index.js

// Requires jsbn.js and jsbn2.js
var BigInteger = (__webpack_require__(109).BigInteger)
var Barrett = BigInteger.prototype.Barrett

// ----------------
// ECFieldElementFp

// constructor
function ECFieldElementFp(q,x) {
    this.x = x;
    // TODO if(x.compareTo(q) >= 0) error
    this.q = q;
}

function feFpEquals(other) {
    if(other == this) return true;
    return (this.q.equals(other.q) && this.x.equals(other.x));
}

function feFpToBigInteger() {
    return this.x;
}

function feFpNegate() {
    return new ECFieldElementFp(this.q, this.x.negate().mod(this.q));
}

function feFpAdd(b) {
    return new ECFieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q));
}

function feFpSubtract(b) {
    return new ECFieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));
}

function feFpMultiply(b) {
    return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));
}

function feFpSquare() {
    return new ECFieldElementFp(this.q, this.x.square().mod(this.q));
}

function feFpDivide(b) {
    return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));
}

ECFieldElementFp.prototype.equals = feFpEquals;
ECFieldElementFp.prototype.toBigInteger = feFpToBigInteger;
ECFieldElementFp.prototype.negate = feFpNegate;
ECFieldElementFp.prototype.add = feFpAdd;
ECFieldElementFp.prototype.subtract = feFpSubtract;
ECFieldElementFp.prototype.multiply = feFpMultiply;
ECFieldElementFp.prototype.square = feFpSquare;
ECFieldElementFp.prototype.divide = feFpDivide;

// ----------------
// ECPointFp

// constructor
function ECPointFp(curve,x,y,z) {
    this.curve = curve;
    this.x = x;
    this.y = y;
    // Projective coordinates: either zinv == null or z * zinv == 1
    // z and zinv are just BigIntegers, not fieldElements
    if(z == null) {
      this.z = BigInteger.ONE;
    }
    else {
      this.z = z;
    }
    this.zinv = null;
    //TODO: compression flag
}

function pointFpGetX() {
    if(this.zinv == null) {
      this.zinv = this.z.modInverse(this.curve.q);
    }
    var r = this.x.toBigInteger().multiply(this.zinv);
    this.curve.reduce(r);
    return this.curve.fromBigInteger(r);
}

function pointFpGetY() {
    if(this.zinv == null) {
      this.zinv = this.z.modInverse(this.curve.q);
    }
    var r = this.y.toBigInteger().multiply(this.zinv);
    this.curve.reduce(r);
    return this.curve.fromBigInteger(r);
}

function pointFpEquals(other) {
    if(other == this) return true;
    if(this.isInfinity()) return other.isInfinity();
    if(other.isInfinity()) return this.isInfinity();
    var u, v;
    // u = Y2 * Z1 - Y1 * Z2
    u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);
    if(!u.equals(BigInteger.ZERO)) return false;
    // v = X2 * Z1 - X1 * Z2
    v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);
    return v.equals(BigInteger.ZERO);
}

function pointFpIsInfinity() {
    if((this.x == null) && (this.y == null)) return true;
    return this.z.equals(BigInteger.ZERO) && !this.y.toBigInteger().equals(BigInteger.ZERO);
}

function pointFpNegate() {
    return new ECPointFp(this.curve, this.x, this.y.negate(), this.z);
}

function pointFpAdd(b) {
    if(this.isInfinity()) return b;
    if(b.isInfinity()) return this;

    // u = Y2 * Z1 - Y1 * Z2
    var u = b.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(b.z)).mod(this.curve.q);
    // v = X2 * Z1 - X1 * Z2
    var v = b.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(b.z)).mod(this.curve.q);

    if(BigInteger.ZERO.equals(v)) {
        if(BigInteger.ZERO.equals(u)) {
            return this.twice(); // this == b, so double
        }
	return this.curve.getInfinity(); // this = -b, so infinity
    }

    var THREE = new BigInteger("3");
    var x1 = this.x.toBigInteger();
    var y1 = this.y.toBigInteger();
    var x2 = b.x.toBigInteger();
    var y2 = b.y.toBigInteger();

    var v2 = v.square();
    var v3 = v2.multiply(v);
    var x1v2 = x1.multiply(v2);
    var zu2 = u.square().multiply(this.z);

    // x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
    var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.q);
    // y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
    var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.q);
    // z3 = v^3 * z1 * z2
    var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q);

    return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
}

function pointFpTwice() {
    if(this.isInfinity()) return this;
    if(this.y.toBigInteger().signum() == 0) return this.curve.getInfinity();

    // TODO: optimized handling of constants
    var THREE = new BigInteger("3");
    var x1 = this.x.toBigInteger();
    var y1 = this.y.toBigInteger();

    var y1z1 = y1.multiply(this.z);
    var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q);
    var a = this.curve.a.toBigInteger();

    // w = 3 * x1^2 + a * z1^2
    var w = x1.square().multiply(THREE);
    if(!BigInteger.ZERO.equals(a)) {
      w = w.add(this.z.square().multiply(a));
    }
    w = w.mod(this.curve.q);
    //this.curve.reduce(w);
    // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
    var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q);
    // y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
    var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.square().multiply(w)).mod(this.curve.q);
    // z3 = 8 * (y1 * z1)^3
    var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q);

    return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
}

// Simple NAF (Non-Adjacent Form) multiplication algorithm
// TODO: modularize the multiplication algorithm
function pointFpMultiply(k) {
    if(this.isInfinity()) return this;
    if(k.signum() == 0) return this.curve.getInfinity();

    var e = k;
    var h = e.multiply(new BigInteger("3"));

    var neg = this.negate();
    var R = this;

    var i;
    for(i = h.bitLength() - 2; i > 0; --i) {
	R = R.twice();

	var hBit = h.testBit(i);
	var eBit = e.testBit(i);

	if (hBit != eBit) {
	    R = R.add(hBit ? this : neg);
	}
    }

    return R;
}

// Compute this*j + x*k (simultaneous multiplication)
function pointFpMultiplyTwo(j,x,k) {
  var i;
  if(j.bitLength() > k.bitLength())
    i = j.bitLength() - 1;
  else
    i = k.bitLength() - 1;

  var R = this.curve.getInfinity();
  var both = this.add(x);
  while(i >= 0) {
    R = R.twice();
    if(j.testBit(i)) {
      if(k.testBit(i)) {
        R = R.add(both);
      }
      else {
        R = R.add(this);
      }
    }
    else {
      if(k.testBit(i)) {
        R = R.add(x);
      }
    }
    --i;
  }

  return R;
}

ECPointFp.prototype.getX = pointFpGetX;
ECPointFp.prototype.getY = pointFpGetY;
ECPointFp.prototype.equals = pointFpEquals;
ECPointFp.prototype.isInfinity = pointFpIsInfinity;
ECPointFp.prototype.negate = pointFpNegate;
ECPointFp.prototype.add = pointFpAdd;
ECPointFp.prototype.twice = pointFpTwice;
ECPointFp.prototype.multiply = pointFpMultiply;
ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo;

// ----------------
// ECCurveFp

// constructor
function ECCurveFp(q,a,b) {
    this.q = q;
    this.a = this.fromBigInteger(a);
    this.b = this.fromBigInteger(b);
    this.infinity = new ECPointFp(this, null, null);
    this.reducer = new Barrett(this.q);
}

function curveFpGetQ() {
    return this.q;
}

function curveFpGetA() {
    return this.a;
}

function curveFpGetB() {
    return this.b;
}

function curveFpEquals(other) {
    if(other == this) return true;
    return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));
}

function curveFpGetInfinity() {
    return this.infinity;
}

function curveFpFromBigInteger(x) {
    return new ECFieldElementFp(this.q, x);
}

function curveReduce(x) {
    this.reducer.reduce(x);
}

// for now, work with hex strings because they're easier in JS
function curveFpDecodePointHex(s) {
    switch(parseInt(s.substr(0,2), 16)) { // first byte
    case 0:
	return this.infinity;
    case 2:
    case 3:
	// point compression not supported yet
	return null;
    case 4:
    case 6:
    case 7:
	var len = (s.length - 2) / 2;
	var xHex = s.substr(2, len);
	var yHex = s.substr(len+2, len);

	return new ECPointFp(this,
			     this.fromBigInteger(new BigInteger(xHex, 16)),
			     this.fromBigInteger(new BigInteger(yHex, 16)));

    default: // unsupported
	return null;
    }
}

function curveFpEncodePointHex(p) {
	if (p.isInfinity()) return "00";
	var xHex = p.getX().toBigInteger().toString(16);
	var yHex = p.getY().toBigInteger().toString(16);
	var oLen = this.getQ().toString(16).length;
	if ((oLen % 2) != 0) oLen++;
	while (xHex.length < oLen) {
		xHex = "0" + xHex;
	}
	while (yHex.length < oLen) {
		yHex = "0" + yHex;
	}
	return "04" + xHex + yHex;
}

ECCurveFp.prototype.getQ = curveFpGetQ;
ECCurveFp.prototype.getA = curveFpGetA;
ECCurveFp.prototype.getB = curveFpGetB;
ECCurveFp.prototype.equals = curveFpEquals;
ECCurveFp.prototype.getInfinity = curveFpGetInfinity;
ECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger;
ECCurveFp.prototype.reduce = curveReduce;
//ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex;
ECCurveFp.prototype.encodePointHex = curveFpEncodePointHex;

// from: https://github.com/kaielvin/jsbn-ec-point-compression
ECCurveFp.prototype.decodePointHex = function(s)
{
	var yIsEven;
    switch(parseInt(s.substr(0,2), 16)) { // first byte
    case 0:
	return this.infinity;
    case 2:
	yIsEven = false;
    case 3:
	if(yIsEven == undefined) yIsEven = true;
	var len = s.length - 2;
	var xHex = s.substr(2, len);
	var x = this.fromBigInteger(new BigInteger(xHex,16));
	var alpha = x.multiply(x.square().add(this.getA())).add(this.getB());
	var beta = alpha.sqrt();

    if (beta == null) throw "Invalid point compression";

    var betaValue = beta.toBigInteger();
    if (betaValue.testBit(0) != yIsEven)
    {
        // Use the other root
        beta = this.fromBigInteger(this.getQ().subtract(betaValue));
    }
    return new ECPointFp(this,x,beta);
    case 4:
    case 6:
    case 7:
	var len = (s.length - 2) / 2;
	var xHex = s.substr(2, len);
	var yHex = s.substr(len+2, len);

	return new ECPointFp(this,
			     this.fromBigInteger(new BigInteger(xHex, 16)),
			     this.fromBigInteger(new BigInteger(yHex, 16)));

    default: // unsupported
	return null;
    }
}
ECCurveFp.prototype.encodeCompressedPointHex = function(p)
{
	if (p.isInfinity()) return "00";
	var xHex = p.getX().toBigInteger().toString(16);
	var oLen = this.getQ().toString(16).length;
	if ((oLen % 2) != 0) oLen++;
	while (xHex.length < oLen)
		xHex = "0" + xHex;
	var yPrefix;
	if(p.getY().toBigInteger().isEven()) yPrefix = "02";
	else                                 yPrefix = "03";

	return yPrefix + xHex;
}


ECFieldElementFp.prototype.getR = function()
{
	if(this.r != undefined) return this.r;

    this.r = null;
    var bitLength = this.q.bitLength();
    if (bitLength > 128)
    {
        var firstWord = this.q.shiftRight(bitLength - 64);
        if (firstWord.intValue() == -1)
        {
            this.r = BigInteger.ONE.shiftLeft(bitLength).subtract(this.q);
        }
    }
    return this.r;
}
ECFieldElementFp.prototype.modMult = function(x1,x2)
{
    return this.modReduce(x1.multiply(x2));
}
ECFieldElementFp.prototype.modReduce = function(x)
{
    if (this.getR() != null)
    {
        var qLen = q.bitLength();
        while (x.bitLength() > (qLen + 1))
        {
            var u = x.shiftRight(qLen);
            var v = x.subtract(u.shiftLeft(qLen));
            if (!this.getR().equals(BigInteger.ONE))
            {
                u = u.multiply(this.getR());
            }
            x = u.add(v); 
        }
        while (x.compareTo(q) >= 0)
        {
            x = x.subtract(q);
        }
    }
    else
    {
        x = x.mod(q);
    }
    return x;
}
ECFieldElementFp.prototype.sqrt = function()
{
    if (!this.q.testBit(0)) throw "unsupported";

    // p mod 4 == 3
    if (this.q.testBit(1))
    {
    	var z = new ECFieldElementFp(this.q,this.x.modPow(this.q.shiftRight(2).add(BigInteger.ONE),this.q));
    	return z.square().equals(this) ? z : null;
    }

    // p mod 4 == 1
    var qMinusOne = this.q.subtract(BigInteger.ONE);

    var legendreExponent = qMinusOne.shiftRight(1);
    if (!(this.x.modPow(legendreExponent, this.q).equals(BigInteger.ONE)))
    {
        return null;
    }

    var u = qMinusOne.shiftRight(2);
    var k = u.shiftLeft(1).add(BigInteger.ONE);

    var Q = this.x;
    var fourQ = modDouble(modDouble(Q));

    var U, V;
    do
    {
        var P;
        do
        {
            P = new BigInteger(this.q.bitLength(), new SecureRandom());
        }
        while (P.compareTo(this.q) >= 0
            || !(P.multiply(P).subtract(fourQ).modPow(legendreExponent, this.q).equals(qMinusOne)));

        var result = this.lucasSequence(P, Q, k);
        U = result[0];
        V = result[1];

        if (this.modMult(V, V).equals(fourQ))
        {
            // Integer division by 2, mod q
            if (V.testBit(0))
            {
                V = V.add(q);
            }

            V = V.shiftRight(1);

            return new ECFieldElementFp(q,V);
        }
    }
    while (U.equals(BigInteger.ONE) || U.equals(qMinusOne));

    return null;
}
ECFieldElementFp.prototype.lucasSequence = function(P,Q,k)
{
    var n = k.bitLength();
    var s = k.getLowestSetBit();

    var Uh = BigInteger.ONE;
    var Vl = BigInteger.TWO;
    var Vh = P;
    var Ql = BigInteger.ONE;
    var Qh = BigInteger.ONE;

    for (var j = n - 1; j >= s + 1; --j)
    {
        Ql = this.modMult(Ql, Qh);

        if (k.testBit(j))
        {
            Qh = this.modMult(Ql, Q);
            Uh = this.modMult(Uh, Vh);
            Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
            Vh = this.modReduce(Vh.multiply(Vh).subtract(Qh.shiftLeft(1)));
        }
        else
        {
            Qh = Ql;
            Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));
            Vh = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
            Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));
        }
    }

    Ql = this.modMult(Ql, Qh);
    Qh = this.modMult(Ql, Q);
    Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));
    Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
    Ql = this.modMult(Ql, Qh);

    for (var j = 1; j <= s; ++j)
    {
        Uh = this.modMult(Uh, Vl);
        Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));
        Ql = this.modMult(Ql, Ql);
    }

    return [ Uh, Vl ];
}

var exports = {
  ECCurveFp: ECCurveFp,
  ECPointFp: ECPointFp,
  ECFieldElementFp: ECFieldElementFp
}

module.exports = exports


/***/ }),
/* 109 */
/***/ (function(module, exports) {

(function(){

    // Copyright (c) 2005  Tom Wu
    // All Rights Reserved.
    // See "LICENSE" for details.

    // Basic JavaScript BN library - subset useful for RSA encryption.

    // Bits per digit
    var dbits;

    // JavaScript engine analysis
    var canary = 0xdeadbeefcafe;
    var j_lm = ((canary&0xffffff)==0xefcafe);

    // (public) Constructor
    function BigInteger(a,b,c) {
      if(a != null)
        if("number" == typeof a) this.fromNumber(a,b,c);
        else if(b == null && "string" != typeof a) this.fromString(a,256);
        else this.fromString(a,b);
    }

    // return new, unset BigInteger
    function nbi() { return new BigInteger(null); }

    // am: Compute w_j += (x*this_i), propagate carries,
    // c is initial carry, returns final carry.
    // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
    // We need to select the fastest one that works in this environment.

    // am1: use a single mult and divide to get the high bits,
    // max digit bits should be 26 because
    // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
    function am1(i,x,w,j,c,n) {
      while(--n >= 0) {
        var v = x*this[i++]+w[j]+c;
        c = Math.floor(v/0x4000000);
        w[j++] = v&0x3ffffff;
      }
      return c;
    }
    // am2 avoids a big mult-and-extract completely.
    // Max digit bits should be <= 30 because we do bitwise ops
    // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
    function am2(i,x,w,j,c,n) {
      var xl = x&0x7fff, xh = x>>15;
      while(--n >= 0) {
        var l = this[i]&0x7fff;
        var h = this[i++]>>15;
        var m = xh*l+h*xl;
        l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
        c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
        w[j++] = l&0x3fffffff;
      }
      return c;
    }
    // Alternately, set max digit bits to 28 since some
    // browsers slow down when dealing with 32-bit numbers.
    function am3(i,x,w,j,c,n) {
      var xl = x&0x3fff, xh = x>>14;
      while(--n >= 0) {
        var l = this[i]&0x3fff;
        var h = this[i++]>>14;
        var m = xh*l+h*xl;
        l = xl*l+((m&0x3fff)<<14)+w[j]+c;
        c = (l>>28)+(m>>14)+xh*h;
        w[j++] = l&0xfffffff;
      }
      return c;
    }
    var inBrowser = typeof navigator !== "undefined";
    if(inBrowser && j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
      BigInteger.prototype.am = am2;
      dbits = 30;
    }
    else if(inBrowser && j_lm && (navigator.appName != "Netscape")) {
      BigInteger.prototype.am = am1;
      dbits = 26;
    }
    else { // Mozilla/Netscape seems to prefer am3
      BigInteger.prototype.am = am3;
      dbits = 28;
    }

    BigInteger.prototype.DB = dbits;
    BigInteger.prototype.DM = ((1<<dbits)-1);
    BigInteger.prototype.DV = (1<<dbits);

    var BI_FP = 52;
    BigInteger.prototype.FV = Math.pow(2,BI_FP);
    BigInteger.prototype.F1 = BI_FP-dbits;
    BigInteger.prototype.F2 = 2*dbits-BI_FP;

    // Digit conversions
    var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
    var BI_RC = new Array();
    var rr,vv;
    rr = "0".charCodeAt(0);
    for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
    rr = "a".charCodeAt(0);
    for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
    rr = "A".charCodeAt(0);
    for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;

    function int2char(n) { return BI_RM.charAt(n); }
    function intAt(s,i) {
      var c = BI_RC[s.charCodeAt(i)];
      return (c==null)?-1:c;
    }

    // (protected) copy this to r
    function bnpCopyTo(r) {
      for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
      r.t = this.t;
      r.s = this.s;
    }

    // (protected) set from integer value x, -DV <= x < DV
    function bnpFromInt(x) {
      this.t = 1;
      this.s = (x<0)?-1:0;
      if(x > 0) this[0] = x;
      else if(x < -1) this[0] = x+this.DV;
      else this.t = 0;
    }

    // return bigint initialized to value
    function nbv(i) { var r = nbi(); r.fromInt(i); return r; }

    // (protected) set from string and radix
    function bnpFromString(s,b) {
      var k;
      if(b == 16) k = 4;
      else if(b == 8) k = 3;
      else if(b == 256) k = 8; // byte array
      else if(b == 2) k = 1;
      else if(b == 32) k = 5;
      else if(b == 4) k = 2;
      else { this.fromRadix(s,b); return; }
      this.t = 0;
      this.s = 0;
      var i = s.length, mi = false, sh = 0;
      while(--i >= 0) {
        var x = (k==8)?s[i]&0xff:intAt(s,i);
        if(x < 0) {
          if(s.charAt(i) == "-") mi = true;
          continue;
        }
        mi = false;
        if(sh == 0)
          this[this.t++] = x;
        else if(sh+k > this.DB) {
          this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
          this[this.t++] = (x>>(this.DB-sh));
        }
        else
          this[this.t-1] |= x<<sh;
        sh += k;
        if(sh >= this.DB) sh -= this.DB;
      }
      if(k == 8 && (s[0]&0x80) != 0) {
        this.s = -1;
        if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
      }
      this.clamp();
      if(mi) BigInteger.ZERO.subTo(this,this);
    }

    // (protected) clamp off excess high words
    function bnpClamp() {
      var c = this.s&this.DM;
      while(this.t > 0 && this[this.t-1] == c) --this.t;
    }

    // (public) return string representation in given radix
    function bnToString(b) {
      if(this.s < 0) return "-"+this.negate().toString(b);
      var k;
      if(b == 16) k = 4;
      else if(b == 8) k = 3;
      else if(b == 2) k = 1;
      else if(b == 32) k = 5;
      else if(b == 4) k = 2;
      else return this.toRadix(b);
      var km = (1<<k)-1, d, m = false, r = "", i = this.t;
      var p = this.DB-(i*this.DB)%k;
      if(i-- > 0) {
        if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
        while(i >= 0) {
          if(p < k) {
            d = (this[i]&((1<<p)-1))<<(k-p);
            d |= this[--i]>>(p+=this.DB-k);
          }
          else {
            d = (this[i]>>(p-=k))&km;
            if(p <= 0) { p += this.DB; --i; }
          }
          if(d > 0) m = true;
          if(m) r += int2char(d);
        }
      }
      return m?r:"0";
    }

    // (public) -this
    function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }

    // (public) |this|
    function bnAbs() { return (this.s<0)?this.negate():this; }

    // (public) return + if this > a, - if this < a, 0 if equal
    function bnCompareTo(a) {
      var r = this.s-a.s;
      if(r != 0) return r;
      var i = this.t;
      r = i-a.t;
      if(r != 0) return (this.s<0)?-r:r;
      while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
      return 0;
    }

    // returns bit length of the integer x
    function nbits(x) {
      var r = 1, t;
      if((t=x>>>16) != 0) { x = t; r += 16; }
      if((t=x>>8) != 0) { x = t; r += 8; }
      if((t=x>>4) != 0) { x = t; r += 4; }
      if((t=x>>2) != 0) { x = t; r += 2; }
      if((t=x>>1) != 0) { x = t; r += 1; }
      return r;
    }

    // (public) return the number of bits in "this"
    function bnBitLength() {
      if(this.t <= 0) return 0;
      return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
    }

    // (protected) r = this << n*DB
    function bnpDLShiftTo(n,r) {
      var i;
      for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
      for(i = n-1; i >= 0; --i) r[i] = 0;
      r.t = this.t+n;
      r.s = this.s;
    }

    // (protected) r = this >> n*DB
    function bnpDRShiftTo(n,r) {
      for(var i = n; i < this.t; ++i) r[i-n] = this[i];
      r.t = Math.max(this.t-n,0);
      r.s = this.s;
    }

    // (protected) r = this << n
    function bnpLShiftTo(n,r) {
      var bs = n%this.DB;
      var cbs = this.DB-bs;
      var bm = (1<<cbs)-1;
      var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
      for(i = this.t-1; i >= 0; --i) {
        r[i+ds+1] = (this[i]>>cbs)|c;
        c = (this[i]&bm)<<bs;
      }
      for(i = ds-1; i >= 0; --i) r[i] = 0;
      r[ds] = c;
      r.t = this.t+ds+1;
      r.s = this.s;
      r.clamp();
    }

    // (protected) r = this >> n
    function bnpRShiftTo(n,r) {
      r.s = this.s;
      var ds = Math.floor(n/this.DB);
      if(ds >= this.t) { r.t = 0; return; }
      var bs = n%this.DB;
      var cbs = this.DB-bs;
      var bm = (1<<bs)-1;
      r[0] = this[ds]>>bs;
      for(var i = ds+1; i < this.t; ++i) {
        r[i-ds-1] |= (this[i]&bm)<<cbs;
        r[i-ds] = this[i]>>bs;
      }
      if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
      r.t = this.t-ds;
      r.clamp();
    }

    // (protected) r = this - a
    function bnpSubTo(a,r) {
      var i = 0, c = 0, m = Math.min(a.t,this.t);
      while(i < m) {
        c += this[i]-a[i];
        r[i++] = c&this.DM;
        c >>= this.DB;
      }
      if(a.t < this.t) {
        c -= a.s;
        while(i < this.t) {
          c += this[i];
          r[i++] = c&this.DM;
          c >>= this.DB;
        }
        c += this.s;
      }
      else {
        c += this.s;
        while(i < a.t) {
          c -= a[i];
          r[i++] = c&this.DM;
          c >>= this.DB;
        }
        c -= a.s;
      }
      r.s = (c<0)?-1:0;
      if(c < -1) r[i++] = this.DV+c;
      else if(c > 0) r[i++] = c;
      r.t = i;
      r.clamp();
    }

    // (protected) r = this * a, r != this,a (HAC 14.12)
    // "this" should be the larger one if appropriate.
    function bnpMultiplyTo(a,r) {
      var x = this.abs(), y = a.abs();
      var i = x.t;
      r.t = i+y.t;
      while(--i >= 0) r[i] = 0;
      for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
      r.s = 0;
      r.clamp();
      if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
    }

    // (protected) r = this^2, r != this (HAC 14.16)
    function bnpSquareTo(r) {
      var x = this.abs();
      var i = r.t = 2*x.t;
      while(--i >= 0) r[i] = 0;
      for(i = 0; i < x.t-1; ++i) {
        var c = x.am(i,x[i],r,2*i,0,1);
        if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
          r[i+x.t] -= x.DV;
          r[i+x.t+1] = 1;
        }
      }
      if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
      r.s = 0;
      r.clamp();
    }

    // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
    // r != q, this != m.  q or r may be null.
    function bnpDivRemTo(m,q,r) {
      var pm = m.abs();
      if(pm.t <= 0) return;
      var pt = this.abs();
      if(pt.t < pm.t) {
        if(q != null) q.fromInt(0);
        if(r != null) this.copyTo(r);
        return;
      }
      if(r == null) r = nbi();
      var y = nbi(), ts = this.s, ms = m.s;
      var nsh = this.DB-nbits(pm[pm.t-1]);   // normalize modulus
      if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
      else { pm.copyTo(y); pt.copyTo(r); }
      var ys = y.t;
      var y0 = y[ys-1];
      if(y0 == 0) return;
      var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
      var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
      var i = r.t, j = i-ys, t = (q==null)?nbi():q;
      y.dlShiftTo(j,t);
      if(r.compareTo(t) >= 0) {
        r[r.t++] = 1;
        r.subTo(t,r);
      }
      BigInteger.ONE.dlShiftTo(ys,t);
      t.subTo(y,y);  // "negative" y so we can replace sub with am later
      while(y.t < ys) y[y.t++] = 0;
      while(--j >= 0) {
        // Estimate quotient digit
        var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
        if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) {   // Try it out
          y.dlShiftTo(j,t);
          r.subTo(t,r);
          while(r[i] < --qd) r.subTo(t,r);
        }
      }
      if(q != null) {
        r.drShiftTo(ys,q);
        if(ts != ms) BigInteger.ZERO.subTo(q,q);
      }
      r.t = ys;
      r.clamp();
      if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
      if(ts < 0) BigInteger.ZERO.subTo(r,r);
    }

    // (public) this mod a
    function bnMod(a) {
      var r = nbi();
      this.abs().divRemTo(a,null,r);
      if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
      return r;
    }

    // Modular reduction using "classic" algorithm
    function Classic(m) { this.m = m; }
    function cConvert(x) {
      if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
      else return x;
    }
    function cRevert(x) { return x; }
    function cReduce(x) { x.divRemTo(this.m,null,x); }
    function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
    function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }

    Classic.prototype.convert = cConvert;
    Classic.prototype.revert = cRevert;
    Classic.prototype.reduce = cReduce;
    Classic.prototype.mulTo = cMulTo;
    Classic.prototype.sqrTo = cSqrTo;

    // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
    // justification:
    //         xy == 1 (mod m)
    //         xy =  1+km
    //   xy(2-xy) = (1+km)(1-km)
    // x[y(2-xy)] = 1-k^2m^2
    // x[y(2-xy)] == 1 (mod m^2)
    // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
    // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
    // JS multiply "overflows" differently from C/C++, so care is needed here.