# Source: crypto/public_key/jsbn.js

    /*
     * Copyright (c) 2003-2005  Tom Wu (tjw@cs.Stanford.EDU)
     * All Rights Reserved.
     *
     * Modified by Recurity Labs GmbH
     *
     * Permission is hereby granted, free of charge, to any person obtaining
     * a copy of this software and associated documentation files (the
     * "Software"), to deal in the Software without restriction, including
     * without limitation the rights to use, copy, modify, merge, publish,
     * distribute, sublicense, and/or sell copies of the Software, and to
     * permit persons to whom the Software is furnished to do so, subject to
     * the following conditions:
     *
     * The above copyright notice and this permission notice shall be
     * included in all copies or substantial portions of the Software.
     *
     * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
     * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
     * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
     *
     * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
     * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
     * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
     * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
     * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
     *
     * In addition, the following condition applies:
     *
     * All redistributions must retain an intact copy of this copyright notice
     * and disclaimer.
     */

    /** @module crypto/public_key/jsbn */

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

    // 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;
    }
    /*if(j_lm && (navigator != undefined &&
    	navigator.appName == "Microsoft Internet Explorer")) {
      BigInteger.prototype.am = am2;
      dbits = 30;
    }
    else if(j_lm && (navigator != undefined && 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 + 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 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.

    function bnpInvDigit() {
      if (this.t < 1) return 0;
      var x = this[0];
      if ((x & 1) == 0) return 0;
      var y = x & 3; // y == 1/x mod 2^2
      y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4
      y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8
      y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16
      // last step - calculate inverse mod DV directly;
      // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
      y = (y * (2 - x * y % this.DV)) % this.DV; // y == 1/x mod 2^dbits
      // we really want the negative inverse, and -DV < y < DV
      return (y > 0) ? this.DV - y : -y;
    }

    // Montgomery reduction

    function Montgomery(m) {
      this.m = m;
      this.mp = m.invDigit();
      this.mpl = this.mp & 0x7fff;
      this.mph = this.mp >> 15;
      this.um = (1 << (m.DB - 15)) - 1;
      this.mt2 = 2 * m.t;
    }

    // xR mod m

    function montConvert(x) {
      var r = nbi();
      x.abs().dlShiftTo(this.m.t, r);
      r.divRemTo(this.m, null, r);
      if (x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r, r);
      return r;
    }

    // x/R mod m

    function montRevert(x) {
      var r = nbi();
      x.copyTo(r);
      this.reduce(r);
      return r;
    }

    // x = x/R mod m (HAC 14.32)

    function montReduce(x) {
      while (x.t <= this.mt2) // pad x so am has enough room later
        x[x.t++] = 0;
      for (var i = 0; i < this.m.t; ++i) {
        // faster way of calculating u0 = x[i]*mp mod DV
        var j = x[i] & 0x7fff;
        var u0 = (j * this.mpl + (((j * this.mph + (x[i] >> 15) * this.mpl) & this.um) << 15)) & x.DM;
        // use am to combine the multiply-shift-add into one call
        j = i + this.m.t;
        x[j] += this.m.am(0, u0, x, i, 0, this.m.t);
        // propagate carry
        while (x[j] >= x.DV) {
          x[j] -= x.DV;
          x[++j]++;
        }
      }
      x.clamp();
      x.drShiftTo(this.m.t, x);
      if (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
    }

    // r = "x^2/R mod m"; x != r

    function montSqrTo(x, r) {
      x.squareTo(r);
      this.reduce(r);
    }

    // r = "xy/R mod m"; x,y != r

    function montMulTo(x, y, r) {
      x.multiplyTo(y, r);
      this.reduce(r);
    }

    Montgomery.prototype.convert = montConvert;
    Montgomery.prototype.revert = montRevert;
    Montgomery.prototype.reduce = montReduce;
    Montgomery.prototype.mulTo = montMulTo;
    Montgomery.prototype.sqrTo = montSqrTo;

    // (protected) true iff this is even

    function bnpIsEven() {
      return ((this.t > 0) ? (this[0] & 1) : this.s) == 0;
    }

    // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)

    function bnpExp(e, z) {
      if (e > 0xffffffff || e < 1) return BigInteger.ONE;
      var r = nbi(),
        r2 = nbi(),
        g = z.convert(this),
        i = nbits(e) - 1;
      g.copyTo(r);
      while (--i >= 0) {
        z.sqrTo(r, r2);
        if ((e & (1 << i)) > 0) z.mulTo(r2, g, r);
        else {
          var t = r;
          r = r2;
          r2 = t;
        }
      }
      return z.revert(r);
    }

    // (public) this^e % m, 0 <= e < 2^32

    function bnModPowInt(e, m) {
      var z;
      if (e < 256 || m.isEven()) z = new Classic(m);
      else z = new Montgomery(m);
      return this.exp(e, z);
    }

    // protected
    BigInteger.prototype.copyTo = bnpCopyTo;
    BigInteger.prototype.fromInt = bnpFromInt;
    BigInteger.prototype.fromString = bnpFromString;
    BigInteger.prototype.clamp = bnpClamp;
    BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
    BigInteger.prototype.drShiftTo = bnpDRShiftTo;
    BigInteger.prototype.lShiftTo = bnpLShiftTo;
    BigInteger.prototype.rShiftTo = bnpRShiftTo;
    BigInteger.prototype.subTo = bnpSubTo;
    BigInteger.prototype.multiplyTo = bnpMultiplyTo;
    BigInteger.prototype.squareTo = bnpSquareTo;
    BigInteger.prototype.divRemTo = bnpDivRemTo;
    BigInteger.prototype.invDigit = bnpInvDigit;
    BigInteger.prototype.isEven = bnpIsEven;
    BigInteger.prototype.exp = bnpExp;

    // public
    BigInteger.prototype.toString = bnToString;
    BigInteger.prototype.negate = bnNegate;
    BigInteger.prototype.abs = bnAbs;
    BigInteger.prototype.compareTo = bnCompareTo;
    BigInteger.prototype.bitLength = bnBitLength;
    BigInteger.prototype.mod = bnMod;
    BigInteger.prototype.modPowInt = bnModPowInt;

    // "constants"
    BigInteger.ZERO = nbv(0);
    BigInteger.ONE = nbv(1);

    module.exports = BigInteger;

    /*
     * Copyright (c) 2003-2005  Tom Wu (tjw@cs.Stanford.EDU)
     * All Rights Reserved.
     *
     * Modified by Recurity Labs GmbH
     *
     * Permission is hereby granted, free of charge, to any person obtaining
     * a copy of this software and associated documentation files (the
     * "Software"), to deal in the Software without restriction, including
     * without limitation the rights to use, copy, modify, merge, publish,
     * distribute, sublicense, and/or sell copies of the Software, and to
     * permit persons to whom the Software is furnished to do so, subject to
     * the following conditions:
     *
     * The above copyright notice and this permission notice shall be
     * included in all copies or substantial portions of the Software.
     *
     * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
     * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
     * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
     *
     * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
     * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
     * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
     * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
     * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
     *
     * In addition, the following condition applies:
     *
     * All redistributions must retain an intact copy of this copyright notice
     * and disclaimer.
     */

    // Extended JavaScript BN functions, required for RSA private ops.

    // Version 1.1: new BigInteger("0", 10) returns "proper" zero
    // Version 1.2: square() API, isProbablePrime fix

    // (public)
    function bnClone() {
      var r = nbi();
      this.copyTo(r);
      return r;
    }

    // (public) return value as integer

    function bnIntValue() {
      if (this.s < 0) {
        if (this.t == 1) return this[0] - this.DV;
        else if (this.t == 0) return -1;
      } else if (this.t == 1) return this[0];
      else if (this.t == 0) return 0;
      // assumes 16 < DB < 32
      return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0];
    }

    // (public) return value as byte

    function bnByteValue() {
      return (this.t == 0) ? this.s : (this[0] << 24) >> 24;
    }

    // (public) return value as short (assumes DB>=16)

    function bnShortValue() {
      return (this.t == 0) ? this.s : (this[0] << 16) >> 16;
    }

    // (protected) return x s.t. r^x < DV

    function bnpChunkSize(r) {
      return Math.floor(Math.LN2 * this.DB / Math.log(r));
    }

    // (public) 0 if this == 0, 1 if this > 0

    function bnSigNum() {
      if (this.s < 0) return -1;
      else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
      else return 1;
    }

    // (protected) convert to radix string

    function bnpToRadix(b) {
      if (b == null) b = 10;
      if (this.signum() == 0 || b < 2 || b > 36) return "0";
      var cs = this.chunkSize(b);
      var a = Math.pow(b, cs);
      var d = nbv(a),
        y = nbi(),
        z = nbi(),
        r = "";
      this.divRemTo(d, y, z);
      while (y.signum() > 0) {
        r = (a + z.intValue()).toString(b).substr(1) + r;
        y.divRemTo(d, y, z);
      }
      return z.intValue().toString(b) + r;
    }

    // (protected) convert from radix string

    function bnpFromRadix(s, b) {
      this.fromInt(0);
      if (b == null) b = 10;
      var cs = this.chunkSize(b);
      var d = Math.pow(b, cs),
        mi = false,
        j = 0,
        w = 0;
      for (var i = 0; i < s.length; ++i) {
        var x = intAt(s, i);
        if (x < 0) {
          if (s.charAt(i) == "-" && this.signum() == 0) mi = true;
          continue;
        }
        w = b * w + x;
        if (++j >= cs) {
          this.dMultiply(d);
          this.dAddOffset(w, 0);
          j = 0;
          w = 0;
        }
      }
      if (j > 0) {
        this.dMultiply(Math.pow(b, j));
        this.dAddOffset(w, 0);
      }
      if (mi) BigInteger.ZERO.subTo(this, this);
    }

    // (protected) alternate constructor

    function bnpFromNumber(a, b, c) {
      if ("number" == typeof b) {
        // new BigInteger(int,int,RNG)
        if (a < 2) this.fromInt(1);
        else {
          this.fromNumber(a, c);
          if (!this.testBit(a - 1)) // force MSB set
            this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this);
          if (this.isEven()) this.dAddOffset(1, 0); // force odd
          while (!this.isProbablePrime(b)) {
            this.dAddOffset(2, 0);
            if (this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a - 1), this);
          }
        }
      } else {
        // new BigInteger(int,RNG)
        var x = new Array(),
          t = a & 7;
        x.length = (a >> 3) + 1;
        b.nextBytes(x);
        if (t > 0) x[0] &= ((1 << t) - 1);
        else x[0] = 0;
        this.fromString(x, 256);
      }
    }

    // (public) convert to bigendian byte array

    function bnToByteArray() {
      var i = this.t,
        r = new Array();
      r[0] = this.s;
      var p = this.DB - (i * this.DB) % 8,
        d, k = 0;
      if (i-- > 0) {
        if (p < this.DB && (d = this[i] >> p) != (this.s & this.DM) >> p)
          r[k++] = d | (this.s << (this.DB - p));
        while (i >= 0) {
          if (p < 8) {
            d = (this[i] & ((1 << p) - 1)) << (8 - p);
            d |= this[--i] >> (p += this.DB - 8);
          } else {
            d = (this[i] >> (p -= 8)) & 0xff;
            if (p <= 0) {
              p += this.DB;
              --i;
            }
          }
          //if((d&0x80) != 0) d |= -256;
          //if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
          if (k > 0 || d != this.s) r[k++] = d;
        }
      }
      return r;
    }

    function bnEquals(a) {
      return (this.compareTo(a) == 0);
    }

    function bnMin(a) {
      return (this.compareTo(a) < 0) ? this : a;
    }

    function bnMax(a) {
      return (this.compareTo(a) > 0) ? this : a;
    }

    // (protected) r = this op a (bitwise)

    function bnpBitwiseTo(a, op, r) {
      var i, f, m = Math.min(a.t, this.t);
      for (i = 0; i < m; ++i) r[i] = op(this[i], a[i]);
      if (a.t < this.t) {
        f = a.s & this.DM;
        for (i = m; i < this.t; ++i) r[i] = op(this[i], f);
        r.t = this.t;
      } else {
        f = this.s & this.DM;
        for (i = m; i < a.t; ++i) r[i] = op(f, a[i]);
        r.t = a.t;
      }
      r.s = op(this.s, a.s);
      r.clamp();
    }

    // (public) this & a

    function op_and(x, y) {
      return x & y;
    }

    function bnAnd(a) {
      var r = nbi();
      this.bitwiseTo(a, op_and, r);
      return r;
    }

    // (public) this | a

    function op_or(x, y) {
      return x | y;
    }

    function bnOr(a) {
      var r = nbi();
      this.bitwiseTo(a, op_or, r);
      return r;
    }

    // (public) this ^ a

    function op_xor(x, y) {
      return x ^ y;
    }

    function bnXor(a) {
      var r = nbi();
      this.bitwiseTo(a, op_xor, r);
      return r;
    }

    // (public) this & ~a

    function op_andnot(x, y) {
      return x & ~y;
    }

    function bnAndNot(a) {
      var r = nbi();
      this.bitwiseTo(a, op_andnot, r);
      return r;
    }

    // (public) ~this

    function bnNot() {
      var r = nbi();
      for (var i = 0; i < this.t; ++i) r[i] = this.DM & ~this[i];
      r.t = this.t;
      r.s = ~this.s;
      return r;
    }

    // (public) this << n

    function bnShiftLeft(n) {
      var r = nbi();
      if (n < 0) this.rShiftTo(-n, r);
      else this.lShiftTo(n, r);
      return r;
    }

    // (public) this >> n

    function bnShiftRight(n) {
      var r = nbi();
      if (n < 0) this.lShiftTo(-n, r);
      else this.rShiftTo(n, r);
      return r;
    }

    // return index of lowest 1-bit in x, x < 2^31

    function lbit(x) {
      if (x == 0) return -1;
      var r = 0;
      if ((x & 0xffff) == 0) {
        x >>= 16;
        r += 16;
      }
      if ((x & 0xff) == 0) {
        x >>= 8;
        r += 8;
      }
      if ((x & 0xf) == 0) {
        x >>= 4;
        r += 4;
      }
      if ((x & 3) == 0) {
        x >>= 2;
        r += 2;
      }
      if ((x & 1) == 0)++r;
      return r;
    }

    // (public) returns index of lowest 1-bit (or -1 if none)

    function bnGetLowestSetBit() {
      for (var i = 0; i < this.t; ++i)
        if (this[i] != 0) return i * this.DB + lbit(this[i]);
      if (this.s < 0) return this.t * this.DB;
      return -1;
    }

    // return number of 1 bits in x

    function cbit(x) {
      var r = 0;
      while (x != 0) {
        x &= x - 1;
        ++r;
      }
      return r;
    }

    // (public) return number of set bits

    function bnBitCount() {
      var r = 0,
        x = this.s & this.DM;
      for (var i = 0; i < this.t; ++i) r += cbit(this[i] ^ x);
      return r;
    }

    // (public) true iff nth bit is set

    function bnTestBit(n) {
      var j = Math.floor(n / this.DB);
      if (j >= this.t) return (this.s != 0);
      return ((this[j] & (1 << (n % this.DB))) != 0);
    }

    // (protected) this op (1<<n)

    function bnpChangeBit(n, op) {
      var r = BigInteger.ONE.shiftLeft(n);
      this.bitwiseTo(r, op, r);
      return r;
    }

    // (public) this | (1<<n)

    function bnSetBit(n) {
      return this.changeBit(n, op_or);
    }

    // (public) this & ~(1<<n)

    function bnClearBit(n) {
      return this.changeBit(n, op_andnot);
    }

    // (public) this ^ (1<<n)

    function bnFlipBit(n) {
      return this.changeBit(n, op_xor);
    }

    // (protected) r = this + a

    function bnpAddTo(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 > 0) r[i++] = c;
      else if (c < -1) r[i++] = this.DV + c;
      r.t = i;
      r.clamp();
    }

    // (public) this + a

    function bnAdd(a) {
      var r = nbi();
      this.addTo(a, r);
      return r;
    }

    // (public) this - a

    function bnSubtract(a) {
      var r = nbi();
      this.subTo(a, r);
      return r;
    }

    // (public) this * a

    function bnMultiply(a) {
      var r = nbi();
      this.multiplyTo(a, r);
      return r;
    }

    // (public) this^2

    function bnSquare() {
      var r = nbi();
      this.squareTo(r);
      return r;
    }

    // (public) this / a

    function bnDivide(a) {
      var r = nbi();
      this.divRemTo(a, r, null);
      return r;
    }

    // (public) this % a

    function bnRemainder(a) {
      var r = nbi();
      this.divRemTo(a, null, r);
      return r;
    }

    // (public) [this/a,this%a]

    function bnDivideAndRemainder(a) {
      var q = nbi(),
        r = nbi();
      this.divRemTo(a, q, r);
      return new Array(q, r);
    }

    // (protected) this *= n, this >= 0, 1 < n < DV

    function bnpDMultiply(n) {
      this[this.t] = this.am(0, n - 1, this, 0, 0, this.t);
      ++this.t;
      this.clamp();
    }

    // (protected) this += n << w words, this >= 0

    function bnpDAddOffset(n, w) {
      if (n == 0) return;
      while (this.t <= w) this[this.t++] = 0;
      this[w] += n;
      while (this[w] >= this.DV) {
        this[w] -= this.DV;
        if (++w >= this.t) this[this.t++] = 0;
        ++this[w];
      }
    }

    // A "null" reducer

    function NullExp() {}

    function nNop(x) {
      return x;
    }

    function nMulTo(x, y, r) {
      x.multiplyTo(y, r);
    }

    function nSqrTo(x, r) {
      x.squareTo(r);
    }

    NullExp.prototype.convert = nNop;
    NullExp.prototype.revert = nNop;
    NullExp.prototype.mulTo = nMulTo;
    NullExp.prototype.sqrTo = nSqrTo;

    // (public) this^e

    function bnPow(e) {
      return this.exp(e, new NullExp());
    }

    // (protected) r = lower n words of "this * a", a.t <= n
    // "this" should be the larger one if appropriate.

    function bnpMultiplyLowerTo(a, n, r) {
      var i = Math.min(this.t + a.t, n);
      r.s = 0; // assumes a,this >= 0
      r.t = i;
      while (i > 0) r[--i] = 0;
      var j;
      for (j = r.t - this.t; i < j; ++i) r[i + this.t] = this.am(0, a[i], r, i, 0, this.t);
      for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a[i], r, i, 0, n - i);
      r.clamp();
    }

    // (protected) r = "this * a" without lower n words, n > 0
    // "this" should be the larger one if appropriate.

    function bnpMultiplyUpperTo(a, n, r) {
      --n;
      var i = r.t = this.t + a.t - n;
      r.s = 0; // assumes a,this >= 0
      while (--i >= 0) r[i] = 0;
      for (i = Math.max(n - this.t, 0); i < a.t; ++i)
        r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n);
      r.clamp();
      r.drShiftTo(1, r);
    }

    // Barrett modular reduction

    function Barrett(m) {
      // setup Barrett
      this.r2 = nbi();
      this.q3 = nbi();
      BigInteger.ONE.dlShiftTo(2 * m.t, this.r2);
      this.mu = this.r2.divide(m);
      this.m = m;
    }

    function barrettConvert(x) {
      if (x.s < 0 || x.t > 2 * this.m.t) return x.mod(this.m);
      else if (x.compareTo(this.m) < 0) return x;
      else {
        var r = nbi();
        x.copyTo(r);
        this.reduce(r);
        return r;
      }
    }

    function barrettRevert(x) {
      return x;
    }

    // x = x mod m (HAC 14.42)

    function barrettReduce(x) {
      x.drShiftTo(this.m.t - 1, this.r2);
      if (x.t > this.m.t + 1) {
        x.t = this.m.t + 1;
        x.clamp();
      }
      this.mu.multiplyUpperTo(this.r2, this.m.t + 1, this.q3);
      this.m.multiplyLowerTo(this.q3, this.m.t + 1, this.r2);
      while (x.compareTo(this.r2) < 0) x.dAddOffset(1, this.m.t + 1);
      x.subTo(this.r2, x);
      while (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
    }

    // r = x^2 mod m; x != r

    function barrettSqrTo(x, r) {
      x.squareTo(r);
      this.reduce(r);
    }

    // r = x*y mod m; x,y != r

    function barrettMulTo(x, y, r) {
      x.multiplyTo(y, r);
      this.reduce(r);
    }

    Barrett.prototype.convert = barrettConvert;
    Barrett.prototype.revert = barrettRevert;
    Barrett.prototype.reduce = barrettReduce;
    Barrett.prototype.mulTo = barrettMulTo;
    Barrett.prototype.sqrTo = barrettSqrTo;

    // (public) this^e % m (HAC 14.85)

    function bnModPow(e, m) {
      var i = e.bitLength(),
        k, r = nbv(1),
        z;
      if (i <= 0) return r;
      else if (i < 18) k = 1;
      else if (i < 48) k = 3;
      else if (i < 144) k = 4;
      else if (i < 768) k = 5;
      else k = 6;
      if (i < 8)
        z = new Classic(m);
      else if (m.isEven())
        z = new Barrett(m);
      else
        z = new Montgomery(m);

      // precomputation
      var g = new Array(),
        n = 3,
        k1 = k - 1,
        km = (1 << k) - 1;
      g[1] = z.convert(this);
      if (k > 1) {
        var g2 = nbi();
        z.sqrTo(g[1], g2);
        while (n <= km) {
          g[n] = nbi();
          z.mulTo(g2, g[n - 2], g[n]);
          n += 2;
        }
      }

      var j = e.t - 1,
        w, is1 = true,
        r2 = nbi(),
        t;
      i = nbits(e[j]) - 1;
      while (j >= 0) {
        if (i >= k1) w = (e[j] >> (i - k1)) & km;
        else {
          w = (e[j] & ((1 << (i + 1)) - 1)) << (k1 - i);
          if (j > 0) w |= e[j - 1] >> (this.DB + i - k1);
        }

        n = k;
        while ((w & 1) == 0) {
          w >>= 1;
          --n;
        }
        if ((i -= n) < 0) {
          i += this.DB;
          --j;
        }
        if (is1) { // ret == 1, don't bother squaring or multiplying it
          g[w].copyTo(r);
          is1 = false;
        } else {
          while (n > 1) {
            z.sqrTo(r, r2);
            z.sqrTo(r2, r);
            n -= 2;
          }
          if (n > 0) z.sqrTo(r, r2);
          else {
            t = r;
            r = r2;
            r2 = t;
          }
          z.mulTo(r2, g[w], r);
        }

        while (j >= 0 && (e[j] & (1 << i)) == 0) {
          z.sqrTo(r, r2);
          t = r;
          r = r2;
          r2 = t;
          if (--i < 0) {
            i = this.DB - 1;
            --j;
          }
        }
      }
      return z.revert(r);
    }

    // (public) gcd(this,a) (HAC 14.54)

    function bnGCD(a) {
      var x = (this.s < 0) ? this.negate() : this.clone();
      var y = (a.s < 0) ? a.negate() : a.clone();
      if (x.compareTo(y) < 0) {
        var t = x;
        x = y;
        y = t;
      }
      var i = x.getLowestSetBit(),
        g = y.getLowestSetBit();
      if (g < 0) return x;
      if (i < g) g = i;
      if (g > 0) {
        x.rShiftTo(g, x);
        y.rShiftTo(g, y);
      }
      while (x.signum() > 0) {
        if ((i = x.getLowestSetBit()) > 0) x.rShiftTo(i, x);
        if ((i = y.getLowestSetBit()) > 0) y.rShiftTo(i, y);
        if (x.compareTo(y) >= 0) {
          x.subTo(y, x);
          x.rShiftTo(1, x);
        } else {
          y.subTo(x, y);
          y.rShiftTo(1, y);
        }
      }
      if (g > 0) y.lShiftTo(g, y);
      return y;
    }

    // (protected) this % n, n < 2^26

    function bnpModInt(n) {
      if (n <= 0) return 0;
      var d = this.DV % n,
        r = (this.s < 0) ? n - 1 : 0;
      if (this.t > 0)
        if (d == 0) r = this[0] % n;
        else for (var i = this.t - 1; i >= 0; --i) r = (d * r + this[i]) % n;
      return r;
    }

    // (public) 1/this % m (HAC 14.61)

    function bnModInverse(m) {
      var ac = m.isEven();
      if ((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
      var u = m.clone(),
        v = this.clone();
      var a = nbv(1),
        b = nbv(0),
        c = nbv(0),
        d = nbv(1);
      while (u.signum() != 0) {
        while (u.isEven()) {
          u.rShiftTo(1, u);
          if (ac) {
            if (!a.isEven() || !b.isEven()) {
              a.addTo(this, a);
              b.subTo(m, b);
            }
            a.rShiftTo(1, a);
          } else if (!b.isEven()) b.subTo(m, b);
          b.rShiftTo(1, b);
        }
        while (v.isEven()) {
          v.rShiftTo(1, v);
          if (ac) {
            if (!c.isEven() || !d.isEven()) {
              c.addTo(this, c);
              d.subTo(m, d);
            }
            c.rShiftTo(1, c);
          } else if (!d.isEven()) d.subTo(m, d);
          d.rShiftTo(1, d);
        }
        if (u.compareTo(v) >= 0) {
          u.subTo(v, u);
          if (ac) a.subTo(c, a);
          b.subTo(d, b);
        } else {
          v.subTo(u, v);
          if (ac) c.subTo(a, c);
          d.subTo(b, d);
        }
      }
      if (v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
      if (d.compareTo(m) >= 0) return d.subtract(m);
      if (d.signum() < 0) d.addTo(m, d);
      else return d;
      if (d.signum() < 0) return d.add(m);
      else return d;
    }

    var lowprimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
        103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227,
        229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359,
        367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499,
        503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647,
        653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
        821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971,
        977, 983, 991, 997
    ];
    var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];

    // (public) test primality with certainty >= 1-.5^t

    function bnIsProbablePrime(t) {
      var i, x = this.abs();
      if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) {
        for (i = 0; i < lowprimes.length; ++i)
          if (x[0] == lowprimes[i]) return true;
        return false;
      }
      if (x.isEven()) return false;
      i = 1;
      while (i < lowprimes.length) {
        var m = lowprimes[i],
          j = i + 1;
        while (j < lowprimes.length && m < lplim) m *= lowprimes[j++];
        m = x.modInt(m);
        while (i < j) if (m % lowprimes[i++] == 0) return false;
      }
      return x.millerRabin(t);
    }

    /* added by Recurity Labs */

    function nbits(x) {
      var n = 1,
        t;
      if ((t = x >>> 16) != 0) {
        x = t;
        n += 16;
      }
      if ((t = x >> 8) != 0) {
        x = t;
        n += 8;
      }
      if ((t = x >> 4) != 0) {
        x = t;
        n += 4;
      }
      if ((t = x >> 2) != 0) {
        x = t;
        n += 2;
      }
      if ((t = x >> 1) != 0) {
        x = t;
        n += 1;
      }
      return n;
    }

    function bnToMPI() {
      var ba = this.toByteArray();
      var size = (ba.length - 1) * 8 + nbits(ba[0]);
      var result = "";
      result += String.fromCharCode((size & 0xFF00) >> 8);
      result += String.fromCharCode(size & 0xFF);
      result += util.bin2str(ba);
      return result;
    }
    /* END of addition */

    // (protected) true if probably prime (HAC 4.24, Miller-Rabin)
    function bnpMillerRabin(t) {
      var n1 = this.subtract(BigInteger.ONE);
      var k = n1.getLowestSetBit();
      if (k <= 0) return false;
      var r = n1.shiftRight(k);
      t = (t + 1) >> 1;
      if (t > lowprimes.length) t = lowprimes.length;
      var a = nbi();
      var j, bases = [];
      for (var i = 0; i < t; ++i) {
        //Pick bases at random, instead of starting at 2
        for (;;) {
          j = lowprimes[Math.floor(Math.random() * lowprimes.length)];
          if (bases.indexOf(j) == -1) break;
        }
        bases.push(j);
        a.fromInt(j);
        var y = a.modPow(r, this);
        if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
          var j = 1;
          while (j++ < k && y.compareTo(n1) != 0) {
            y = y.modPowInt(2, this);
            if (y.compareTo(BigInteger.ONE) == 0) return false;
          }
          if (y.compareTo(n1) != 0) return false;
        }
      }
      return true;
    }

    var BigInteger = require('./jsbn.js');

    // protected
    BigInteger.prototype.chunkSize = bnpChunkSize;
    BigInteger.prototype.toRadix = bnpToRadix;
    BigInteger.prototype.fromRadix = bnpFromRadix;
    BigInteger.prototype.fromNumber = bnpFromNumber;
    BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
    BigInteger.prototype.changeBit = bnpChangeBit;
    BigInteger.prototype.addTo = bnpAddTo;
    BigInteger.prototype.dMultiply = bnpDMultiply;
    BigInteger.prototype.dAddOffset = bnpDAddOffset;
    BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
    BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
    BigInteger.prototype.modInt = bnpModInt;
    BigInteger.prototype.millerRabin = bnpMillerRabin;

    // public
    BigInteger.prototype.clone = bnClone;
    BigInteger.prototype.intValue = bnIntValue;
    BigInteger.prototype.byteValue = bnByteValue;
    BigInteger.prototype.shortValue = bnShortValue;
    BigInteger.prototype.signum = bnSigNum;
    BigInteger.prototype.toByteArray = bnToByteArray;
    BigInteger.prototype.equals = bnEquals;
    BigInteger.prototype.min = bnMin;
    BigInteger.prototype.max = bnMax;
    BigInteger.prototype.and = bnAnd;
    BigInteger.prototype.or = bnOr;
    BigInteger.prototype.xor = bnXor;
    BigInteger.prototype.andNot = bnAndNot;
    BigInteger.prototype.not = bnNot;
    BigInteger.prototype.shiftLeft = bnShiftLeft;
    BigInteger.prototype.shiftRight = bnShiftRight;
    BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
    BigInteger.prototype.bitCount = bnBitCount;
    BigInteger.prototype.testBit = bnTestBit;
    BigInteger.prototype.setBit = bnSetBit;
    BigInteger.prototype.clearBit = bnClearBit;
    BigInteger.prototype.flipBit = bnFlipBit;
    BigInteger.prototype.add = bnAdd;
    BigInteger.prototype.subtract = bnSubtract;
    BigInteger.prototype.multiply = bnMultiply;
    BigInteger.prototype.divide = bnDivide;
    BigInteger.prototype.remainder = bnRemainder;
    BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
    BigInteger.prototype.modPow = bnModPow;
    BigInteger.prototype.modInverse = bnModInverse;
    BigInteger.prototype.pow = bnPow;
    BigInteger.prototype.gcd = bnGCD;
    BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
    BigInteger.prototype.toMPI = bnToMPI;

    // JSBN-specific extension
    BigInteger.prototype.square = bnSquare;