xff;
    }
  }
  return res;
}
utils.split32 = split32;

function rotr32(w, b) {
  return (w >>> b) | (w << (32 - b));
}
utils.rotr32 = rotr32;

function rotl32(w, b) {
  return (w << b) | (w >>> (32 - b));
}
utils.rotl32 = rotl32;

function sum32(a, b) {
  return (a + b) >>> 0;
}
utils.sum32 = sum32;

function sum32_3(a, b, c) {
  return (a + b + c) >>> 0;
}
utils.sum32_3 = sum32_3;

function sum32_4(a, b, c, d) {
  return (a + b + c + d) >>> 0;
}
utils.sum32_4 = sum32_4;

function sum32_5(a, b, c, d, e) {
  return (a + b + c + d + e) >>> 0;
}
utils.sum32_5 = sum32_5;

function assert(cond, msg) {
  if (!cond)
    throw new Error(msg || 'Assertion failed');
}
utils.assert = assert;

utils.inherits = inherits;

function sum64(buf, pos, ah, al) {
  var bh = buf[pos];
  var bl = buf[pos + 1];

  var lo = (al + bl) >>> 0;
  var hi = (lo < al ? 1 : 0) + ah + bh;
  buf[pos] = hi >>> 0;
  buf[pos + 1] = lo;
}
exports.sum64 = sum64;

function sum64_hi(ah, al, bh, bl) {
  var lo = (al + bl) >>> 0;
  var hi = (lo < al ? 1 : 0) + ah + bh;
  return hi >>> 0;
};
exports.sum64_hi = sum64_hi;

function sum64_lo(ah, al, bh, bl) {
  var lo = al + bl;
  return lo >>> 0;
};
exports.sum64_lo = sum64_lo;

function sum64_4_hi(ah, al, bh, bl, ch, cl, dh, dl) {
  var carry = 0;
  var lo = al;
  lo = (lo + bl) >>> 0;
  carry += lo < al ? 1 : 0;
  lo = (lo + cl) >>> 0;
  carry += lo < cl ? 1 : 0;
  lo = (lo + dl) >>> 0;
  carry += lo < dl ? 1 : 0;

  var hi = ah + bh + ch + dh + carry;
  return hi >>> 0;
};
exports.sum64_4_hi = sum64_4_hi;

function sum64_4_lo(ah, al, bh, bl, ch, cl, dh, dl) {
  var lo = al + bl + cl + dl;
  return lo >>> 0;
};
exports.sum64_4_lo = sum64_4_lo;

function sum64_5_hi(ah, al, bh, bl, ch, cl, dh, dl, eh, el) {
  var carry = 0;
  var lo = al;
  lo = (lo + bl) >>> 0;
  carry += lo < al ? 1 : 0;
  lo = (lo + cl) >>> 0;
  carry += lo < cl ? 1 : 0;
  lo = (lo + dl) >>> 0;
  carry += lo < dl ? 1 : 0;
  lo = (lo + el) >>> 0;
  carry += lo < el ? 1 : 0;

  var hi = ah + bh + ch + dh + eh + carry;
  return hi >>> 0;
};
exports.sum64_5_hi = sum64_5_hi;

function sum64_5_lo(ah, al, bh, bl, ch, cl, dh, dl, eh, el) {
  var lo = al + bl + cl + dl + el;

  return lo >>> 0;
};
exports.sum64_5_lo = sum64_5_lo;

function rotr64_hi(ah, al, num) {
  var r = (al << (32 - num)) | (ah >>> num);
  return r >>> 0;
};
exports.rotr64_hi = rotr64_hi;

function rotr64_lo(ah, al, num) {
  var r = (ah << (32 - num)) | (al >>> num);
  return r >>> 0;
};
exports.rotr64_lo = rotr64_lo;

function shr64_hi(ah, al, num) {
  return ah >>> num;
};
exports.shr64_hi = shr64_hi;

function shr64_lo(ah, al, num) {
  var r = (ah << (32 - num)) | (al >>> num);
  return r >>> 0;
};
exports.shr64_lo = shr64_lo;

},{"inherits":22}],22:[function(require,module,exports){
if (typeof Object.create === 'function') {
  // implementation from standard node.js 'util' module
  module.exports = function inherits(ctor, superCtor) {
    ctor.super_ = superCtor
    ctor.prototype = Object.create(superCtor.prototype, {
      constructor: {
        value: ctor,
        enumerable: false,
        writable: true,
        configurable: true
      }
    });
  };
} else {
  // old school shim for old browsers
  module.exports = function inherits(ctor, superCtor) {
    ctor.super_ = superCtor
    var TempCtor = function () {}
    TempCtor.prototype = superCtor.prototype
    ctor.prototype = new TempCtor()
    ctor.prototype.constructor = ctor
  }
}

},{}],23:[function(require,module,exports){
module.exports={
  "name": "elliptic",
  "version": "3.0.3",
  "description": "EC cryptography",
  "main": "lib/elliptic.js",
  "scripts": {
    "test": "make lint && mocha --reporter=spec test/*-test.js"
  },
  "repository": {
    "type": "git",
    "url": "[email protected]:indutny/elliptic"
  },
  "keywords": [
    "EC",
    "Elliptic",
    "curve",
    "Cryptography"
  ],
  "author": "Fedor Indutny <[email protected]>",
  "license": "MIT",
  "bugs": {
    "url": "https://github.com/indutny/elliptic/issues"
  },
  "homepage": "https://github.com/indutny/elliptic",
  "devDependencies": {
    "browserify": "^3.44.2",
    "jscs": "^1.11.3",
    "jshint": "^2.6.0",
    "mocha": "^2.1.0",
    "uglify-js": "^2.4.13"
  },
  "dependencies": {
    "bn.js": "^2.0.0",
    "brorand": "^1.0.1",
    "hash.js": "^1.0.0",
    "inherits": "^2.0.1"
  }
}

},{}]},{},[1])(1)
});