(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, bitLength) {
      var byteLength;
      if (BN.isBN(msg) || typeof msg === 'number') {
        msg = new BN(msg, 16);
        byteLength = msg.byteLength();
      } else if (typeof msg === 'object') {
        // BN assumes an array-like input and asserts length
        byteLength = msg.length;
        msg = new BN(msg, 16);
      } else {
        // BN converts the value to string
        var str = msg.toString();
        // HEX encoding
        byteLength = (str.length + 1) >>> 1;
        msg = new BN(str, 16);
      }
      // Allow overriding
      if (typeof bitLength !== 'number') {
        bitLength = byteLength * 8;
      }
      var delta = bitLength - 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 = {};
    
      if (typeof msg !== 'string' && typeof msg !== 'number' && !BN.isBN(msg)) {
        assert(typeof msg === 'object' && msg && typeof msg.length === 'number',
          'Expected message to be an array-like, a hex string, or a BN instance');
        assert((msg.length >>> 0) === msg.length); // non-negative 32-bit integer
        for (var i = 0; i < msg.length; i++) assert((msg[i] & 255) === msg[i]);
      }
    
      key = this.keyFromPrivate(key, enc);
      msg = this._truncateToN(msg, false, options.msgBitLength);
    
      // Would fail further checks, but let's make the error message clear
      assert(!msg.isNeg(), 'Can not sign a negative message');
    
      // 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);
    
      // Recheck nonce to be bijective to msg
      assert((new BN(nonce)).eq(msg), 'Can not sign message');
    
      // 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, options) {
      if (!options)
        options = {};
    
      msg = this._truncateToN(msg, false, options.msgBitLength);
      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, options) {
      return this.ec.verify(msg, signature, this, undefined, options);
    };
    
    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;
      }
    
      if(buf[p.place] === 0x00) {
        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;
      }
      if ((data[p.place] & 128) !== 0) {
        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;
      }
      if ((data[p.place] & 128) !== 0) {
        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);
      if (sig.S().gte(sig.eddsa.curve.n) || sig.S().isNeg()) {
        return false;
      }
      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)) {
        assert(sig.length === eddsa.encodingLength * 2, 'Signature has invalid size');
        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',
          ],
          [
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            '893fb578951ad2537f718f2eacbfbbbb82314eef7880cfe917e735d9699a84c3',
          ],
          [
            'd895626548b65b81e264c7637c972877d1d72e5f3a925014372e9f6588f6c14b',
            'febfaa38f2bc7eae728ec60818c340eb03428d632bb067e179363ed75d7d991f',
          ],
          [
            'b8da94032a957518eb0f6433571e8761ceffc73693e84edd49150a564f676e03',
            '2804dfa44805a1e4d7c99cc9762808b092cc584d95ff3b511488e4e74efdf6e7',
          ],
          [
            'e80fea14441fb33a7d8adab9475d7fab2019effb5156a792f1a11778e3c0df5d',
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          [
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          ],
          [
            '90ad85b389d6b936463f9d0512678de208cc330b11307fffab7ac63e3fb04ed4',
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          [
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          [
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          [
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          [
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          [
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          [
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          ],
          [
            '9c3919a84a474870faed8a9c1cc66021523489054d7f0308cbfc99c8ac1f98cd',
            'ddb84f0f4a4ddd57584f044bf260e641905326f76c64c8e6be7e5e03d4fc599d',
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          [
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            '9a1af0b26a6a4807add9a2daf71df262465152bc3ee24c65e899be932385a2a8',
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          [
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            '40a6bf20e76640b2c92b97afe58cd82c432e10a7f514d9f3ee8be11ae1b28ec8',
          ],
          [
            '7778a78c28dec3e30a05fe9629de8c38bb30d1f5cf9a3a208f763889be58ad71',
            '34626d9ab5a5b22ff7098e12f2ff580087b38411ff24ac563b513fc1fd9f43ac',
          ],
          [
            '928955ee637a84463729fd30e7afd2ed5f96274e5ad7e5cb09eda9c06d903ac',
            'c25621003d3f42a827b78a13093a95eeac3d26efa8a8d83fc5180e935bcd091f',
          ],
          [
            '85d0fef3ec6db109399064f3a0e3b2855645b4a907ad354527aae75163d82751',
            '1f03648413a38c0be29d496e582cf5663e8751e96877331582c237a24eb1f962',
          ],
          [
            'ff2b0dce97eece97c1c9b6041798b85dfdfb6d8882da20308f5404824526087e',
            '493d13fef524ba188af4c4dc54d07936c7b7ed6fb90e2ceb2c951e01f0c29907',
          ],
          [
            '827fbbe4b1e880ea9ed2b2e6301b212b57f1ee148cd6dd28780e5e2cf856e241',
            'c60f9c923c727b0b71bef2c67d1d12687ff7a63186903166d605b68baec293ec',
          ],
          [
            'eaa649f21f51bdbae7be4ae34ce6e5217a58fdce7f47f9aa7f3b58fa2120e2b3',
            'be3279ed5bbbb03ac69a80f89879aa5a01a6b965f13f7e59d47a5305ba5ad93d',
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            'ee163026e9fd6fe017c38f06a5be6fc125424b371ce2708e7bf4491691e5764a',
            '1acb250f255dd61c43d94ccc670d0f58f49ae3fa15b96623e5430da0ad6c62b2',
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            'b268f5ef9ad51e4d78de3a750c2dc89b1e626d43505867999932e5db33af3d80',
            '5f310d4b3c99b9ebb19f77d41c1dee018cf0d34fd4191614003e945a1216e423',
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          [
            '32b78c7de9ee512a72895be6b9cbefa6e2f3c4ccce445c96b9f2c81e2778ad58',
            'ee1849f513df71e32efc3896ee28260c73bb80547ae2275ba497237794c8753c',
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            'e2cb74fddc8e9fbcd076eef2a7c72b0ce37d50f08269dfc074b581550547a4f7',
            'd3aa2ed71c9dd2247a62df062736eb0baddea9e36122d2be8641abcb005cc4a4',
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            '8438447566d4d7bedadc299496ab357426009a35f235cb141be0d99cd10ae3a8',
            'c4e1020916980a4da5d01ac5e6ad330734ef0d7906631c4f2390426b2edd791f',
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          [
            '4162d488b89402039b584c6fc6c308870587d9c46f660b878ab65c82c711d67e',
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            '3fad3fa84caf0f34f0f89bfd2dcf54fc175d767aec3e50684f3ba4a4bf5f683d',
            'cd1bc7cb6cc407bb2f0ca647c718a730cf71872e7d0d2a53fa20efcdfe61826',
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          [
            '674f2600a3007a00568c1a7ce05d0816c1fb84bf1370798f1c69532faeb1a86b',
            '299d21f9413f33b3edf43b257004580b70db57da0b182259e09eecc69e0d38a5',
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          [
            'd32f4da54ade74abb81b815ad1fb3b263d82d6c692714bcff87d29bd5ee9f08f',
            'f9429e738b8e53b968e99016c059707782e14f4535359d582fc416910b3eea87',
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            '30e4e670435385556e593657135845d36fbb6931f72b08cb1ed954f1e3ce3ff6',
            '462f9bce619898638499350113bbc9b10a878d35da70740dc695a559eb88db7b',
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          [
            'be2062003c51cc3004682904330e4dee7f3dcd10b01e580bf1971b04d4cad297',
            '62188bc49d61e5428573d48a74e1c655b1c61090905682a0d5558ed72dccb9bc',
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            '7c10dfb164c3425f5c71a3f9d7992038f1065224f72bb9d1d902a6d13037b47c',
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            'ab8c1e086d04e813744a655b2df8d5f83b3cdc6faa3088c1d3aea1454e3a1d5f',
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            '712fcdd1b9053f09003a3481fa7762e9ffd7c8ef35a38509e2fbf2629008373',
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          [
            '176e26989a43c9cfeba4029c202538c28172e566e3c4fce7322857f3be327d66',
            'ed8cc9d04b29eb877d270b4878dc43c19aefd31f4eee09ee7b47834c1fa4b1c3',
          ],
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            '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);
      var i;
      for (i = 0; i < naf.length; i += 1) {
        naf[i] = 0;
      }
    
      var ws = 1 << (w + 1);
      var k = num.clone();
    
      for (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": "6.6.1",
      "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",
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