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.elliptic = f()}})(function(){var define,module,exports;return (function(){function r(e,n,t){function o(i,f){if(!n[i]){if(!e[i]){var c="function"==typeof require&&require;if(!f&&c)return c(i,!0);if(u)return u(i,!0);var a=new Error("Cannot find module '"+i+"'");throw a.code="MODULE_NOT_FOUND",a}var p=n[i]={exports:{}};e[i][0].call(p.exports,function(r){var n=e[i][1][r];return o(n||r)},p,p.exports,r,e,n,t)}return n[i].exports}for(var u="function"==typeof require&&require,i=0;i<t.length;i++)o(t[i]);return o}return r})()({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.curve = require('./elliptic/curve');
elliptic.curves = require('./elliptic/curves');

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

},{"../package.json":35,"./elliptic/curve":4,"./elliptic/curves":7,"./elliptic/ec":8,"./elliptic/eddsa":11,"./elliptic/utils":15,"brorand":17}],2:[function(require,module,exports){
'use strict';

var BN = require('bn.js');
var utils = require('../utils');
var getNAF = utils.getNAF;
var getJSF = utils.getJSF;
var assert = 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);

  this._bitLength = this.n ? this.n.bitLength() : 0;

  // Generalized Greg Maxwell's trick
  var adjustCount = this.n && this.p.div(this.n);
  if (!adjustCount || adjustCount.cmpn(100) > 0) {
    this.redN = null;
  } else {
    this._maxwellTrick = true;
    this.redN = this.n.toRed(this.red);
  }
}
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) {
  assert(p.precomputed);
  var doubles = p._getDoubles();

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

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

  // 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 l = 0; i >= 0 && naf[i] === 0; i--)
      l++;
    if (i >= 0)
      l++;
    acc = acc.dblp(l);

    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,
  jacobianResult) {
  var wndWidth = this._wnafT1;
  var wnd = this._wnafT2;
  var naf = this._wnafT3;

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

  // Comb small window NAFs
  for (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], this._bitLength);
      naf[b] = getNAF(coeffs[b], wndWidth[b], this._bitLength);
      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 (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 (i = max; i >= 0; i--) {
    var k = 0;

    while (i >= 0) {
      var zero = true;
      for (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 (j = 0; j < len; j++) {
      var z = tmp[j];
      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 (i = 0; i < len; i++)
    wnd[i] = null;

  if (jacobianResult)
    return acc;
  else
    return acc.toP();
};

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

BasePoint.prototype.eq = function eq(/*other*/) {
  throw new Error('Not implemented');
};

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

BaseCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
  bytes = utils.toArray(bytes, enc);

  var len = this.p.byteLength();

  // uncompressed, hybrid-odd, hybrid-even
  if ((bytes[0] === 0x04 || bytes[0] === 0x06 || bytes[0] === 0x07) &&
      bytes.length - 1 === 2 * len) {
    if (bytes[0] === 0x06)
      assert(bytes[bytes.length - 1] % 2 === 0);
    else if (bytes[0] === 0x07)
      assert(bytes[bytes.length - 1] % 2 === 1);

    var res =  this.point(bytes.slice(1, 1 + len),
      bytes.slice(1 + len, 1 + 2 * len));

    return res;
  } else if ((bytes[0] === 0x02 || bytes[0] === 0x03) &&
              bytes.length - 1 === len) {
    return this.pointFromX(bytes.slice(1, 1 + len), bytes[0] === 0x03);
  }
  throw new Error('Unknown point format');
};

BasePoint.prototype.encodeCompressed = function encodeCompressed(enc) {
  return this.encode(enc, true);
};

BasePoint.prototype._encode = function _encode(compact) {
  var len = this.curve.p.byteLength();
  var x = this.getX().toArray('be', len);

  if (compact)
    return [ this.getY().isEven() ? 0x02 : 0x03 ].concat(x);

  return [ 0x04 ].concat(x, this.getY().toArray('be', len));
};

BasePoint.prototype.encode = function encode(enc, compact) {
  return utils.encode(this._encode(compact), enc);
};

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._hasDoubles = function _hasDoubles(k) {
  if (!this.precomputed)
    return false;

  var doubles = this.precomputed.doubles;
  if (!doubles)
    return false;

  return doubles.points.length >= Math.ceil((k.bitLength() + 1) / doubles.step);
};

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;
};

},{"../utils":15,"bn.js":16}],3:[function(require,module,exports){
'use strict';

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

var assert = 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).umod(this.red.m);
  this.a = this.a.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(x, odd) {
  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 y2 = rhs.redMul(lhs.redInvm());
  var y = y2.redSqrt();
  if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
    throw new Error('invalid point');

  var isOdd = y.fromRed().isOdd();
  if (odd && !isOdd || !odd && isOdd)
    y = y.redNeg();

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

EdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {
  y = new BN(y, 16);
  if (!y.red)
    y = y.toRed(this.red);

  // x^2 = (y^2 - c^2) / (c^2 d y^2 - a)
  var y2 = y.redSqr();
  var lhs = y2.redSub(this.c2);
  var rhs = y2.redMul(this.d).redMul(this.c2).redSub(this.a);
  var x2 = lhs.redMul(rhs.redInvm());

  if (x2.cmp(this.zero) === 0) {
    if (odd)
      throw new Error('invalid point');
    else
      return this.point(this.zero, y);
  }

  var x = x2.redSqrt();
  if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)
    throw new Error('invalid point');

  if (x.fromRed().isOdd() !== odd)
    x = x.redNeg();

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

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 ||
    (this.zOne && this.y.cmp(this.curve.c) === 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;
  var e;
  var h;
  var j;
  if (this.curve.twisted) {
    // E = a * C
    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
      h = this.z.redSqr();
      // J = F - 2 * H
      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
    e = c.redAdd(d);
    // H = (c * Z1)^2
    h = this.curve._mulC(this.z).redSqr();
    // J = E - 2 * H
    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._hasDoubles(k))
    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, false);
};

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

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();
};

Point.prototype.eq = function eq(other) {
  return this === other ||
         this.getX().cmp(other.getX()) === 0 &&
         this.getY().cmp(other.getY()) === 0;
};

Point.prototype.eqXToP = function eqXToP(x) {
  var rx = x.toRed(this.curve.red).redMul(this.z);
  if (this.x.cmp(rx) === 0)
    return true;

  var xc = x.clone();
  var t = this.curve.redN.redMul(this.z);
  for (;;) {
    xc.iadd(this.curve.n);
    if (xc.cmp(this.curve.p) >= 0)
      return false;

    rx.redIAdd(t);
    if (this.x.cmp(rx) === 0)
      return true;
  }
};

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

},{"../utils":15,"./base":2,"bn.js":16,"inherits":32}],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 BN = require('bn.js');
var inherits = require('inherits');
var Base = require('./base');

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

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.decodePoint = function decodePoint(bytes, enc) {
  return this.point(utils.toArray(bytes, enc), 1);
};

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.prototype._encode = function _encode() {
  return this.getX().toArray('be', this.curve.p.byteLength());
};

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.iushrn(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.jumlAdd = function jumlAdd() {
  throw new Error('Not supported on Montgomery curve');
};

Point.prototype.eq = function eq(other) {
  return this.getX().cmp(other.getX()) === 0;
};

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();
};

},{"../utils":15,"./base":2,"bn.js":16,"inherits":32}],6:[function(require,module,exports){
'use strict';

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

var assert = 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.ushrn(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.negative) {
    a1 = a1.neg();
    b1 = b1.neg();
  }
  if (a2.negative) {
    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(x, odd) {
  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();
  if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
    throw new Error('invalid point');

  // 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, jacobianResult) {
      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.negative) {
          split.k1.ineg();
          p = p.neg(true);
        }
        if (split.k2.negative) {
          split.k2.ineg();
          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, jacobianResult);

      // 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.isInfinity())
    return this;
  else if (this._hasDoubles(k))
    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.jmulAdd = function jmulAdd(k1, p2, k2) {
  var points = [ this, p2 ];
  var coeffs = [ k1, k2 ];
  if (this.curve.endo)
    return this.curve._endoWnafMulAdd(points, coeffs, true);
  else
    return this.curve._wnafMulAdd(1, points, coeffs, 2, true);
};

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();

  var i;
  if (this.curve.zeroA || this.curve.threeA) {
    var r = this;
    for (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 (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.eqXToP = function eqXToP(x) {
  var zs = this.z.redSqr();
  var rx = x.toRed(this.curve.red).redMul(zs);
  if (this.x.cmp(rx) === 0)
    return true;

  var xc = x.clone();
  var t = this.curve.redN.redMul(zs);
  for (;;) {
    xc.iadd(this.curve.n);
    if (xc.cmp(this.curve.p) >= 0)
      return false;

    rx.redIAdd(t);
    if (this.x.cmp(rx) === 0)
      return true;
  }
};

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;
};

},{"../utils":15,"./base":2,"bn.js":16,"inherits":32}],7:[function(require,module,exports){
'use strict';

var curves = exports;

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

var assert = utils.assert;

function PresetCurve(options) {
  if (options.type === 'short')
    this.curve = new curve.short(options);
  else if (options.type === 'edwards')
    this.curve = new curve.edwards(options);
  else
    this.curve = new 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('p384', {
  type: 'short',
  prime: null,
  p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'fffffffe ffffffff 00000000 00000000 ffffffff',
  a: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'fffffffe ffffffff 00000000 00000000 fffffffc',
  b: 'b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112 0314088f ' +
     '5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef',
  n: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff c7634d81 ' +
     'f4372ddf 581a0db2 48b0a77a ecec196a ccc52973',
  hash: hash.sha384,
  gRed: false,
  g: [
    'aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98 59f741e0 82542a38 ' +
    '5502f25d bf55296c 3a545e38 72760ab7',
    '3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c e9da3113 b5f0b8c0 ' +
    '0a60b1ce 1d7e819d 7a431d7c 90ea0e5f',
  ],
});

defineCurve('p521', {
  type: 'short',
  prime: null,
  p: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'ffffffff ffffffff ffffffff ffffffff ffffffff',
  a: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'ffffffff ffffffff ffffffff ffffffff fffffffc',
  b: '00000051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b ' +
     '99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd ' +
     '3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00',
  n: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
     'ffffffff ffffffff fffffffa 51868783 bf2f966b 7fcc0148 ' +
     'f709a5d0 3bb5c9b8 899c47ae bb6fb71e 91386409',
  hash: hash.sha512,
  gRed: false,
  g: [
    '000000c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 ' +
    '053fb521 f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 ' +
    'a2ffa8de 3348b3c1 856a429b f97e7e31 c2e5bd66',
    '00000118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 ' +
    '579b4468 17afbd17 273e662c 97ee7299 5ef42640 c550b901 ' +
    '3fad0761 353c7086 a272c240 88be9476 9fd16650',
  ],
});

defineCurve('curve25519', {
  type: 'mont',
  prime: 'p25519',
  p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
  a: '76d06',
  b: '1',
  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,
  ],
});

},{"./curve":4,"./precomputed/secp256k1":14,"./utils":15,"hash.js":19}],8:[function(require,module,exports){
'use strict';

var BN = require('bn.js');
var HmacDRBG = require('hmac-drbg');
var utils = require('../utils');
var curves = require('../curves');
var rand = require('brorand');
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(Object.prototype.hasOwnProperty.call(curves, options),
      'Unknown curve ' + options);

    options = curves[options];
  }

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

  this.curve = options.curve.curve;
  this.n = this.curve.n;
  this.nh = this.n.ushrn(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 HmacDRBG({
    hash: this.hash,
    pers: options.pers,
    persEnc: options.persEnc || 'utf8',
    entropy: options.entropy || rand(this.hash.hmacStrength),
    entropyEnc: options.entropy && options.entropyEnc || 'utf8',
    nonce: this.n.toArray(),
  });

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

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

EC.prototype._truncateToN = function _truncateToN(msg, truncOnly) {
  var delta = msg.byteLength() * 8 - this.n.bitLength();
  if (delta > 0)
    msg = msg.ushrn(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('be', bytes);

  // Zero-extend nonce to have the same byte size as N
  var nonce = msg.toArray('be', bytes);

  // Instantiate Hmac_DRBG
  var drbg = new HmacDRBG({
    hash: this.hash,
    entropy: bkey,
    nonce: nonce,
    pers: options.pers,
    persEnc: options.persEnc || 'utf8',
  });

  // Number of bytes to generate
  var ns1 = this.n.sub(new BN(1));

  for (var iter = 0; ; iter++) {
    var k = options.k ?
      options.k(iter) :
      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 kpX = kp.getX();
    var r = kpX.umod(this.n);
    if (r.cmpn(0) === 0)
      continue;

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

    var recoveryParam = (kp.getY().isOdd() ? 1 : 0) |
                        (kpX.cmp(r) !== 0 ? 2 : 0);

    // Use complement of `s`, if it is > `n / 2`
    if (options.canonical && s.cmp(this.nh) > 0) {
      s = this.n.sub(s);
      recoveryParam ^= 1;
    }

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

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).umod(this.n);
  var u2 = sinv.mul(r).umod(this.n);
  var p;

  if (!this.curve._maxwellTrick) {
    p = this.g.mulAdd(u1, key.getPublic(), u2);
    if (p.isInfinity())
      return false;

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

  // NOTE: Greg Maxwell's trick, inspired by:
  // https://git.io/vad3K

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

  // Compare `p.x` of Jacobian point with `r`,
  // this will do `p.x == r * p.z^2` instead of multiplying `p.x` by the
  // inverse of `p.z^2`
  return p.eqXToP(r);
};

EC.prototype.recoverPubKey = function(msg, signature, j, enc) {
  assert((3 & j) === j, 'The recovery param is more than two bits');
  signature = new Signature(signature, enc);

  var n = this.n;
  var e = new BN(msg);
  var r = signature.r;
  var s = signature.s;

  // A set LSB signifies that the y-coordinate is odd
  var isYOdd = j & 1;
  var isSecondKey = j >> 1;
  if (r.cmp(this.curve.p.umod(this.curve.n)) >= 0 && isSecondKey)
    throw new Error('Unable to find sencond key candinate');

  // 1.1. Let x = r + jn.
  if (isSecondKey)
    r = this.curve.pointFromX(r.add(this.curve.n), isYOdd);
  else
    r = this.curve.pointFromX(r, isYOdd);

  var rInv = signature.r.invm(n);
  var s1 = n.sub(e).mul(rInv).umod(n);
  var s2 = s.mul(rInv).umod(n);

  // 1.6.1 Compute Q = r^-1 (sR -  eG)
  //               Q = r^-1 (sR + -eG)
  return this.g.mulAdd(s1, r, s2);
};

EC.prototype.getKeyRecoveryParam = function(e, signature, Q, enc) {
  signature = new Signature(signature, enc);
  if (signature.recoveryParam !== null)
    return signature.recoveryParam;

  for (var i = 0; i < 4; i++) {
    var Qprime;
    try {
      Qprime = this.recoverPubKey(e, signature, i);
    } catch (e) {
      continue;
    }

    if (Qprime.eq(Q))
      return i;
  }
  throw new Error('Unable to find valid recovery factor');
};

},{"../curves":7,"../utils":15,"./key":9,"./signature":10,"bn.js":16,"brorand":17,"hmac-drbg":31}],9:[function(require,module,exports){
'use strict';

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

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

  if (!this.pub)
    this.pub = this.ec.g.mul(this.priv);

  if (!enc)
    return this.pub;

  return this.pub.encode(enc, compact);
};

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.umod(this.ec.curve.n);
};

KeyPair.prototype._importPublic = function _importPublic(key, enc) {
  if (key.x || key.y) {
    // Montgomery points only have an `x` coordinate.
    // Weierstrass/Edwards points on the other hand have both `x` and
    // `y` coordinates.
    if (this.ec.curve.type === 'mont') {
      assert(key.x, 'Need x coordinate');
    } else if (this.ec.curve.type === 'short' ||
               this.ec.curve.type === 'edwards') {
      assert(key.x && key.y, 'Need both x and y coordinate');
    }
    this.pub = this.ec.curve.point(key.x, key.y);
    return;
  }
  this.pub = this.ec.curve.decodePoint(key, enc);
};

// ECDH
KeyPair.prototype.derive = function derive(pub) {
  if(!pub.validate()) {
    assert(pub.validate(), 'public point not validated');
  }
  return pub.mul(this.priv).getX();
};

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

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()) + ' >';
};

},{"../utils":15,"bn.js":16}],10:[function(require,module,exports){
'use strict';

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

var utils = require('../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);
  if (options.recoveryParam === undefined)
    this.recoveryParam = null;
  else
    this.recoveryParam = options.recoveryParam;
}
module.exports = Signature;

function Position() {
  this.place = 0;
}

function getLength(buf, p) {
  var initial = buf[p.place++];
  if (!(initial & 0x80)) {
    return initial;
  }
  var octetLen = initial & 0xf;

  // Indefinite length or overflow
  if (octetLen === 0 || octetLen > 4) {
    return false;
  }

  var val = 0;
  for (var i = 0, off = p.place; i < octetLen; i++, off++) {
    val <<= 8;
    val |= buf[off];
    val >>>= 0;
  }

  // Leading zeroes
  if (val <= 0x7f) {
    return false;
  }

  p.place = off;
  return val;
}

function rmPadding(buf) {
  var i = 0;
  var len = buf.length - 1;
  while (!buf[i] && !(buf[i + 1] & 0x80) && i < len) {
    i++;
  }
  if (i === 0) {
    return buf;
  }
  return buf.slice(i);
}

Signature.prototype._importDER = function _importDER(data, enc) {
  data = utils.toArray(data, enc);
  var p = new Position();
  if (data[p.place++] !== 0x30) {
    return false;
  }
  var len = getLength(data, p);
  if (len === false) {
    return false;
  }
  if ((len + p.place) !== data.length) {
    return false;
  }
  if (data[p.place++] !== 0x02) {
    return false;
  }
  var rlen = getLength(data, p);
  if (rlen === false) {
    return false;
  }
  var r = data.slice(p.place, rlen + p.place);
  p.place += rlen;
  if (data[p.place++] !== 0x02) {
    return false;
  }
  var slen = getLength(data, p);
  if (slen === false) {
    return false;
  }
  if (data.length !== slen + p.place) {
    return false;
  }
  var s = data.slice(p.place, slen + p.place);
  if (r[0] === 0) {
    if (r[1] & 0x80) {
      r = r.slice(1);
    } else {
      // Leading zeroes
      return false;
    }
  }
  if (s[0] === 0) {
    if (s[1] & 0x80) {
      s = s.slice(1);
    } else {
      // Leading zeroes
      return false;
    }
  }

  this.r = new BN(r);
  this.s = new BN(s);
  this.recoveryParam = null;

  return true;
};

function constructLength(arr, len) {
  if (len < 0x80) {
    arr.push(len);
    return;
  }
  var octets = 1 + (Math.log(len) / Math.LN2 >>> 3);
  arr.push(octets | 0x80);
  while (--octets) {
    arr.push((len >>> (octets << 3)) & 0xff);
  }
  arr.push(len);
}

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);

  r = rmPadding(r);
  s = rmPadding(s);

  while (!s[0] && !(s[1] & 0x80)) {
    s = s.slice(1);
  }
  var arr = [ 0x02 ];
  constructLength(arr, r.length);
  arr = arr.concat(r);
  arr.push(0x02);
  constructLength(arr, s.length);
  var backHalf = arr.concat(s);
  var res = [ 0x30 ];
  constructLength(res, backHalf.length);
  res = res.concat(backHalf);
  return utils.encode(res, enc);
};

},{"../utils":15,"bn.js":16}],11:[function(require,module,exports){
'use strict';

var hash = require('hash.js');
var curves = require('../curves');
var utils = require('../utils');
var assert = utils.assert;
var parseBytes = utils.parseBytes;
var KeyPair = require('./key');
var Signature = require('./signature');

function EDDSA(curve) {
  assert(curve === 'ed25519', 'only tested with ed25519 so far');

  if (!(this instanceof EDDSA))
    return new EDDSA(curve);

  curve = curves[curve].curve;
  this.curve = curve;
  this.g = curve.g;
  this.g.precompute(curve.n.bitLength() + 1);

  this.pointClass = curve.point().constructor;
  this.encodingLength = Math.ceil(curve.n.bitLength() / 8);
  this.hash = hash.sha512;
}

module.exports = EDDSA;

/**
* @param {Array|String} message - message bytes
* @param {Array|String|KeyPair} secret - secret bytes or a keypair
* @returns {Signature} - signature
*/
EDDSA.prototype.sign = function sign(message, secret) {
  message = parseBytes(message);
  var key = this.keyFromSecret(secret);
  var r = this.hashInt(key.messagePrefix(), message);
  var R = this.g.mul(r);
  var Rencoded = this.encodePoint(R);
  var s_ = this.hashInt(Rencoded, key.pubBytes(), message)
    .mul(key.priv());
  var S = r.add(s_).umod(this.curve.n);
  return this.makeSignature({ R: R, S: S, Rencoded: Rencoded });
};

/**
* @param {Array} message - message bytes
* @param {Array|String|Signature} sig - sig bytes
* @param {Array|String|Point|KeyPair} pub - public key
* @returns {Boolean} - true if public key matches sig of message
*/
EDDSA.prototype.verify = function verify(message, sig, pub) {
  message = parseBytes(message);
  sig = this.makeSignature(sig);
  var key = this.keyFromPublic(pub);
  var h = this.hashInt(sig.Rencoded(), key.pubBytes(), message);
  var SG = this.g.mul(sig.S());
  var RplusAh = sig.R().add(key.pub().mul(h));
  return RplusAh.eq(SG);
};

EDDSA.prototype.hashInt = function hashInt() {
  var hash = this.hash();
  for (var i = 0; i < arguments.length; i++)
    hash.update(arguments[i]);
  return utils.intFromLE(hash.digest()).umod(this.curve.n);
};

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

EDDSA.prototype.keyFromSecret = function keyFromSecret(secret) {
  return KeyPair.fromSecret(this, secret);
};

EDDSA.prototype.makeSignature = function makeSignature(sig) {
  if (sig instanceof Signature)
    return sig;
  return new Signature(this, sig);
};

/**
* * https://tools.ietf.org/html/draft-josefsson-eddsa-ed25519-03#section-5.2
*
* EDDSA defines methods for encoding and decoding points and integers. These are
* helper convenience methods, that pass along to utility functions implied
* parameters.
*
*/
EDDSA.prototype.encodePoint = function encodePoint(point) {
  var enc = point.getY().toArray('le', this.encodingLength);
  enc[this.encodingLength - 1] |= point.getX().isOdd() ? 0x80 : 0;
  return enc;
};

EDDSA.prototype.decodePoint = function decodePoint(bytes) {
  bytes = utils.parseBytes(bytes);

  var lastIx = bytes.length - 1;
  var normed = bytes.slice(0, lastIx).concat(bytes[lastIx] & ~0x80);
  var xIsOdd = (bytes[lastIx] & 0x80) !== 0;

  var y = utils.intFromLE(normed);
  return this.curve.pointFromY(y, xIsOdd);
};

EDDSA.prototype.encodeInt = function encodeInt(num) {
  return num.toArray('le', this.encodingLength);
};

EDDSA.prototype.decodeInt = function decodeInt(bytes) {
  return utils.intFromLE(bytes);
};

EDDSA.prototype.isPoint = function isPoint(val) {
  return val instanceof this.pointClass;
};

},{"../curves":7,"../utils":15,"./key":12,"./signature":13,"hash.js":19}],12:[function(require,module,exports){
'use strict';

var utils = require('../utils');
var assert = utils.assert;
var parseBytes = utils.parseBytes;
var cachedProperty = utils.cachedProperty;

/**
* @param {EDDSA} eddsa - instance
* @param {Object} params - public/private key parameters
*
* @param {Array<Byte>} [params.secret] - secret seed bytes
* @param {Point} [params.pub] - public key point (aka `A` in eddsa terms)
* @param {Array<Byte>} [params.pub] - public key point encoded as bytes
*
*/
function KeyPair(eddsa, params) {
  this.eddsa = eddsa;
  this._secret = parseBytes(params.secret);
  if (eddsa.isPoint(params.pub))
    this._pub = params.pub;
  else
    this._pubBytes = parseBytes(params.pub);
}

KeyPair.fromPublic = function fromPublic(eddsa, pub) {
  if (pub instanceof KeyPair)
    return pub;
  return new KeyPair(eddsa, { pub: pub });
};

KeyPair.fromSecret = function fromSecret(eddsa, secret) {
  if (secret instanceof KeyPair)
    return secret;
  return new KeyPair(eddsa, { secret: secret });
};

KeyPair.prototype.secret = function secret() {
  return this._secret;
};

cachedProperty(KeyPair, 'pubBytes', function pubBytes() {
  return this.eddsa.encodePoint(this.pub());
});

cachedProperty(KeyPair, 'pub', function pub() {
  if (this._pubBytes)
    return this.eddsa.decodePoint(this._pubBytes);
  return this.eddsa.g.mul(this.priv());
});

cachedProperty(KeyPair, 'privBytes', function privBytes() {
  var eddsa = this.eddsa;
  var hash = this.hash();
  var lastIx = eddsa.encodingLength - 1;

  var a = hash.slice(0, eddsa.encodingLength);
  a[0] &= 248;
  a[lastIx] &= 127;
  a[lastIx] |= 64;

  return a;
});

cachedProperty(KeyPair, 'priv', function priv() {
  return this.eddsa.decodeInt(this.privBytes());
});

cachedProperty(KeyPair, 'hash', function hash() {
  return this.eddsa.hash().update(this.secret()).digest();
});

cachedProperty(KeyPair, 'messagePrefix', function messagePrefix() {
  return this.hash().slice(this.eddsa.encodingLength);
});

KeyPair.prototype.sign = function sign(message) {
  assert(this._secret, 'KeyPair can only verify');
  return this.eddsa.sign(message, this);
};

KeyPair.prototype.verify = function verify(message, sig) {
  return this.eddsa.verify(message, sig, this);
};

KeyPair.prototype.getSecret = function getSecret(enc) {
  assert(this._secret, 'KeyPair is public only');
  return utils.encode(this.secret(), enc);
};

KeyPair.prototype.getPublic = function getPublic(enc) {
  return utils.encode(this.pubBytes(), enc);
};

module.exports = KeyPair;

},{"../utils":15}],13:[function(require,module,exports){
'use strict';

var BN = require('bn.js');
var utils = require('../utils');
var assert = utils.assert;
var cachedProperty = utils.cachedProperty;
var parseBytes = utils.parseBytes;

/**
* @param {EDDSA} eddsa - eddsa instance
* @param {Array<Bytes>|Object} sig -
* @param {Array<Bytes>|Point} [sig.R] - R point as Point or bytes
* @param {Array<Bytes>|bn} [sig.S] - S scalar as bn or bytes
* @param {Array<Bytes>} [sig.Rencoded] - R point encoded
* @param {Array<Bytes>} [sig.Sencoded] - S scalar encoded
*/
function Signature(eddsa, sig) {
  this.eddsa = eddsa;

  if (typeof sig !== 'object')
    sig = parseBytes(sig);

  if (Array.isArray(sig)) {
    sig = {
      R: sig.slice(0, eddsa.encodingLength),
      S: sig.slice(eddsa.encodingLength),
    };
  }

  assert(sig.R && sig.S, 'Signature without R or S');

  if (eddsa.isPoint(sig.R))
    this._R = sig.R;
  if (sig.S instanceof BN)
    this._S = sig.S;

  this._Rencoded = Array.isArray(sig.R) ? sig.R : sig.Rencoded;
  this._Sencoded = Array.isArray(sig.S) ? sig.S : sig.Sencoded;
}

cachedProperty(Signature, 'S', function S() {
  return this.eddsa.decodeInt(this.Sencoded());
});

cachedProperty(Signature, 'R', function R() {
  return this.eddsa.decodePoint(this.Rencoded());
});

cachedProperty(Signature, 'Rencoded', function Rencoded() {
  return this.eddsa.encodePoint(this.R());
});

cachedProperty(Signature, 'Sencoded', function Sencoded() {
  return this.eddsa.encodeInt(this.S());
});

Signature.prototype.toBytes = function toBytes() {
  return this.Rencoded().concat(this.Sencoded());
};

Signature.prototype.toHex = function toHex() {
  return utils.encode(this.toBytes(), 'hex').toUpperCase();
};

module.exports = Signature;

},{"../utils":15,"bn.js":16}],14:[function(require,module,exports){
module.exports = {
  doubles: {
    step: 4,
    points: [
      [
        'e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a',
        'f7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821',
      ],
      [
        '8282263212c609d9ea2a6e3e172de238d8c39cabd5ac1ca10646e23fd5f51508',
        '11f8a8098557dfe45e8256e830b60ace62d613ac2f7b17bed31b6eaff6e26caf',
      ],
      [
        '175e159f728b865a72f99cc6c6fc846de0b93833fd2222ed73fce5b551e5b739',
        'd3506e0d9e3c79eba4ef97a51ff71f5eacb5955add24345c6efa6ffee9fed695',
      ],
      [
        '363d90d447b00c9c99ceac05b6262ee053441c7e55552ffe526bad8f83ff4640',
        '4e273adfc732221953b445397f3363145b9a89008199ecb62003c7f3bee9de9',
      ],
      [
        '8b4b5f165df3c2be8c6244b5b745638843e4a781a15bcd1b69f79a55dffdf80c',
        '4aad0a6f68d308b4b3fbd7813ab0da04f9e336546162ee56b3eff0c65fd4fd36',
      ],
      [
        '723cbaa6e5db996d6bf771c00bd548c7b700dbffa6c0e77bcb6115925232fcda',
        '96e867b5595cc498a921137488824d6e2660a0653779494801dc069d9eb39f5f',
      ],
      [
        'eebfa4d493bebf98ba5feec812c2d3b50947961237a919839a533eca0e7dd7fa',
        '5d9a8ca3970ef0f269ee7edaf178089d9ae4cdc3a711f712ddfd4fdae1de8999',
      ],
      [
        '100f44da696e71672791d0a09b7bde459f1215a29b3c03bfefd7835b39a48db0',
        'cdd9e13192a00b772ec8f3300c090666b7ff4a18ff5195ac0fbd5cd62bc65a09',
      ],
      [
        'e1031be262c7ed1b1dc9227a4a04c017a77f8d4464f3b3852c8acde6e534fd2d',
        '9d7061928940405e6bb6a4176597535af292dd419e1ced79a44f18f29456a00d',
      ],
      [
        'feea6cae46d55b530ac2839f143bd7ec5cf8b266a41d6af52d5e688d9094696d',
        'e57c6b6c97dce1bab06e4e12bf3ecd5c981c8957cc41442d3155debf18090088',
      ],
      [
        'da67a91d91049cdcb367be4be6ffca3cfeed657d808583de33fa978bc1ec6cb1',
        '9bacaa35481642bc41f463f7ec9780e5dec7adc508f740a17e9ea8e27a68be1d',
      ],
      [
        '53904faa0b334cdda6e000935ef22151ec08d0f7bb11069f57545ccc1a37b7c0',
        '5bc087d0bc80106d88c9eccac20d3c1c13999981e14434699dcb096b022771c8',
      ],
      [
        '8e7bcd0bd35983a7719cca7764ca906779b53a043a9b8bcaeff959f43ad86047',
        '10b7770b2a3da4b3940310420ca9514579e88e2e47fd68b3ea10047e8460372a',
      ],
      [
        '385eed34c1cdff21e6d0818689b81bde71a7f4f18397e6690a841e1599c43862',
        '283bebc3e8ea23f56701de19e9ebf4576b304eec2086dc8cc0458fe5542e5453',
      ],
      [
        '6f9d9b803ecf191637c73a4413dfa180fddf84a5947fbc9c606ed86c3fac3a7',
        '7c80c68e603059ba69b8e2a30e45c4d47ea4dd2f5c281002d86890603a842160',
      ],
      [
        '3322d401243c4e2582a2147c104d6ecbf774d163db0f5e5313b7e0e742d0e6bd',
        '56e70797e9664ef5bfb019bc4ddaf9b72805f63ea2873af624f3a2e96c28b2a0',
      ],
      [
        '85672c7d2de0b7da2bd1770d89665868741b3f9af7643397721d74d28134ab83',
        '7c481b9b5b43b2eb6374049bfa62c2e5e77f17fcc5298f44c8e3094f790313a6',
      ],
      [
        '948bf809b1988a46b06c9f1919413b10f9226c60f668832ffd959af60c82a0a',
        '53a562856dcb6646dc6b74c5d1c3418c6d4dff08c97cd2bed4cb7f88d8c8e589',
      ],
      [
        '6260ce7f461801c34f067ce0f02873a8f1b0e44dfc69752accecd819f38fd8e8',
        'bc2da82b6fa5b571a7f09049776a1ef7ecd292238051c198c1a84e95b2b4ae17',
      ],
      [
        'e5037de0afc1d8d43d8348414bbf4103043ec8f575bfdc432953cc8d2037fa2d',
        '4571534baa94d3b5f9f98d09fb990bddbd5f5b03ec481f10e0e5dc841d755bda',
      ],
      [
        'e06372b0f4a207adf5ea905e8f1771b4e7e8dbd1c6a6c5b725866a0ae4fce725',
        '7a908974bce18cfe12a27bb2ad5a488cd7484a7787104870b27034f94eee31dd',
      ],
      [
        '213c7a715cd5d45358d0bbf9dc0ce02204b10bdde2a3f58540ad6908d0559754',
        '4b6dad0b5ae462507013ad06245ba190bb4850f5f36a7eeddff2c27534b458f2',
      ],
      [
        '4e7c272a7af4b34e8dbb9352a5419a87e2838c70adc62cddf0cc3a3b08fbd53c',
        '17749c766c9d0b18e16fd09f6def681b530b9614bff7dd33e0b3941817dcaae6',
      ],
      [
        'fea74e3dbe778b1b10f238ad61686aa5c76e3db2be43057632427e2840fb27b6',
        '6e0568db9b0b13297cf674deccb6af93126b596b973f7b77701d3db7f23cb96f',
      ],
      [
        '76e64113f677cf0e10a2570d599968d31544e179b760432952c02a4417bdde39',
        'c90ddf8dee4e95cf577066d70681f0d35e2a33d2b56d2032b4b1752d1901ac01',
      ],
      [
        'c738c56b03b2abe1e8281baa743f8f9a8f7cc643df26cbee3ab150242bcbb891',
        '893fb578951ad2537f718f2eacbfbbbb82314eef7880cfe917e735d9699a84c3',
      ],
      [
        'd895626548b65b81e264c7637c972877d1d72e5f3a925014372e9f6588f6c14b',
        'febfaa38f2bc7eae728ec60818c340eb03428d632bb067e179363ed75d7d991f',
      ],
      [
        'b8da94032a957518eb0f6433571e8761ceffc73693e84edd49150a564f676e03',
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      [
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      ],
      [
        '90ad85b389d6b936463f9d0512678de208cc330b11307fffab7ac63e3fb04ed4',
        'e507a3620a38261affdcbd9427222b839aefabe1582894d991d4d48cb6ef150',
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      [
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      [
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      [
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      ],
    ],
  },
  naf: {
    wnd: 7,
    points: [
      [
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      ],
      [
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        'cc338921b0a7d9fd64380971763b61e9add888a4375f8e0f05cc262ac64f9c37',
      ],
      [
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        'd984a032eb6b5e190243dd56d7b7b365372db1e2dff9d6a8301d74c9c953c61b',
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        'ecfb7056cf1de042f9420bab396793c0c390bde74b4bbdff16a83ae09a9a7517',
      ],
      [
        '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',
      ],
    ],
  },
};

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

var utils = exports;
var BN = require('bn.js');
var minAssert = require('minimalistic-assert');
var minUtils = require('minimalistic-crypto-utils');

utils.assert = minAssert;
utils.toArray = minUtils.toArray;
utils.zero2 = minUtils.zero2;
utils.toHex = minUtils.toHex;
utils.encode = minUtils.encode;

// Represent num in a w-NAF form
function getNAF(num, w, bits) {
  var naf = new Array(Math.max(num.bitLength(), bits) + 1);
  naf.fill(0);

  var ws = 1 << (w + 1);
  var k = num.clone();

  for (var i = 0; i < naf.length; i++) {
    var z;
    var mod = k.andln(ws - 1);
    if (k.isOdd()) {
      if (mod > (ws >> 1) - 1)
        z = (ws >> 1) - mod;
      else
        z = mod;
      k.isubn(z);
    } else {
      z = 0;
    }

    naf[i] = z;
    k.iushrn(1);
  }

  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;
  var m8;
  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 {
      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 {
      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.iushrn(1);
    k2.iushrn(1);
  }

  return jsf;
}
utils.getJSF = getJSF;

function cachedProperty(obj, name, computer) {
  var key = '_' + name;
  obj.prototype[name] = function cachedProperty() {
    return this[key] !== undefined ? this[key] :
      this[key] = computer.call(this);
  };
}
utils.cachedProperty = cachedProperty;

function parseBytes(bytes) {
  return typeof bytes === 'string' ? utils.toArray(bytes, 'hex') :
    bytes;
}
utils.parseBytes = parseBytes;

function intFromLE(bytes) {
  return new BN(bytes, 'hex', 'le');
}
utils.intFromLE = intFromLE;


},{"bn.js":16,"minimalistic-assert":33,"minimalistic-crypto-utils":34}],16:[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) {
    if (BN.isBN(number)) {
      return number;
    }

    this.negative = 0;
    this.words = null;
    this.length = 0;

    // Reduction context
    this.red = null;

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

      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;

  var Buffer;
  try {
    Buffer = require('buffer').Buffer;
  } catch (e) {
  }

  BN.isBN = function isBN (num) {
    if (num instanceof BN) {
      return true;
    }

    return num !== null && typeof num === 'object' &&
      num.constructor.wordSize === BN.wordSize && Array.isArray(num.words);
  };

  BN.max = function max (left, right) {
    if (left.cmp(right) > 0) return left;
    return right;
  };

  BN.min = function min (left, right) {
    if (left.cmp(right) < 0) return left;
    return right;
  };

  BN.prototype._init = function init (number, base, endian) {
    if (typeof number === 'number') {
      return this._initNumber(number, base, endian);
    }

    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.negative = 1;
    }

    this.strip();

    if (endian !== 'le') return;

    this._initArray(this.toArray(), base, endian);
  };

  BN.prototype._initNumber = function _initNumber (number, base, endian) {
    if (number < 0) {
      this.negative = 1;
      number = -number;
    }
    if (number < 0x4000000) {
      this.words = [ number & 0x3ffffff ];
      this.length = 1;
    } else if (number < 0x10000000000000) {
      this.words = [
        number & 0x3ffffff,
        (number / 0x4000000) & 0x3ffffff
      ];
      this.length = 2;
    } else {
      assert(number < 0x20000000000000); // 2 ^ 53 (unsafe)
      this.words = [
        number & 0x3ffffff,
        (number / 0x4000000) & 0x3ffffff,
        1
      ];
      this.length = 3;
    }

    if (endian !== 'le') return;

    // Reverse the bytes
    this._initArray(this.toArray(), base, endian);
  };

  BN.prototype._initArray = function _initArray (number, base, endian) {
    // Perhaps a Uint8Array
    assert(typeof number.length === 'number');
    if (number.length <= 0) {
      this.words = [ 0 ];
      this.length = 1;
      return this;
    }

    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 j, w;
    var off = 0;
    if (endian === 'be') {
      for (i = number.length - 1, j = 0; i >= 0; i -= 3) {
        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 (i = 0, j = 0; i < number.length; i += 3) {
        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;
    }

    var j, w;
    // Scan 24-bit chunks and add them to the number
    var off = 0;
    for (i = number.length - 6, j = 0; i >= start; i -= 6) {
      w = parseHex(number, i, i + 6);
      this.words[j] |= (w << off) & 0x3ffffff;
      // NOTE: `0x3fffff` is intentional here, 26bits max shift + 24bit hex limb
      this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
      off += 24;
      if (off >= 26) {
        off -= 26;
        j++;
      }
    }
    if (i + 6 !== start) {
      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;
      word = parseBase(number, i, number.length, base);

      for (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.negative = this.negative;
    dest.red = this.red;
  };

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

  BN.prototype._expand = function _expand (size) {
    while (this.length < size) {
      this.words[this.length++] = 0;
    }
    return this;
  };

  // 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.negative = 0;
    }
    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;
    padding = padding | 0 || 1;

    var out;
    if (base === 16 || base === 'hex') {
      out = '';
      var off = 0;
      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.negative !== 0) {
        out = '-' + out;
      }
      return out;
    }

    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];
      out = '';
      var c = this.clone();
      c.negative = 0;
      while (!c.isZero()) {
        var r = c.modn(groupBase).toString(base);
        c = c.idivn(groupBase);

        if (!c.isZero()) {
          out = zeros[groupSize - r.length] + r + out;
        } else {
          out = r + out;
        }
      }
      if (this.isZero()) {
        out = '0' + out;
      }
      while (out.length % padding !== 0) {
        out = '0' + out;
      }
      if (this.negative !== 0) {
        out = '-' + out;
      }
      return out;
    }

    assert(false, 'Base should be between 2 and 36');
  };

  BN.prototype.toNumber = function toNumber () {
    var ret = this.words[0];
    if (this.length === 2) {
      ret += this.words[1] * 0x4000000;
    } else if (this.length === 3 && this.words[2] === 0x01) {
      // NOTE: at this stage it is known that the top bit is set
      ret += 0x10000000000000 + (this.words[1] * 0x4000000);
    } else if (this.length > 2) {
      assert(false, 'Number can only safely store up to 53 bits');
    }
    return (this.negative !== 0) ? -ret : ret;
  };

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

  BN.prototype.toBuffer = function toBuffer (endian, length) {
    assert(typeof Buffer !== 'undefined');
    return this.toArrayLike(Buffer, endian, length);
  };

  BN.prototype.toArray = function toArray (endian, length) {
    return this.toArrayLike(Array, endian, length);
  };

  BN.prototype.toArrayLike = function toArrayLike (ArrayType, endian, length) {
    var byteLength = this.byteLength();
    var reqLength = length || Math.max(1, byteLength);
    assert(byteLength <= reqLength, 'byte array longer than desired length');
    assert(reqLength > 0, 'Requested array length <= 0');

    this.strip();
    var littleEndian = endian === 'le';
    var res = new ArrayType(reqLength);

    var b, i;
    var q = this.clone();
    if (!littleEndian) {
      // Assume big-endian
      for (i = 0; i < reqLength - byteLength; i++) {
        res[i] = 0;
      }

      for (i = 0; !q.isZero(); i++) {
        b = q.andln(0xff);
        q.iushrn(8);

        res[reqLength - i - 1] = b;
      }
    } else {
      for (i = 0; !q.isZero(); i++) {
        b = q.andln(0xff);
        q.iushrn(8);

        res[i] = b;
      }

      for (; i < reqLength; i++) {
        res[i] = 0;
      }
    }

    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 w = this.words[this.length - 1];
    var hi = this._countBits(w);
    return (this.length - 1) * 26 + hi;
  };

  function toBitArray (num) {
    var w = new Array(num.bitLength());

    for (var bit = 0; bit < w.length; bit++) {
      var off = (bit / 26) | 0;
      var wbit = bit % 26;

      w[bit] = (num.words[off] & (1 << wbit)) >>> wbit;
    }

    return w;
  }

  // Number of trailing zero bits
  BN.prototype.zeroBits = function zeroBits () {
    if (this.isZero()) 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);
  };

  BN.prototype.toTwos = function toTwos (width) {
    if (this.negative !== 0) {
      return this.abs().inotn(width).iaddn(1);
    }
    return this.clone();
  };

  BN.prototype.fromTwos = function fromTwos (width) {
    if (this.testn(width - 1)) {
      return this.notn(width).iaddn(1).ineg();
    }
    return this.clone();
  };

  BN.prototype.isNeg = function isNeg () {
    return this.negative !== 0;
  };

  // Return negative clone of `this`
  BN.prototype.neg = function neg () {
    return this.clone().ineg();
  };

  BN.prototype.ineg = function ineg () {
    if (!this.isZero()) {
      this.negative ^= 1;
    }

    return this;
  };

  // Or `num` with `this` in-place
  BN.prototype.iuor = function iuor (num) {
    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();
  };

  BN.prototype.ior = function ior (num) {
    assert((this.negative | num.negative) === 0);
    return this.iuor(num);
  };

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

  BN.prototype.uor = function uor (num) {
    if (this.length > num.length) return this.clone().iuor(num);
    return num.clone().iuor(this);
  };

  // And `num` with `this` in-place
  BN.prototype.iuand = function iuand (num) {
    // 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();
  };

  BN.prototype.iand = function iand (num) {
    assert((this.negative | num.negative) === 0);
    return this.iuand(num);
  };

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

  BN.prototype.uand = function uand (num) {
    if (this.length > num.length) return this.clone().iuand(num);
    return num.clone().iuand(this);
  };

  // Xor `num` with `this` in-place
  BN.prototype.iuxor = function iuxor (num) {
    // 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();
  };

  BN.prototype.ixor = function ixor (num) {
    assert((this.negative | num.negative) === 0);
    return this.iuxor(num);
  };

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

  BN.prototype.uxor = function uxor (num) {
    if (this.length > num.length) return this.clone().iuxor(num);
    return num.clone().iuxor(this);
  };

  // Not ``this`` with ``width`` bitwidth
  BN.prototype.inotn = function inotn (width) {
    assert(typeof width === 'number' && width >= 0);

    var bytesNeeded = Math.ceil(width / 26) | 0;
    var bitsLeft = width % 26;

    // Extend the buffer with leading zeroes
    this._expand(bytesNeeded);

    if (bitsLeft > 0) {
      bytesNeeded--;
    }

    // Handle complete words
    for (var i = 0; i < bytesNeeded; i++) {
      this.words[i] = ~this.words[i] & 0x3ffffff;
    }

    // Handle the residue
    if (bitsLeft > 0) {
      this.words[i] = ~this.words[i] & (0x3ffffff >> (26 - bitsLeft));
    }

    // And remove leading zeroes
    return this.strip();
  };

  BN.prototype.notn = function notn (width) {
    return this.clone().inotn(width);
  };

  // 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;

    this._expand(off + 1);

    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) {
    var r;

    // negative + positive
    if (this.negative !== 0 && num.negative === 0) {
      this.negative = 0;
      r = this.isub(num);
      this.negative ^= 1;
      return this._normSign();

    // positive + negative
    } else if (this.negative === 0 && num.negative !== 0) {
      num.negative = 0;
      r = this.isub(num);
      num.negative = 1;
      return r._normSign();
    }

    // a.length > b.length
    var a, 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++) {
      r = (a.words[i] | 0) + (b.words[i] | 0) + carry;
      this.words[i] = r & 0x3ffffff;
      carry = r >>> 26;
    }
    for (; carry !== 0 && i < a.length; i++) {
      r = (a.words[i] | 0) + 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) {
    var res;
    if (num.negative !== 0 && this.negative === 0) {
      num.negative = 0;
      res = this.sub(num);
      num.negative ^= 1;
      return res;
    } else if (num.negative === 0 && this.negative !== 0) {
      this.negative = 0;
      res = num.sub(this);
      this.negative = 1;
      return res;
    }

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

    return num.clone().iadd(this);
  };

  // Subtract `num` from `this` in-place
  BN.prototype.isub = function isub (num) {
    // this - (-num) = this + num
    if (num.negative !== 0) {
      num.negative = 0;
      var r = this.iadd(num);
      num.negative = 1;
      return r._normSign();

    // -this - num = -(this + num)
    } else if (this.negative !== 0) {
      this.negative = 0;
      this.iadd(num);
      this.negative = 1;
      return this._normSign();
    }

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

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

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

    var carry = 0;
    for (var i = 0; i < b.length; i++) {
      r = (a.words[i] | 0) - (b.words[i] | 0) + carry;
      carry = r >> 26;
      this.words[i] = r & 0x3ffffff;
    }
    for (; carry !== 0 && i < a.length; i++) {
      r = (a.words[i] | 0) + 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.negative = 1;
    }

    return this.strip();
  };

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

  function smallMulTo (self, num, out) {
    out.negative = num.negative ^ self.negative;
    var len = (self.length + num.length) | 0;
    out.length = len;
    len = (len - 1) | 0;

    // Peel one iteration (compiler can't do it, because of code complexity)
    var a = self.words[0] | 0;
    var b = num.words[0] | 0;
    var r = a * b;

    var lo = r & 0x3ffffff;
    var carry = (r / 0x4000000) | 0;
    out.words[0] = lo;

    for (var k = 1; k < len; 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 - self.length + 1); j <= maxJ; j++) {
        var i = (k - j) | 0;
        a = self.words[i] | 0;
        b = num.words[j] | 0;
        r = a * b + rword;
        ncarry += (r / 0x4000000) | 0;
        rword = r & 0x3ffffff;
      }
      out.words[k] = rword | 0;
      carry = ncarry | 0;
    }
    if (carry !== 0) {
      out.words[k] = carry | 0;
    } else {
      out.length--;
    }

    return out.strip();
  }

  // TODO(indutny): it may be reasonable to omit it for users who don't need
  // to work with 256-bit numbers, otherwise it gives 20% improvement for 256-bit
  // multiplication (like elliptic secp256k1).
  var comb10MulTo = function comb10MulTo (self, num, out) {
    var a = self.words;
    var b = num.words;
    var o = out.words;
    var c = 0;
    var lo;
    var mid;
    var hi;
    var a0 = a[0] | 0;
    var al0 = a0 & 0x1fff;
    var ah0 = a0 >>> 13;
    var a1 = a[1] | 0;
    var al1 = a1 & 0x1fff;
    var ah1 = a1 >>> 13;
    var a2 = a[2] | 0;
    var al2 = a2 & 0x1fff;
    var ah2 = a2 >>> 13;
    var a3 = a[3] | 0;
    var al3 = a3 & 0x1fff;
    var ah3 = a3 >>> 13;
    var a4 = a[4] | 0;
    var al4 = a4 & 0x1fff;
    var ah4 = a4 >>> 13;
    var a5 = a[5] | 0;
    var al5 = a5 & 0x1fff;
    var ah5 = a5 >>> 13;
    var a6 = a[6] | 0;
    var al6 = a6 & 0x1fff;
    var ah6 = a6 >>> 13;
    var a7 = a[7] | 0;
    var al7 = a7 & 0x1fff;
    var ah7 = a7 >>> 13;
    var a8 = a[8] | 0;
    var al8 = a8 & 0x1fff;
    var ah8 = a8 >>> 13;
    var a9 = a[9] | 0;
    var al9 = a9 & 0x1fff;
    var ah9 = a9 >>> 13;
    var b0 = b[0] | 0;
    var bl0 = b0 & 0x1fff;
    var bh0 = b0 >>> 13;
    var b1 = b[1] | 0;
    var bl1 = b1 & 0x1fff;
    var bh1 = b1 >>> 13;
    var b2 = b[2] | 0;
    var bl2 = b2 & 0x1fff;
    var bh2 = b2 >>> 13;
    var b3 = b[3] | 0;
    var bl3 = b3 & 0x1fff;
    var bh3 = b3 >>> 13;
    var b4 = b[4] | 0;
    var bl4 = b4 & 0x1fff;
    var bh4 = b4 >>> 13;
    var b5 = b[5] | 0;
    var bl5 = b5 & 0x1fff;
    var bh5 = b5 >>> 13;
    var b6 = b[6] | 0;
    var bl6 = b6 & 0x1fff;
    var bh6 = b6 >>> 13;
    var b7 = b[7] | 0;
    var bl7 = b7 & 0x1fff;
    var bh7 = b7 >>> 13;
    var b8 = b[8] | 0;
    var bl8 = b8 & 0x1fff;
    var bh8 = b8 >>> 13;
    var b9 = b[9] | 0;
    var bl9 = b9 & 0x1fff;
    var bh9 = b9 >>> 13;

    out.negative = self.negative ^ num.negative;
    out.length = 19;
    /* k = 0 */
    lo = Math.imul(al0, bl0);
    mid = Math.imul(al0, bh0);
    mid = (mid + Math.imul(ah0, bl0)) | 0;
    hi = Math.imul(ah0, bh0);
    var w0 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w0 >>> 26)) | 0;
    w0 &= 0x3ffffff;
    /* k = 1 */
    lo = Math.imul(al1, bl0);
    mid = Math.imul(al1, bh0);
    mid = (mid + Math.imul(ah1, bl0)) | 0;
    hi = Math.imul(ah1, bh0);
    lo = (lo + Math.imul(al0, bl1)) | 0;
    mid = (mid + Math.imul(al0, bh1)) | 0;
    mid = (mid + Math.imul(ah0, bl1)) | 0;
    hi = (hi + Math.imul(ah0, bh1)) | 0;
    var w1 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w1 >>> 26)) | 0;
    w1 &= 0x3ffffff;
    /* k = 2 */
    lo = Math.imul(al2, bl0);
    mid = Math.imul(al2, bh0);
    mid = (mid + Math.imul(ah2, bl0)) | 0;
    hi = Math.imul(ah2, bh0);
    lo = (lo + Math.imul(al1, bl1)) | 0;
    mid = (mid + Math.imul(al1, bh1)) | 0;
    mid = (mid + Math.imul(ah1, bl1)) | 0;
    hi = (hi + Math.imul(ah1, bh1)) | 0;
    lo = (lo + Math.imul(al0, bl2)) | 0;
    mid = (mid + Math.imul(al0, bh2)) | 0;
    mid = (mid + Math.imul(ah0, bl2)) | 0;
    hi = (hi + Math.imul(ah0, bh2)) | 0;
    var w2 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w2 >>> 26)) | 0;
    w2 &= 0x3ffffff;
    /* k = 3 */
    lo = Math.imul(al3, bl0);
    mid = Math.imul(al3, bh0);
    mid = (mid + Math.imul(ah3, bl0)) | 0;
    hi = Math.imul(ah3, bh0);
    lo = (lo + Math.imul(al2, bl1)) | 0;
    mid = (mid + Math.imul(al2, bh1)) | 0;
    mid = (mid + Math.imul(ah2, bl1)) | 0;
    hi = (hi + Math.imul(ah2, bh1)) | 0;
    lo = (lo + Math.imul(al1, bl2)) | 0;
    mid = (mid + Math.imul(al1, bh2)) | 0;
    mid = (mid + Math.imul(ah1, bl2)) | 0;
    hi = (hi + Math.imul(ah1, bh2)) | 0;
    lo = (lo + Math.imul(al0, bl3)) | 0;
    mid = (mid + Math.imul(al0, bh3)) | 0;
    mid = (mid + Math.imul(ah0, bl3)) | 0;
    hi = (hi + Math.imul(ah0, bh3)) | 0;
    var w3 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w3 >>> 26)) | 0;
    w3 &= 0x3ffffff;
    /* k = 4 */
    lo = Math.imul(al4, bl0);
    mid = Math.imul(al4, bh0);
    mid = (mid + Math.imul(ah4, bl0)) | 0;
    hi = Math.imul(ah4, bh0);
    lo = (lo + Math.imul(al3, bl1)) | 0;
    mid = (mid + Math.imul(al3, bh1)) | 0;
    mid = (mid + Math.imul(ah3, bl1)) | 0;
    hi = (hi + Math.imul(ah3, bh1)) | 0;
    lo = (lo + Math.imul(al2, bl2)) | 0;
    mid = (mid + Math.imul(al2, bh2)) | 0;
    mid = (mid + Math.imul(ah2, bl2)) | 0;
    hi = (hi + Math.imul(ah2, bh2)) | 0;
    lo = (lo + Math.imul(al1, bl3)) | 0;
    mid = (mid + Math.imul(al1, bh3)) | 0;
    mid = (mid + Math.imul(ah1, bl3)) | 0;
    hi = (hi + Math.imul(ah1, bh3)) | 0;
    lo = (lo + Math.imul(al0, bl4)) | 0;
    mid = (mid + Math.imul(al0, bh4)) | 0;
    mid = (mid + Math.imul(ah0, bl4)) | 0;
    hi = (hi + Math.imul(ah0, bh4)) | 0;
    var w4 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w4 >>> 26)) | 0;
    w4 &= 0x3ffffff;
    /* k = 5 */
    lo = Math.imul(al5, bl0);
    mid = Math.imul(al5, bh0);
    mid = (mid + Math.imul(ah5, bl0)) | 0;
    hi = Math.imul(ah5, bh0);
    lo = (lo + Math.imul(al4, bl1)) | 0;
    mid = (mid + Math.imul(al4, bh1)) | 0;
    mid = (mid + Math.imul(ah4, bl1)) | 0;
    hi = (hi + Math.imul(ah4, bh1)) | 0;
    lo = (lo + Math.imul(al3, bl2)) | 0;
    mid = (mid + Math.imul(al3, bh2)) | 0;
    mid = (mid + Math.imul(ah3, bl2)) | 0;
    hi = (hi + Math.imul(ah3, bh2)) | 0;
    lo = (lo + Math.imul(al2, bl3)) | 0;
    mid = (mid + Math.imul(al2, bh3)) | 0;
    mid = (mid + Math.imul(ah2, bl3)) | 0;
    hi = (hi + Math.imul(ah2, bh3)) | 0;
    lo = (lo + Math.imul(al1, bl4)) | 0;
    mid = (mid + Math.imul(al1, bh4)) | 0;
    mid = (mid + Math.imul(ah1, bl4)) | 0;
    hi = (hi + Math.imul(ah1, bh4)) | 0;
    lo = (lo + Math.imul(al0, bl5)) | 0;
    mid = (mid + Math.imul(al0, bh5)) | 0;
    mid = (mid + Math.imul(ah0, bl5)) | 0;
    hi = (hi + Math.imul(ah0, bh5)) | 0;
    var w5 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w5 >>> 26)) | 0;
    w5 &= 0x3ffffff;
    /* k = 6 */
    lo = Math.imul(al6, bl0);
    mid = Math.imul(al6, bh0);
    mid = (mid + Math.imul(ah6, bl0)) | 0;
    hi = Math.imul(ah6, bh0);
    lo = (lo + Math.imul(al5, bl1)) | 0;
    mid = (mid + Math.imul(al5, bh1)) | 0;
    mid = (mid + Math.imul(ah5, bl1)) | 0;
    hi = (hi + Math.imul(ah5, bh1)) | 0;
    lo = (lo + Math.imul(al4, bl2)) | 0;
    mid = (mid + Math.imul(al4, bh2)) | 0;
    mid = (mid + Math.imul(ah4, bl2)) | 0;
    hi = (hi + Math.imul(ah4, bh2)) | 0;
    lo = (lo + Math.imul(al3, bl3)) | 0;
    mid = (mid + Math.imul(al3, bh3)) | 0;
    mid = (mid + Math.imul(ah3, bl3)) | 0;
    hi = (hi + Math.imul(ah3, bh3)) | 0;
    lo = (lo + Math.imul(al2, bl4)) | 0;
    mid = (mid + Math.imul(al2, bh4)) | 0;
    mid = (mid + Math.imul(ah2, bl4)) | 0;
    hi = (hi + Math.imul(ah2, bh4)) | 0;
    lo = (lo + Math.imul(al1, bl5)) | 0;
    mid = (mid + Math.imul(al1, bh5)) | 0;
    mid = (mid + Math.imul(ah1, bl5)) | 0;
    hi = (hi + Math.imul(ah1, bh5)) | 0;
    lo = (lo + Math.imul(al0, bl6)) | 0;
    mid = (mid + Math.imul(al0, bh6)) | 0;
    mid = (mid + Math.imul(ah0, bl6)) | 0;
    hi = (hi + Math.imul(ah0, bh6)) | 0;
    var w6 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w6 >>> 26)) | 0;
    w6 &= 0x3ffffff;
    /* k = 7 */
    lo = Math.imul(al7, bl0);
    mid = Math.imul(al7, bh0);
    mid = (mid + Math.imul(ah7, bl0)) | 0;
    hi = Math.imul(ah7, bh0);
    lo = (lo + Math.imul(al6, bl1)) | 0;
    mid = (mid + Math.imul(al6, bh1)) | 0;
    mid = (mid + Math.imul(ah6, bl1)) | 0;
    hi = (hi + Math.imul(ah6, bh1)) | 0;
    lo = (lo + Math.imul(al5, bl2)) | 0;
    mid = (mid + Math.imul(al5, bh2)) | 0;
    mid = (mid + Math.imul(ah5, bl2)) | 0;
    hi = (hi + Math.imul(ah5, bh2)) | 0;
    lo = (lo + Math.imul(al4, bl3)) | 0;
    mid = (mid + Math.imul(al4, bh3)) | 0;
    mid = (mid + Math.imul(ah4, bl3)) | 0;
    hi = (hi + Math.imul(ah4, bh3)) | 0;
    lo = (lo + Math.imul(al3, bl4)) | 0;
    mid = (mid + Math.imul(al3, bh4)) | 0;
    mid = (mid + Math.imul(ah3, bl4)) | 0;
    hi = (hi + Math.imul(ah3, bh4)) | 0;
    lo = (lo + Math.imul(al2, bl5)) | 0;
    mid = (mid + Math.imul(al2, bh5)) | 0;
    mid = (mid + Math.imul(ah2, bl5)) | 0;
    hi = (hi + Math.imul(ah2, bh5)) | 0;
    lo = (lo + Math.imul(al1, bl6)) | 0;
    mid = (mid + Math.imul(al1, bh6)) | 0;
    mid = (mid + Math.imul(ah1, bl6)) | 0;
    hi = (hi + Math.imul(ah1, bh6)) | 0;
    lo = (lo + Math.imul(al0, bl7)) | 0;
    mid = (mid + Math.imul(al0, bh7)) | 0;
    mid = (mid + Math.imul(ah0, bl7)) | 0;
    hi = (hi + Math.imul(ah0, bh7)) | 0;
    var w7 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w7 >>> 26)) | 0;
    w7 &= 0x3ffffff;
    /* k = 8 */
    lo = Math.imul(al8, bl0);
    mid = Math.imul(al8, bh0);
    mid = (mid + Math.imul(ah8, bl0)) | 0;
    hi = Math.imul(ah8, bh0);
    lo = (lo + Math.imul(al7, bl1)) | 0;
    mid = (mid + Math.imul(al7, bh1)) | 0;
    mid = (mid + Math.imul(ah7, bl1)) | 0;
    hi = (hi + Math.imul(ah7, bh1)) | 0;
    lo = (lo + Math.imul(al6, bl2)) | 0;
    mid = (mid + Math.imul(al6, bh2)) | 0;
    mid = (mid + Math.imul(ah6, bl2)) | 0;
    hi = (hi + Math.imul(ah6, bh2)) | 0;
    lo = (lo + Math.imul(al5, bl3)) | 0;
    mid = (mid + Math.imul(al5, bh3)) | 0;
    mid = (mid + Math.imul(ah5, bl3)) | 0;
    hi = (hi + Math.imul(ah5, bh3)) | 0;
    lo = (lo + Math.imul(al4, bl4)) | 0;
    mid = (mid + Math.imul(al4, bh4)) | 0;
    mid = (mid + Math.imul(ah4, bl4)) | 0;
    hi = (hi + Math.imul(ah4, bh4)) | 0;
    lo = (lo + Math.imul(al3, bl5)) | 0;
    mid = (mid + Math.imul(al3, bh5)) | 0;
    mid = (mid + Math.imul(ah3, bl5)) | 0;
    hi = (hi + Math.imul(ah3, bh5)) | 0;
    lo = (lo + Math.imul(al2, bl6)) | 0;
    mid = (mid + Math.imul(al2, bh6)) | 0;
    mid = (mid + Math.imul(ah2, bl6)) | 0;
    hi = (hi + Math.imul(ah2, bh6)) | 0;
    lo = (lo + Math.imul(al1, bl7)) | 0;
    mid = (mid + Math.imul(al1, bh7)) | 0;
    mid = (mid + Math.imul(ah1, bl7)) | 0;
    hi = (hi + Math.imul(ah1, bh7)) | 0;
    lo = (lo + Math.imul(al0, bl8)) | 0;
    mid = (mid + Math.imul(al0, bh8)) | 0;
    mid = (mid + Math.imul(ah0, bl8)) | 0;
    hi = (hi + Math.imul(ah0, bh8)) | 0;
    var w8 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w8 >>> 26)) | 0;
    w8 &= 0x3ffffff;
    /* k = 9 */
    lo = Math.imul(al9, bl0);
    mid = Math.imul(al9, bh0);
    mid = (mid + Math.imul(ah9, bl0)) | 0;
    hi = Math.imul(ah9, bh0);
    lo = (lo + Math.imul(al8, bl1)) | 0;
    mid = (mid + Math.imul(al8, bh1)) | 0;
    mid = (mid + Math.imul(ah8, bl1)) | 0;
    hi = (hi + Math.imul(ah8, bh1)) | 0;
    lo = (lo + Math.imul(al7, bl2)) | 0;
    mid = (mid + Math.imul(al7, bh2)) | 0;
    mid = (mid + Math.imul(ah7, bl2)) | 0;
    hi = (hi + Math.imul(ah7, bh2)) | 0;
    lo = (lo + Math.imul(al6, bl3)) | 0;
    mid = (mid + Math.imul(al6, bh3)) | 0;
    mid = (mid + Math.imul(ah6, bl3)) | 0;
    hi = (hi + Math.imul(ah6, bh3)) | 0;
    lo = (lo + Math.imul(al5, bl4)) | 0;
    mid = (mid + Math.imul(al5, bh4)) | 0;
    mid = (mid + Math.imul(ah5, bl4)) | 0;
    hi = (hi + Math.imul(ah5, bh4)) | 0;
    lo = (lo + Math.imul(al4, bl5)) | 0;
    mid = (mid + Math.imul(al4, bh5)) | 0;
    mid = (mid + Math.imul(ah4, bl5)) | 0;
    hi = (hi + Math.imul(ah4, bh5)) | 0;
    lo = (lo + Math.imul(al3, bl6)) | 0;
    mid = (mid + Math.imul(al3, bh6)) | 0;
    mid = (mid + Math.imul(ah3, bl6)) | 0;
    hi = (hi + Math.imul(ah3, bh6)) | 0;
    lo = (lo + Math.imul(al2, bl7)) | 0;
    mid = (mid + Math.imul(al2, bh7)) | 0;
    mid = (mid + Math.imul(ah2, bl7)) | 0;
    hi = (hi + Math.imul(ah2, bh7)) | 0;
    lo = (lo + Math.imul(al1, bl8)) | 0;
    mid = (mid + Math.imul(al1, bh8)) | 0;
    mid = (mid + Math.imul(ah1, bl8)) | 0;
    hi = (hi + Math.imul(ah1, bh8)) | 0;
    lo = (lo + Math.imul(al0, bl9)) | 0;
    mid = (mid + Math.imul(al0, bh9)) | 0;
    mid = (mid + Math.imul(ah0, bl9)) | 0;
    hi = (hi + Math.imul(ah0, bh9)) | 0;
    var w9 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w9 >>> 26)) | 0;
    w9 &= 0x3ffffff;
    /* k = 10 */
    lo = Math.imul(al9, bl1);
    mid = Math.imul(al9, bh1);
    mid = (mid + Math.imul(ah9, bl1)) | 0;
    hi = Math.imul(ah9, bh1);
    lo = (lo + Math.imul(al8, bl2)) | 0;
    mid = (mid + Math.imul(al8, bh2)) | 0;
    mid = (mid + Math.imul(ah8, bl2)) | 0;
    hi = (hi + Math.imul(ah8, bh2)) | 0;
    lo = (lo + Math.imul(al7, bl3)) | 0;
    mid = (mid + Math.imul(al7, bh3)) | 0;
    mid = (mid + Math.imul(ah7, bl3)) | 0;
    hi = (hi + Math.imul(ah7, bh3)) | 0;
    lo = (lo + Math.imul(al6, bl4)) | 0;
    mid = (mid + Math.imul(al6, bh4)) | 0;
    mid = (mid + Math.imul(ah6, bl4)) | 0;
    hi = (hi + Math.imul(ah6, bh4)) | 0;
    lo = (lo + Math.imul(al5, bl5)) | 0;
    mid = (mid + Math.imul(al5, bh5)) | 0;
    mid = (mid + Math.imul(ah5, bl5)) | 0;
    hi = (hi + Math.imul(ah5, bh5)) | 0;
    lo = (lo + Math.imul(al4, bl6)) | 0;
    mid = (mid + Math.imul(al4, bh6)) | 0;
    mid = (mid + Math.imul(ah4, bl6)) | 0;
    hi = (hi + Math.imul(ah4, bh6)) | 0;
    lo = (lo + Math.imul(al3, bl7)) | 0;
    mid = (mid + Math.imul(al3, bh7)) | 0;
    mid = (mid + Math.imul(ah3, bl7)) | 0;
    hi = (hi + Math.imul(ah3, bh7)) | 0;
    lo = (lo + Math.imul(al2, bl8)) | 0;
    mid = (mid + Math.imul(al2, bh8)) | 0;
    mid = (mid + Math.imul(ah2, bl8)) | 0;
    hi = (hi + Math.imul(ah2, bh8)) | 0;
    lo = (lo + Math.imul(al1, bl9)) | 0;
    mid = (mid + Math.imul(al1, bh9)) | 0;
    mid = (mid + Math.imul(ah1, bl9)) | 0;
    hi = (hi + Math.imul(ah1, bh9)) | 0;
    var w10 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w10 >>> 26)) | 0;
    w10 &= 0x3ffffff;
    /* k = 11 */
    lo = Math.imul(al9, bl2);
    mid = Math.imul(al9, bh2);
    mid = (mid + Math.imul(ah9, bl2)) | 0;
    hi = Math.imul(ah9, bh2);
    lo = (lo + Math.imul(al8, bl3)) | 0;
    mid = (mid + Math.imul(al8, bh3)) | 0;
    mid = (mid + Math.imul(ah8, bl3)) | 0;
    hi = (hi + Math.imul(ah8, bh3)) | 0;
    lo = (lo + Math.imul(al7, bl4)) | 0;
    mid = (mid + Math.imul(al7, bh4)) | 0;
    mid = (mid + Math.imul(ah7, bl4)) | 0;
    hi = (hi + Math.imul(ah7, bh4)) | 0;
    lo = (lo + Math.imul(al6, bl5)) | 0;
    mid = (mid + Math.imul(al6, bh5)) | 0;
    mid = (mid + Math.imul(ah6, bl5)) | 0;
    hi = (hi + Math.imul(ah6, bh5)) | 0;
    lo = (lo + Math.imul(al5, bl6)) | 0;
    mid = (mid + Math.imul(al5, bh6)) | 0;
    mid = (mid + Math.imul(ah5, bl6)) | 0;
    hi = (hi + Math.imul(ah5, bh6)) | 0;
    lo = (lo + Math.imul(al4, bl7)) | 0;
    mid = (mid + Math.imul(al4, bh7)) | 0;
    mid = (mid + Math.imul(ah4, bl7)) | 0;
    hi = (hi + Math.imul(ah4, bh7)) | 0;
    lo = (lo + Math.imul(al3, bl8)) | 0;
    mid = (mid + Math.imul(al3, bh8)) | 0;
    mid = (mid + Math.imul(ah3, bl8)) | 0;
    hi = (hi + Math.imul(ah3, bh8)) | 0;
    lo = (lo + Math.imul(al2, bl9)) | 0;
    mid = (mid + Math.imul(al2, bh9)) | 0;
    mid = (mid + Math.imul(ah2, bl9)) | 0;
    hi = (hi + Math.imul(ah2, bh9)) | 0;
    var w11 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w11 >>> 26)) | 0;
    w11 &= 0x3ffffff;
    /* k = 12 */
    lo = Math.imul(al9, bl3);
    mid = Math.imul(al9, bh3);
    mid = (mid + Math.imul(ah9, bl3)) | 0;
    hi = Math.imul(ah9, bh3);
    lo = (lo + Math.imul(al8, bl4)) | 0;
    mid = (mid + Math.imul(al8, bh4)) | 0;
    mid = (mid + Math.imul(ah8, bl4)) | 0;
    hi = (hi + Math.imul(ah8, bh4)) | 0;
    lo = (lo + Math.imul(al7, bl5)) | 0;
    mid = (mid + Math.imul(al7, bh5)) | 0;
    mid = (mid + Math.imul(ah7, bl5)) | 0;
    hi = (hi + Math.imul(ah7, bh5)) | 0;
    lo = (lo + Math.imul(al6, bl6)) | 0;
    mid = (mid + Math.imul(al6, bh6)) | 0;
    mid = (mid + Math.imul(ah6, bl6)) | 0;
    hi = (hi + Math.imul(ah6, bh6)) | 0;
    lo = (lo + Math.imul(al5, bl7)) | 0;
    mid = (mid + Math.imul(al5, bh7)) | 0;
    mid = (mid + Math.imul(ah5, bl7)) | 0;
    hi = (hi + Math.imul(ah5, bh7)) | 0;
    lo = (lo + Math.imul(al4, bl8)) | 0;
    mid = (mid + Math.imul(al4, bh8)) | 0;
    mid = (mid + Math.imul(ah4, bl8)) | 0;
    hi = (hi + Math.imul(ah4, bh8)) | 0;
    lo = (lo + Math.imul(al3, bl9)) | 0;
    mid = (mid + Math.imul(al3, bh9)) | 0;
    mid = (mid + Math.imul(ah3, bl9)) | 0;
    hi = (hi + Math.imul(ah3, bh9)) | 0;
    var w12 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w12 >>> 26)) | 0;
    w12 &= 0x3ffffff;
    /* k = 13 */
    lo = Math.imul(al9, bl4);
    mid = Math.imul(al9, bh4);
    mid = (mid + Math.imul(ah9, bl4)) | 0;
    hi = Math.imul(ah9, bh4);
    lo = (lo + Math.imul(al8, bl5)) | 0;
    mid = (mid + Math.imul(al8, bh5)) | 0;
    mid = (mid + Math.imul(ah8, bl5)) | 0;
    hi = (hi + Math.imul(ah8, bh5)) | 0;
    lo = (lo + Math.imul(al7, bl6)) | 0;
    mid = (mid + Math.imul(al7, bh6)) | 0;
    mid = (mid + Math.imul(ah7, bl6)) | 0;
    hi = (hi + Math.imul(ah7, bh6)) | 0;
    lo = (lo + Math.imul(al6, bl7)) | 0;
    mid = (mid + Math.imul(al6, bh7)) | 0;
    mid = (mid + Math.imul(ah6, bl7)) | 0;
    hi = (hi + Math.imul(ah6, bh7)) | 0;
    lo = (lo + Math.imul(al5, bl8)) | 0;
    mid = (mid + Math.imul(al5, bh8)) | 0;
    mid = (mid + Math.imul(ah5, bl8)) | 0;
    hi = (hi + Math.imul(ah5, bh8)) | 0;
    lo = (lo + Math.imul(al4, bl9)) | 0;
    mid = (mid + Math.imul(al4, bh9)) | 0;
    mid = (mid + Math.imul(ah4, bl9)) | 0;
    hi = (hi + Math.imul(ah4, bh9)) | 0;
    var w13 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w13 >>> 26)) | 0;
    w13 &= 0x3ffffff;
    /* k = 14 */
    lo = Math.imul(al9, bl5);
    mid = Math.imul(al9, bh5);
    mid = (mid + Math.imul(ah9, bl5)) | 0;
    hi = Math.imul(ah9, bh5);
    lo = (lo + Math.imul(al8, bl6)) | 0;
    mid = (mid + Math.imul(al8, bh6)) | 0;
    mid = (mid + Math.imul(ah8, bl6)) | 0;
    hi = (hi + Math.imul(ah8, bh6)) | 0;
    lo = (lo + Math.imul(al7, bl7)) | 0;
    mid = (mid + Math.imul(al7, bh7)) | 0;
    mid = (mid + Math.imul(ah7, bl7)) | 0;
    hi = (hi + Math.imul(ah7, bh7)) | 0;
    lo = (lo + Math.imul(al6, bl8)) | 0;
    mid = (mid + Math.imul(al6, bh8)) | 0;
    mid = (mid + Math.imul(ah6, bl8)) | 0;
    hi = (hi + Math.imul(ah6, bh8)) | 0;
    lo = (lo + Math.imul(al5, bl9)) | 0;
    mid = (mid + Math.imul(al5, bh9)) | 0;
    mid = (mid + Math.imul(ah5, bl9)) | 0;
    hi = (hi + Math.imul(ah5, bh9)) | 0;
    var w14 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w14 >>> 26)) | 0;
    w14 &= 0x3ffffff;
    /* k = 15 */
    lo = Math.imul(al9, bl6);
    mid = Math.imul(al9, bh6);
    mid = (mid + Math.imul(ah9, bl6)) | 0;
    hi = Math.imul(ah9, bh6);
    lo = (lo + Math.imul(al8, bl7)) | 0;
    mid = (mid + Math.imul(al8, bh7)) | 0;
    mid = (mid + Math.imul(ah8, bl7)) | 0;
    hi = (hi + Math.imul(ah8, bh7)) | 0;
    lo = (lo + Math.imul(al7, bl8)) | 0;
    mid = (mid + Math.imul(al7, bh8)) | 0;
    mid = (mid + Math.imul(ah7, bl8)) | 0;
    hi = (hi + Math.imul(ah7, bh8)) | 0;
    lo = (lo + Math.imul(al6, bl9)) | 0;
    mid = (mid + Math.imul(al6, bh9)) | 0;
    mid = (mid + Math.imul(ah6, bl9)) | 0;
    hi = (hi + Math.imul(ah6, bh9)) | 0;
    var w15 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w15 >>> 26)) | 0;
    w15 &= 0x3ffffff;
    /* k = 16 */
    lo = Math.imul(al9, bl7);
    mid = Math.imul(al9, bh7);
    mid = (mid + Math.imul(ah9, bl7)) | 0;
    hi = Math.imul(ah9, bh7);
    lo = (lo + Math.imul(al8, bl8)) | 0;
    mid = (mid + Math.imul(al8, bh8)) | 0;
    mid = (mid + Math.imul(ah8, bl8)) | 0;
    hi = (hi + Math.imul(ah8, bh8)) | 0;
    lo = (lo + Math.imul(al7, bl9)) | 0;
    mid = (mid + Math.imul(al7, bh9)) | 0;
    mid = (mid + Math.imul(ah7, bl9)) | 0;
    hi = (hi + Math.imul(ah7, bh9)) | 0;
    var w16 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w16 >>> 26)) | 0;
    w16 &= 0x3ffffff;
    /* k = 17 */
    lo = Math.imul(al9, bl8);
    mid = Math.imul(al9, bh8);
    mid = (mid + Math.imul(ah9, bl8)) | 0;
    hi = Math.imul(ah9, bh8);
    lo = (lo + Math.imul(al8, bl9)) | 0;
    mid = (mid + Math.imul(al8, bh9)) | 0;
    mid = (mid + Math.imul(ah8, bl9)) | 0;
    hi = (hi + Math.imul(ah8, bh9)) | 0;
    var w17 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w17 >>> 26)) | 0;
    w17 &= 0x3ffffff;
    /* k = 18 */
    lo = Math.imul(al9, bl9);
    mid = Math.imul(al9, bh9);
    mid = (mid + Math.imul(ah9, bl9)) | 0;
    hi = Math.imul(ah9, bh9);
    var w18 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
    c = (((hi + (mid >>> 13)) | 0) + (w18 >>> 26)) | 0;
    w18 &= 0x3ffffff;
    o[0] = w0;
    o[1] = w1;
    o[2] = w2;
    o[3] = w3;
    o[4] = w4;
    o[5] = w5;
    o[6] = w6;
    o[7] = w7;
    o[8] = w8;
    o[9] = w9;
    o[10] = w10;
    o[11] = w11;
    o[12] = w12;
    o[13] = w13;
    o[14] = w14;
    o[15] = w15;
    o[16] = w16;
    o[17] = w17;
    o[18] = w18;
    if (c !== 0) {
      o[19] = c;
      out.length++;
    }
    return out;
  };

  // Polyfill comb
  if (!Math.imul) {
    comb10MulTo = smallMulTo;
  }

  function bigMulTo (self, num, out) {
    out.negative = num.negative ^ self.negative;
    out.length = self.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 - self.length + 1); j <= maxJ; j++) {
        var i = k - j;
        var a = self.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();
  }

  function jumboMulTo (self, num, out) {
    var fftm = new FFTM();
    return fftm.mulp(self, num, out);
  }

  BN.prototype.mulTo = function mulTo (num, out) {
    var res;
    var len = this.length + num.length;
    if (this.length === 10 && num.length === 10) {
      res = comb10MulTo(this, num, out);
    } else if (len < 63) {
      res = smallMulTo(this, num, out);
    } else if (len < 1024) {
      res = bigMulTo(this, num, out);
    } else {
      res = jumboMulTo(this, num, out);
    }

    return res;
  };

  // Cooley-Tukey algorithm for FFT
  // slightly revisited to rely on looping instead of recursion

  function FFTM (x, y) {
    this.x = x;
    this.y = y;
  }

  FFTM.prototype.makeRBT = function makeRBT (N) {
    var t = new Array(N);
    var l = BN.prototype._countBits(N) - 1;
    for (var i = 0; i < N; i++) {
      t[i] = this.revBin(i, l, N);
    }

    return t;
  };

  // Returns binary-reversed representation of `x`
  FFTM.prototype.revBin = function revBin (x, l, N) {
    if (x === 0 || x === N - 1) return x;

    var rb = 0;
    for (var i = 0; i < l; i++) {
      rb |= (x & 1) << (l - i - 1);
      x >>= 1;
    }

    return rb;
  };

  // Performs "tweedling" phase, therefore 'emulating'
  // behaviour of the recursive algorithm
  FFTM.prototype.permute = function permute (rbt, rws, iws, rtws, itws, N) {
    for (var i = 0; i < N; i++) {
      rtws[i] = rws[rbt[i]];
      itws[i] = iws[rbt[i]];
    }
  };

  FFTM.prototype.transform = function transform (rws, iws, rtws, itws, N, rbt) {
    this.permute(rbt, rws, iws, rtws, itws, N);

    for (var s = 1; s < N; s <<= 1) {
      var l = s << 1;

      var rtwdf = Math.cos(2 * Math.PI / l);
      var itwdf = Math.sin(2 * Math.PI / l);

      for (var p = 0; p < N; p += l) {
        var rtwdf_ = rtwdf;
        var itwdf_ = itwdf;

        for (var j = 0; j < s; j++) {
          var re = rtws[p + j];
          var ie = itws[p + j];

          var ro = rtws[p + j + s];
          var io = itws[p + j + s];

          var rx = rtwdf_ * ro - itwdf_ * io;

          io = rtwdf_ * io + itwdf_ * ro;
          ro = rx;

          rtws[p + j] = re + ro;
          itws[p + j] = ie + io;

          rtws[p + j + s] = re - ro;
          itws[p + j + s] = ie - io;

          /* jshint maxdepth : false */
          if (j !== l) {
            rx = rtwdf * rtwdf_ - itwdf * itwdf_;

            itwdf_ = rtwdf * itwdf_ + itwdf * rtwdf_;
            rtwdf_ = rx;
          }
        }
      }
    }
  };

  FFTM.prototype.guessLen13b = function guessLen13b (n, m) {
    var N = Math.max(m, n) | 1;
    var odd = N & 1;
    var i = 0;
    for (N = N / 2 | 0; N; N = N >>> 1) {
      i++;
    }

    return 1 << i + 1 + odd;
  };

  FFTM.prototype.conjugate = function conjugate (rws, iws, N) {
    if (N <= 1) return;

    for (var i = 0; i < N / 2; i++) {
      var t = rws[i];

      rws[i] = rws[N - i - 1];
      rws[N - i - 1] = t;

      t = iws[i];

      iws[i] = -iws[N - i - 1];
      iws[N - i - 1] = -t;
    }
  };

  FFTM.prototype.normalize13b = function normalize13b (ws, N) {
    var carry = 0;
    for (var i = 0; i < N / 2; i++) {
      var w = Math.round(ws[2 * i + 1] / N) * 0x2000 +
        Math.round(ws[2 * i] / N) +
        carry;

      ws[i] = w & 0x3ffffff;

      if (w < 0x4000000) {
        carry = 0;
      } else {
        carry = w / 0x4000000 | 0;
      }
    }

    return ws;
  };

  FFTM.prototype.convert13b = function convert13b (ws, len, rws, N) {
    var carry = 0;
    for (var i = 0; i < len; i++) {
      carry = carry + (ws[i] | 0);

      rws[2 * i] = carry & 0x1fff; carry = carry >>> 13;
      rws[2 * i + 1] = carry & 0x1fff; carry = carry >>> 13;
    }

    // Pad with zeroes
    for (i = 2 * len; i < N; ++i) {
      rws[i] = 0;
    }

    assert(carry === 0);
    assert((carry & ~0x1fff) === 0);
  };

  FFTM.prototype.stub = function stub (N) {
    var ph = new Array(N);
    for (var i = 0; i < N; i++) {
      ph[i] = 0;
    }

    return ph;
  };

  FFTM.prototype.mulp = function mulp (x, y, out) {
    var N = 2 * this.guessLen13b(x.length, y.length);

    var rbt = this.makeRBT(N);

    var _ = this.stub(N);

    var rws = new Array(N);
    var rwst = new Array(N);
    var iwst = new Array(N);

    var nrws = new Array(N);
    var nrwst = new Array(N);
    var niwst = new Array(N);

    var rmws = out.words;
    rmws.length = N;

    this.convert13b(x.words, x.length, rws, N);
    this.convert13b(y.words, y.length, nrws, N);

    this.transform(rws, _, rwst, iwst, N, rbt);
    this.transform(nrws, _, nrwst, niwst, N, rbt);

    for (var i = 0; i < N; i++) {
      var rx = rwst[i] * nrwst[i] - iwst[i] * niwst[i];
      iwst[i] = rwst[i] * niwst[i] + iwst[i] * nrwst[i];
      rwst[i] = rx;
    }

    this.conjugate(rwst, iwst, N);
    this.transform(rwst, iwst, rmws, _, N, rbt);
    this.conjugate(rmws, _, N);
    this.normalize13b(rmws, N);

    out.negative = x.negative ^ y.negative;
    out.length = x.length + y.length;
    return out.strip();
  };

  // 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);
  };

  // Multiply employing FFT
  BN.prototype.mulf = function mulf (num) {
    var out = new BN(null);
    out.words = new Array(this.length + num.length);
    return jumboMulTo(this, num, out);
  };

  // In-place Multiplication
  BN.prototype.imul = function imul (num) {
    return this.clone().mulTo(num, this);
  };

  BN.prototype.imuln = function imuln (num) {
    assert(typeof num === 'number');
    assert(num < 0x4000000);

    // Carry
    var carry = 0;
    for (var i = 0; i < this.length; i++) {
      var w = (this.words[i] | 0) * 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;
  };

  BN.prototype.muln = function muln (num) {
    return this.clone().imuln(num);
  };

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

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

  // Math.pow(`this`, `num`)
  BN.prototype.pow = function pow (num) {
    var w = toBitArray(num);
    if (w.length === 0) return new BN(1);

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

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

        res = res.mul(q);
      }
    }

    return res;
  };

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

    if (r !== 0) {
      var carry = 0;

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

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

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

      for (i = 0; i < s; i++) {
        this.words[i] = 0;
      }

      this.length += s;
    }

    return this.strip();
  };

  BN.prototype.ishln = function ishln (bits) {
    // TODO(indutny): implement me
    assert(this.negative === 0);
    return this.iushln(bits);
  };

  // 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.iushrn = function iushrn (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 (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 (i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) {
      var word = this.words[i] | 0;
      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;
    }

    return this.strip();
  };

  BN.prototype.ishrn = function ishrn (bits, hint, extended) {
    // TODO(indutny): implement me
    assert(this.negative === 0);
    return this.iushrn(bits, hint, extended);
  };

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

  BN.prototype.ushln = function ushln (bits) {
    return this.clone().iushln(bits);
  };

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

  BN.prototype.ushrn = function ushrn (bits) {
    return this.clone().iushrn(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.negative === 0, 'imaskn works only with positive numbers');

    if (this.length <= s) {
      return this;
    }

    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');
    assert(num < 0x4000000);
    if (num < 0) return this.isubn(-num);

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

      this.negative = 0;
      this.isubn(num);
      this.negative = 1;
      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');
    assert(num < 0x4000000);
    if (num < 0) return this.iaddn(-num);

    if (this.negative !== 0) {
      this.negative = 0;
      this.iaddn(num);
      this.negative = 1;
      return this;
    }

    this.words[0] -= num;

    if (this.length === 1 && this.words[0] < 0) {
      this.words[0] = -this.words[0];
      this.negative = 1;
    } else {
      // 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.negative = 0;

    return this;
  };

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

  BN.prototype._ishlnsubmul = function _ishlnsubmul (num, mul, shift) {
    var len = num.length + shift;
    var i;

    this._expand(len);

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

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

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

    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] | 0;
    var bhiBits = this._countBits(bhi);
    shift = 26 - bhiBits;
    if (shift !== 0) {
      b = b.ushln(shift);
      a.iushln(shift);
      bhi = b.words[b.length - 1] | 0;
    }

    // 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.negative === 0) {
      a = diff;
      if (q) {
        q.words[m] = 1;
      }
    }

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

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

      a._ishlnsubmul(b, qj, j);
      while (a.negative !== 0) {
        qj--;
        a.negative = 0;
        a._ishlnsubmul(b, 1, j);
        if (!a.isZero()) {
          a.negative ^= 1;
        }
      }
      if (q) {
        q.words[j] = qj;
      }
    }
    if (q) {
      q.strip();
    }
    a.strip();

    // Denormalize
    if (mode !== 'div' && shift !== 0) {
      a.iushrn(shift);
    }

    return {
      div: q || null,
      mod: a
    };
  };

  // NOTE: 1) `mode` can be set to `mod` to request mod only,
  //       to `div` to request div only, or be absent to
  //       request both div & mod
  //       2) `positive` is true if unsigned mod is requested
  BN.prototype.divmod = function divmod (num, mode, positive) {
    assert(!num.isZero());

    if (this.isZero()) {
      return {
        div: new BN(0),
        mod: new BN(0)
      };
    }

    var div, mod, res;
    if (this.negative !== 0 && num.negative === 0) {
      res = this.neg().divmod(num, mode);

      if (mode !== 'mod') {
        div = res.div.neg();
      }

      if (mode !== 'div') {
        mod = res.mod.neg();
        if (positive && mod.negative !== 0) {
          mod.iadd(num);
        }
      }

      return {
        div: div,
        mod: mod
      };
    }

    if (this.negative === 0 && num.negative !== 0) {
      res = this.divmod(num.neg(), mode);

      if (mode !== 'mod') {
        div = res.div.neg();
      }

      return {
        div: div,
        mod: res.mod
      };
    }

    if ((this.negative & num.negative) !== 0) {
      res = this.neg().divmod(num.neg(), mode);

      if (mode !== 'div') {
        mod = res.mod.neg();
        if (positive && mod.negative !== 0) {
          mod.isub(num);
        }
      }

      return {
        div: res.div,
        mod: mod
      };
    }

    // 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
        };
      }

      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', false).div;
  };

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

  BN.prototype.umod = function umod (num) {
    return this.divmod(num, 'mod', true).mod;
  };

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

    // Fast case - exact division
    if (dm.mod.isZero()) return dm.div;

    var mod = dm.div.negative !== 0 ? dm.mod.isub(num) : dm.mod;

    var half = num.ushrn(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.negative !== 0 ? 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] | 0)) % 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] | 0) + 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.negative === 0);
    assert(!p.isZero());

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

    if (x.negative !== 0) {
      x = x.umod(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.iushrn(1);
      y.iushrn(1);
      ++g;
    }

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

    while (!x.isZero()) {
      for (var i = 0, im = 1; (x.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
      if (i > 0) {
        x.iushrn(i);
        while (i-- > 0) {
          if (A.isOdd() || B.isOdd()) {
            A.iadd(yp);
            B.isub(xp);
          }

          A.iushrn(1);
          B.iushrn(1);
        }
      }

      for (var j = 0, jm = 1; (y.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
      if (j > 0) {
        y.iushrn(j);
        while (j-- > 0) {
          if (C.isOdd() || D.isOdd()) {
            C.iadd(yp);
            D.isub(xp);
          }

          C.iushrn(1);
          D.iushrn(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.iushln(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.negative === 0);
    assert(!p.isZero());

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

    if (a.negative !== 0) {
      a = a.umod(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) {
      for (var i = 0, im = 1; (a.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
      if (i > 0) {
        a.iushrn(i);
        while (i-- > 0) {
          if (x1.isOdd()) {
            x1.iadd(delta);
          }

          x1.iushrn(1);
        }
      }

      for (var j = 0, jm = 1; (b.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
      if (j > 0) {
        b.iushrn(j);
        while (j-- > 0) {
          if (x2.isOdd()) {
            x2.iadd(delta);
          }

          x2.iushrn(1);
        }
      }

      if (a.cmp(b) >= 0) {
        a.isub(b);
        x1.isub(x2);
      } else {
        b.isub(a);
        x2.isub(x1);
      }
    }

    var res;
    if (a.cmpn(1) === 0) {
      res = x1;
    } else {
      res = x2;
    }

    if (res.cmpn(0) < 0) {
      res.iadd(p);
    }

    return res;
  };

  BN.prototype.gcd = function gcd (num) {
    if (this.isZero()) return num.abs();
    if (num.isZero()) return this.abs();

    var a = this.clone();
    var b = num.clone();
    a.negative = 0;
    b.negative = 0;

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

    do {
      while (a.isEven()) {
        a.iushrn(1);
      }
      while (b.isEven()) {
        b.iushrn(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.iushln(shift);
  };

  // Invert number in the field F(num)
  BN.prototype.invm = function invm (num) {
    return this.egcd(num).a.umod(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) {
      this._expand(s + 1);
      this.words[s] |= q;
      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] | 0;
      w += carry;
      carry = w >>> 26;
      w &= 0x3ffffff;
      this.words[i] = w;
    }
    if (carry !== 0) {
      this.words[i] = carry;
      this.length++;
    }
    return this;
  };

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

  BN.prototype.cmpn = function cmpn (num) {
    var negative = num < 0;

    if (this.negative !== 0 && !negative) return -1;
    if (this.negative === 0 && negative) return 1;

    this.strip();

    var res;
    if (this.length > 1) {
      res = 1;
    } else {
      if (negative) {
        num = -num;
      }

      assert(num <= 0x3ffffff, 'Number is too big');

      var w = this.words[0] | 0;
      res = w === num ? 0 : w < num ? -1 : 1;
    }
    if (this.negative !== 0) return -res | 0;
    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.negative !== 0 && num.negative === 0) return -1;
    if (this.negative === 0 && num.negative !== 0) return 1;

    var res = this.ucmp(num);
    if (this.negative !== 0) return -res | 0;
    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;
    if (this.length < num.length) return -1;

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

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

  BN.prototype.gtn = function gtn (num) {
    return this.cmpn(num) === 1;
  };

  BN.prototype.gt = function gt (num) {
    return this.cmp(num) === 1;
  };

  BN.prototype.gten = function gten (num) {
    return this.cmpn(num) >= 0;
  };

  BN.prototype.gte = function gte (num) {
    return this.cmp(num) >= 0;
  };

  BN.prototype.ltn = function ltn (num) {
    return this.cmpn(num) === -1;
  };

  BN.prototype.lt = function lt (num) {
    return this.cmp(num) === -1;
  };

  BN.prototype.lten = function lten (num) {
    return this.cmpn(num) <= 0;
  };

  BN.prototype.lte = function lte (num) {
    return this.cmp(num) <= 0;
  };

  BN.prototype.eqn = function eqn (num) {
    return this.cmpn(num) === 0;
  };

  BN.prototype.eq = function eq (num) {
    return this.cmp(num) === 0;
  };

  //
  // 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.negative === 0, '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).iushln(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 {
      if (r.strip !== undefined) {
        // r is BN v4 instance
        r.strip();
      } else {
        // r is BN v5 instance
        r._strip();
      }
    }

    return r;
  };

  MPrime.prototype.split = function split (input, out) {
    input.iushrn(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 (i = 10; i < input.length; i++) {
      var next = input.words[i] | 0;
      input.words[i - 10] = ((next & mask) << 4) | (prev >>> 22);
      prev = next;
    }
    prev >>>= 22;
    input.words[i - 10] = prev;
    if (prev === 0 && input.length > 10) {
      input.length -= 10;
    } else {
      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 lo = 0;
    for (var i = 0; i < num.length; i++) {
      var w = num.words[i] | 0;
      lo += w * 0x3d1;
      num.words[i] = lo & 0x3ffffff;
      lo = w * 0x40 + ((lo / 0x4000000) | 0);
    }

    // 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] | 0) * 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 {
      assert(m.gtn(1), 'modulus must be greater than 1');
      this.m = m;
      this.prime = null;
    }
  }

  Red.prototype._verify1 = function _verify1 (a) {
    assert(a.negative === 0, 'red works only with positives');
    assert(a.red, 'red works only with red numbers');
  };

  Red.prototype._verify2 = function _verify2 (a, b) {
    assert((a.negative | b.negative) === 0, '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.umod(this.m)._forceRed(this);
  };

  Red.prototype.neg = function neg (a) {
    if (a.isZero()) {
      return a.clone();
    }

    return this.m.sub(a)._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.ushln(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.clone());
  };

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

  Red.prototype.sqrt = function sqrt (a) {
    if (a.isZero()) 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)).iushrn(2);
      return this.pow(a, pow);
    }

    // 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.isZero() && q.andln(1) === 0) {
      s++;
      q.iushrn(1);
    }
    assert(!q.isZero());

    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).iushrn(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).iushrn(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).iushln(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.negative !== 0) {
      inv.negative = 0;
      return this.imod(inv).redNeg();
    } else {
      return this.imod(inv);
    }
  };

  Red.prototype.pow = function pow (a, num) {
    if (num.isZero()) return new BN(1).toRed(this);
    if (num.cmpn(1) === 0) return a.clone();

    var windowSize = 4;
    var wnd = new Array(1 << windowSize);
    wnd[0] = new BN(1).toRed(this);
    wnd[1] = a;
    for (var i = 2; i < wnd.length; i++) {
      wnd[i] = this.mul(wnd[i - 1], a);
    }

    var res = wnd[0];
    var current = 0;
    var currentLen = 0;
    var start = num.bitLength() % 26;
    if (start === 0) {
      start = 26;
    }

    for (i = num.length - 1; i >= 0; i--) {
      var word = num.words[i];
      for (var j = start - 1; j >= 0; j--) {
        var bit = (word >> j) & 1;
        if (res !== wnd[0]) {
          res = this.sqr(res);
        }

        if (bit === 0 && current === 0) {
          currentLen = 0;
          continue;
        }

        current <<= 1;
        current |= bit;
        currentLen++;
        if (currentLen !== windowSize && (i !== 0 || j !== 0)) continue;

        res = this.mul(res, wnd[current]);
        currentLen = 0;
        current = 0;
      }
      start = 26;
    }

    return res;
  };

  Red.prototype.convertTo = function convertTo (num) {
    var r = num.umod(this.m);

    return r === num ? r.clone() : r;
  };

  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).iushln(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 = this.minv.umod(this.r);
    this.minv = this.r.sub(this.minv);
  }
  inherits(Mont, Red);

  Mont.prototype.convertTo = function convertTo (num) {
    return this.imod(num.ushln(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.isZero() || b.isZero()) {
      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).iushrn(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.isZero() || b.isZero()) 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).iushrn(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);

},{"buffer":18}],17:[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);
};

// Emulate crypto API using randy
Rand.prototype._rand = function _rand(n) {
  if (this.rand.getBytes)
    return this.rand.getBytes(n);

  var res = new Uint8Array(n);
  for (var i = 0; i < res.length; i++)
    res[i] = this.rand.getByte();
  return res;
};

if (typeof self === 'object') {
  if (self.crypto && self.crypto.getRandomValues) {
    // Modern browsers
    Rand.prototype._rand = function _rand(n) {
      var arr = new Uint8Array(n);
      self.crypto.getRandomValues(arr);
      return arr;
    };
  } else if (self.msCrypto && self.msCrypto.getRandomValues) {
    // IE
    Rand.prototype._rand = function _rand(n) {
      var arr = new Uint8Array(n);
      self.msCrypto.getRandomValues(arr);
      return arr;
    };

  // Safari's WebWorkers do not have `crypto`
  } else if (typeof window === 'object') {
    // Old junk
    Rand.prototype._rand = function() {
      throw new Error('Not implemented yet');
    };
  }
} else {
  // Node.js or Web worker with no crypto support
  try {
    var crypto = require('crypto');
    if (typeof crypto.randomBytes !== 'function')
      throw new Error('Not supported');

    Rand.prototype._rand = function _rand(n) {
      return crypto.randomBytes(n);
    };
  } catch (e) {
  }
}

},{"crypto":18}],18:[function(require,module,exports){

},{}],19:[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":20,"./hash/hmac":21,"./hash/ripemd":22,"./hash/sha":23,"./hash/utils":30}],20:[function(require,module,exports){
'use strict';

var utils = require('./utils');
var assert = require('minimalistic-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 (t = 8; t < this.padLength; t++)
      res[i++] = 0;
  }

  return res;
};

},{"./utils":30,"minimalistic-assert":33}],21:[function(require,module,exports){
'use strict';

var utils = require('./utils');
var assert = require('minimalistic-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 (i = 0; i < key.length; i++)
    key[i] ^= 0x36;
  this.inner = new this.Hash().update(key);

  // 0x36 ^ 0x5c = 0x6a
  for (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);
};

},{"./utils":30,"minimalistic-assert":33}],22:[function(require,module,exports){
'use strict';

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

var rotl32 = utils.rotl32;
var sum32 = utils.sum32;
var sum32_3 = utils.sum32_3;
var sum32_4 = utils.sum32_4;
var BlockHash = 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
];

},{"./common":20,"./utils":30}],23:[function(require,module,exports){
'use strict';

exports.sha1 = require('./sha/1');
exports.sha224 = require('./sha/224');
exports.sha256 = require('./sha/256');
exports.sha384 = require('./sha/384');
exports.sha512 = require('./sha/512');

},{"./sha/1":24,"./sha/224":25,"./sha/256":26,"./sha/384":27,"./sha/512":28}],24:[function(require,module,exports){
'use strict';

var utils = require('../utils');
var common = require('../common');
var shaCommon = require('./common');

var rotl32 = utils.rotl32;
var sum32 = utils.sum32;
var sum32_5 = utils.sum32_5;
var ft_1 = shaCommon.ft_1;
var BlockHash = common.BlockHash;

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

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);
module.exports = 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 (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');
};

},{"../common":20,"../utils":30,"./common":29}],25:[function(require,module,exports){
'use strict';

var utils = require('../utils');
var SHA256 = require('./256');

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);
module.exports = 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');
};


},{"../utils":30,"./256":26}],26:[function(require,module,exports){
'use strict';

var utils = require('../utils');
var common = require('../common');
var shaCommon = require('./common');
var assert = require('minimalistic-assert');

var sum32 = utils.sum32;
var sum32_4 = utils.sum32_4;
var sum32_5 = utils.sum32_5;
var ch32 = shaCommon.ch32;
var maj32 = shaCommon.maj32;
var s0_256 = shaCommon.s0_256;
var s1_256 = shaCommon.s1_256;
var g0_256 = shaCommon.g0_256;
var g1_256 = shaCommon.g1_256;

var BlockHash = 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
];

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);
module.exports = 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 (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');
};

},{"../common":20,"../utils":30,"./common":29,"minimalistic-assert":33}],27:[function(require,module,exports){
'use strict';

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

var SHA512 = require('./512');

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);
module.exports = 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');
};

},{"../utils":30,"./512":28}],28:[function(require,module,exports){
'use strict';

var utils = require('../utils');
var common = require('../common');
var assert = require('minimalistic-assert');

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 = common.BlockHash;

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
];

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);
module.exports = 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);

    c0_hi = s0_512_hi(ah, al);
    c0_lo = s0_512_lo(ah, al);
    c1_hi = maj64_hi(ah, al, bh, bl, ch, cl);
    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 ch64_hi(xh, xl, yh, yl, zh) {
  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) {
  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;
}

},{"../common":20,"../utils":30,"minimalistic-assert":33}],29:[function(require,module,exports){
'use strict';

var utils = require('../utils');
var rotr32 = utils.rotr32;

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);
}
exports.ft_1 = ft_1;

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

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

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

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

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

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

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

},{"../utils":30}],30:[function(require,module,exports){
'use strict';

var assert = require('minimalistic-assert');
var inherits = require('inherits');

exports.inherits = inherits;

function isSurrogatePair(msg, i) {
  if ((msg.charCodeAt(i) & 0xFC00) !== 0xD800) {
    return false;
  }
  if (i < 0 || i + 1 >= msg.length) {
    return false;
  }
  return (msg.charCodeAt(i + 1) & 0xFC00) === 0xDC00;
}

function toArray(msg, enc) {
  if (Array.isArray(msg))
    return msg.slice();
  if (!msg)
    return [];
  var res = [];
  if (typeof msg === 'string') {
    if (!enc) {
      // Inspired by stringToUtf8ByteArray() in closure-library by Google
      // https://github.com/google/closure-library/blob/8598d87242af59aac233270742c8984e2b2bdbe0/closure/goog/crypt/crypt.js#L117-L143
      // Apache License 2.0
      // https://github.com/google/closure-library/blob/master/LICENSE
      var p = 0;
      for (var i = 0; i < msg.length; i++) {
        var c = msg.charCodeAt(i);
        if (c < 128) {
          res[p++] = c;
        } else if (c < 2048) {
          res[p++] = (c >> 6) | 192;
          res[p++] = (c & 63) | 128;
        } else if (isSurrogatePair(msg, i)) {
          c = 0x10000 + ((c & 0x03FF) << 10) + (msg.charCodeAt(++i) & 0x03FF);
          res[p++] = (c >> 18) | 240;
          res[p++] = ((c >> 12) & 63) | 128;
          res[p++] = ((c >> 6) & 63) | 128;
          res[p++] = (c & 63) | 128;
        } else {
          res[p++] = (c >> 12) | 224;
          res[p++] = ((c >> 6) & 63) | 128;
          res[p++] = (c & 63) | 128;
        }
      }
    } else if (enc === 'hex') {
      msg = msg.replace(/[^a-z0-9]+/ig, '');
      if (msg.length % 2 !== 0)
        msg = '0' + msg;
      for (i = 0; i < msg.length; i += 2)
        res.push(parseInt(msg[i] + msg[i + 1], 16));
    }
  } else {
    for (i = 0; i < msg.length; i++)
      res[i] = msg[i] | 0;
  }
  return res;
}
exports.toArray = toArray;

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

function htonl(w) {
  var res = (w >>> 24) |
            ((w >>> 8) & 0xff00) |
            ((w << 8) & 0xff0000) |
            ((w & 0xff) << 24);
  return res >>> 0;
}
exports.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;
}
exports.toHex32 = toHex32;

function zero2(word) {
  if (word.length === 1)
    return '0' + word;
  else
    return word;
}
exports.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;
}
exports.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;
}
exports.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;
}
exports.split32 = split32;

function rotr32(w, b) {
  return (w >>> b) | (w << (32 - b));
}
exports.rotr32 = rotr32;

function rotl32(w, b) {
  return (w << b) | (w >>> (32 - b));
}
exports.rotl32 = rotl32;

function sum32(a, b) {
  return (a + b) >>> 0;
}
exports.sum32 = sum32;

function sum32_3(a, b, c) {
  return (a + b + c) >>> 0;
}
exports.sum32_3 = sum32_3;

function sum32_4(a, b, c, d) {
  return (a + b + c + d) >>> 0;
}
exports.sum32_4 = sum32_4;

function sum32_5(a, b, c, d, e) {
  return (a + b + c + d + e) >>> 0;
}
exports.sum32_5 = sum32_5;

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":32,"minimalistic-assert":33}],31:[function(require,module,exports){
'use strict';

var hash = require('hash.js');
var utils = require('minimalistic-crypto-utils');
var assert = require('minimalistic-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 || 'hex');
  var nonce = utils.toArray(options.nonce, options.nonceEnc || 'hex');
  var pers = utils.toArray(options.pers, options.persEnc || 'hex');
  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.toArray(entropy, entropyEnc);
  add = utils.toArray(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 || 'hex');
    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);
};

},{"hash.js":19,"minimalistic-assert":33,"minimalistic-crypto-utils":34}],32:[function(require,module,exports){
if (typeof Object.create === 'function') {
  // implementation from standard node.js 'util' module
  module.exports = function inherits(ctor, superCtor) {
    if (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) {
    if (superCtor) {
      ctor.super_ = superCtor
      var TempCtor = function () {}
      TempCtor.prototype = superCtor.prototype
      ctor.prototype = new TempCtor()
      ctor.prototype.constructor = ctor
    }
  }
}

},{}],33:[function(require,module,exports){
module.exports = assert;

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

assert.equal = function assertEqual(l, r, msg) {
  if (l != r)
    throw new Error(msg || ('Assertion failed: ' + l + ' != ' + r));
};

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

var utils = exports;

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 === '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++) {
      var c = msg.charCodeAt(i);
      var hi = c >> 8;
      var lo = c & 0xff;
      if (hi)
        res.push(hi, lo);
      else
        res.push(lo);
    }
  }
  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;
};

},{}],35:[function(require,module,exports){
module.exports={
  "name": "elliptic",
  "version": "6.5.4",
  "description": "EC cryptography",
  "main": "lib/elliptic.js",
  "files": [
    "lib"
  ],
  "scripts": {
    "lint": "eslint lib test",
    "lint:fix": "npm run lint -- --fix",
    "unit": "istanbul test _mocha --reporter=spec test/index.js",
    "test": "npm run lint && npm run unit",
    "version": "grunt dist && git add dist/"
  },
  "repository": {
    "type": "git",
    "url": "git@github.com:indutny/elliptic"
  },
  "keywords": [
    "EC",
    "Elliptic",
    "curve",
    "Cryptography"
  ],
  "author": "Fedor Indutny <fedor@indutny.com>",
  "license": "MIT",
  "bugs": {
    "url": "https://github.com/indutny/elliptic/issues"
  },
  "homepage": "https://github.com/indutny/elliptic",
  "devDependencies": {
    "brfs": "^2.0.2",
    "coveralls": "^3.1.0",
    "eslint": "^7.6.0",
    "grunt": "^1.2.1",
    "grunt-browserify": "^5.3.0",
    "grunt-cli": "^1.3.2",
    "grunt-contrib-connect": "^3.0.0",
    "grunt-contrib-copy": "^1.0.0",
    "grunt-contrib-uglify": "^5.0.0",
    "grunt-mocha-istanbul": "^5.0.2",
    "grunt-saucelabs": "^9.0.1",
    "istanbul": "^0.4.5",
    "mocha": "^8.0.1"
  },
  "dependencies": {
    "bn.js": "^4.11.9",
    "brorand": "^1.1.0",
    "hash.js": "^1.0.0",
    "hmac-drbg": "^1.0.1",
    "inherits": "^2.0.4",
    "minimalistic-assert": "^1.0.1",
    "minimalistic-crypto-utils": "^1.0.1"
  }
}

},{}]},{},[1])(1)
});