/*
 * Copyright (c) 2003-2005  Tom Wu
 * All Rights Reserved.
 *
 * 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.
 */

// The code has been adapted for use as a benchmark by Google.
var Crypto = new BenchmarkSuite("Crypto", 266181, [
  new Benchmark("Encrypt", encrypt),
  new Benchmark("Decrypt", decrypt),
]);

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

// Bits per digit
var dbits;
var BI_DB;
var BI_DM;
var BI_DV;

var BI_FP;
var BI_FV;
var BI_F1;
var BI_F2;

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

// (public) Constructor
function BigInteger(a, b, c) {
  this.array = new Array();
  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) {
  var this_array = this.array;
  var w_array = w.array;
  while (--n >= 0) {
    var v = x * this_array[i++] + w_array[j] + c;
    c = Math.floor(v / 0x4000000);
    w_array[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 this_array = this.array;
  var w_array = w.array;
  var xl = x & 0x7fff,
    xh = x >> 15;
  while (--n >= 0) {
    var l = this_array[i] & 0x7fff;
    var h = this_array[i++] >> 15;
    var m = xh * l + h * xl;
    l = xl * l + ((m & 0x7fff) << 15) + w_array[j] + (c & 0x3fffffff);
    c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);
    w_array[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 this_array = this.array;
  var w_array = w.array;

  var xl = x & 0x3fff,
    xh = x >> 14;
  while (--n >= 0) {
    var l = this_array[i] & 0x3fff;
    var h = this_array[i++] >> 14;
    var m = xh * l + h * xl;
    l = xl * l + ((m & 0x3fff) << 14) + w_array[j] + c;
    c = (l >> 28) + (m >> 14) + xh * h;
    w_array[j++] = l & 0xfffffff;
  }
  return c;
}

// This is tailored to VMs with 2-bit tagging. It makes sure
// that all the computations stay within the 29 bits available.
function am4(i, x, w, j, c, n) {
  var this_array = this.array;
  var w_array = w.array;

  var xl = x & 0x1fff,
    xh = x >> 13;
  while (--n >= 0) {
    var l = this_array[i] & 0x1fff;
    var h = this_array[i++] >> 13;
    var m = xh * l + h * xl;
    l = xl * l + ((m & 0x1fff) << 13) + w_array[j] + c;
    c = (l >> 26) + (m >> 13) + xh * h;
    w_array[j++] = l & 0x3ffffff;
  }
  return c;
}

// am3/28 is best for SM, Rhino, but am4/26 is best for v8.
// Kestrel (Opera 9.5) gets its best result with am4/26.
// IE7 does 9% better with am3/28 than with am4/26.
// Firefox (SM) gets 10% faster with am3/28 than with am4/26.

setupEngine = function (fn, bits) {
  BigInteger.prototype.am = fn;
  dbits = bits;

  BI_DB = dbits;
  BI_DM = (1 << dbits) - 1;
  BI_DV = 1 << dbits;

  BI_FP = 52;
  BI_FV = Math.pow(2, BI_FP);
  BI_F1 = BI_FP - dbits;
  BI_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) {
  var this_array = this.array;
  var r_array = r.array;

  for (var i = this.t - 1; i >= 0; --i) r_array[i] = this_array[i];
  r.t = this.t;
  r.s = this.s;
}

// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
  var this_array = this.array;
  this.t = 1;
  this.s = x < 0 ? -1 : 0;
  if (x > 0) this_array[0] = x;
  else if (x < -1) this_array[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 this_array = this.array;
  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_array[this.t++] = x;
    else if (sh + k > BI_DB) {
      this_array[this.t - 1] |= (x & ((1 << (BI_DB - sh)) - 1)) << sh;
      this_array[this.t++] = x >> (BI_DB - sh);
    } else this_array[this.t - 1] |= x << sh;
    sh += k;
    if (sh >= BI_DB) sh -= BI_DB;
  }
  if (k == 8 && (s[0] & 0x80) != 0) {
    this.s = -1;
    if (sh > 0) this_array[this.t - 1] |= ((1 << (BI_DB - sh)) - 1) << sh;
  }
  this.clamp();
  if (mi) BigInteger.ZERO.subTo(this, this);
}

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

// (public) return string representation in given radix
function bnToString(b) {
  var this_array = this.array;
  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 = BI_DB - ((i * BI_DB) % k);
  if (i-- > 0) {
    if (p < BI_DB && (d = this_array[i] >> p) > 0) {
      m = true;
      r = int2char(d);
    }
    while (i >= 0) {
      if (p < k) {
        d = (this_array[i] & ((1 << p) - 1)) << (k - p);
        d |= this_array[--i] >> (p += BI_DB - k);
      } else {
        d = (this_array[i] >> (p -= k)) & km;
        if (p <= 0) {
          p += BI_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 this_array = this.array;
  var a_array = a.array;

  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_array[i] - a_array[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() {
  var this_array = this.array;
  if (this.t <= 0) return 0;
  return (
    BI_DB * (this.t - 1) + nbits(this_array[this.t - 1] ^ (this.s & BI_DM))
  );
}

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

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

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

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

// (protected) r = this - a
function bnpSubTo(a, r) {
  var this_array = this.array;
  var r_array = r.array;
  var a_array = a.array;
  var i = 0,
    c = 0,
    m = Math.min(a.t, this.t);
  while (i < m) {
    c += this_array[i] - a_array[i];
    r_array[i++] = c & BI_DM;
    c >>= BI_DB;
  }
  if (a.t < this.t) {
    c -= a.s;
    while (i < this.t) {
      c += this_array[i];
      r_array[i++] = c & BI_DM;
      c >>= BI_DB;
    }
    c += this.s;
  } else {
    c += this.s;
    while (i < a.t) {
      c -= a_array[i];
      r_array[i++] = c & BI_DM;
      c >>= BI_DB;
    }
    c -= a.s;
  }
  r.s = c < 0 ? -1 : 0;
  if (c < -1) r_array[i++] = BI_DV + c;
  else if (c > 0) r_array[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 this_array = this.array;
  var r_array = r.array;
  var x = this.abs(),
    y = a.abs();
  var y_array = y.array;

  var i = x.t;
  r.t = i + y.t;
  while (--i >= 0) r_array[i] = 0;
  for (i = 0; i < y.t; ++i)
    r_array[i + x.t] = x.am(0, y_array[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 x_array = x.array;
  var r_array = r.array;

  var i = (r.t = 2 * x.t);
  while (--i >= 0) r_array[i] = 0;
  for (i = 0; i < x.t - 1; ++i) {
    var c = x.am(i, x_array[i], r, 2 * i, 0, 1);
    if (
      (r_array[i + x.t] += x.am(
        i + 1,
        2 * x_array[i],
        r,
        2 * i + 1,
        c,
        x.t - i - 1
      )) >= BI_DV
    ) {
      r_array[i + x.t] -= BI_DV;
      r_array[i + x.t + 1] = 1;
    }
  }
  if (r.t > 0) r_array[r.t - 1] += x.am(i, x_array[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 pm_array = pm.array;
  var nsh = BI_DB - nbits(pm_array[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 y_array = y.array;
  var y0 = y_array[ys - 1];
  if (y0 == 0) return;
  var yt = y0 * (1 << BI_F1) + (ys > 1 ? y_array[ys - 2] >> BI_F2 : 0);
  var d1 = BI_FV / yt,
    d2 = (1 << BI_F1) / yt,
    e = 1 << BI_F2;
  var i = r.t,
    j = i - ys,
    t = q == null ? nbi() : q;
  y.dlShiftTo(j, t);

  var r_array = r.array;
  if (r.compareTo(t) >= 0) {
    r_array[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_array[y.t++] = 0;
  while (--j >= 0) {
    // Estimate quotient digit
    var qd =
      r_array[--i] == y0
        ? BI_DM
        : Math.floor(r_array[i] * d1 + (r_array[i - 1] + e) * d2);
    if ((r_array[i] += y.am(0, qd, r, j, 0, ys)) < qd) {
      // Try it out
      y.dlShiftTo(j, t);
      r.subTo(t, r);
      while (r_array[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() {
  var this_array = this.array;
  if (this.t < 1) return 0;
  var x = this_array[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) % BI_DV))) % BI_DV; // y == 1/x mod 2^dbits
  // we really want the negative inverse, and -DV < y < DV
  return y > 0 ? BI_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 << (BI_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) {
  var x_array = x.array;
  while (x.t <= this.mt2)
    // pad x so am has enough room later
    x_array[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_array[i] & 0x7fff;
    var u0 =
      (j * this.mpl +
        (((j * this.mph + (x_array[i] >> 15) * this.mpl) & this.um) << 15)) &
      BI_DM;
    // use am to combine the multiply-shift-add into one call
    j = i + this.m.t;
    x_array[j] += this.m.am(0, u0, x, i, 0, this.m.t);
    // propagate carry
    while (x_array[j] >= BI_DV) {
      x_array[j] -= BI_DV;
      x_array[++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() {
  var this_array = this.array;
  return (this.t > 0 ? this_array[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);
// Copyright (c) 2005  Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.

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

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

// (public) return value as integer
function bnIntValue() {
  var this_array = this.array;
  if (this.s < 0) {
    if (this.t == 1) return this_array[0] - BI_DV;
    else if (this.t == 0) return -1;
  } else if (this.t == 1) return this_array[0];
  else if (this.t == 0) return 0;
  // assumes 16 < DB < 32
  return ((this_array[1] & ((1 << (32 - BI_DB)) - 1)) << BI_DB) | this_array[0];
}

// (public) return value as byte
function bnByteValue() {
  var this_array = this.array;
  return this.t == 0 ? this.s : (this_array[0] << 24) >> 24;
}

// (public) return value as short (assumes DB>=16)
function bnShortValue() {
  var this_array = this.array;
  return this.t == 0 ? this.s : (this_array[0] << 16) >> 16;
}

// (protected) return x s.t. r^x < DV
function bnpChunkSize(r) {
  return Math.floor((Math.LN2 * BI_DB) / Math.log(r));
}

// (public) 0 if this == 0, 1 if this > 0
function bnSigNum() {
  var this_array = this.array;
  if (this.s < 0) return -1;
  else if (this.t <= 0 || (this.t == 1 && this_array[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 this_array = this.array;
  var i = this.t,
    r = new Array();
  r[0] = this.s;
  var p = BI_DB - ((i * BI_DB) % 8),
    d,
    k = 0;
  if (i-- > 0) {
    if (p < BI_DB && (d = this_array[i] >> p) != (this.s & BI_DM) >> p)
      r[k++] = d | (this.s << (BI_DB - p));
    while (i >= 0) {
      if (p < 8) {
        d = (this_array[i] & ((1 << p) - 1)) << (8 - p);
        d |= this_array[--i] >> (p += BI_DB - 8);
      } else {
        d = (this_array[i] >> (p -= 8)) & 0xff;
        if (p <= 0) {
          p += BI_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 this_array = this.array;
  var a_array = a.array;
  var r_array = r.array;
  var i,
    f,
    m = Math.min(a.t, this.t);
  for (i = 0; i < m; ++i) r_array[i] = op(this_array[i], a_array[i]);
  if (a.t < this.t) {
    f = a.s & BI_DM;
    for (i = m; i < this.t; ++i) r_array[i] = op(this_array[i], f);
    r.t = this.t;
  } else {
    f = this.s & BI_DM;
    for (i = m; i < a.t; ++i) r_array[i] = op(f, a_array[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 this_array = this.array;
  var r = nbi();
  var r_array = r.array;

  for (var i = 0; i < this.t; ++i) r_array[i] = BI_DM & ~this_array[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() {
  var this_array = this.array;
  for (var i = 0; i < this.t; ++i)
    if (this_array[i] != 0) return i * BI_DB + lbit(this_array[i]);
  if (this.s < 0) return this.t * BI_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 & BI_DM;
  for (var i = 0; i < this.t; ++i) r += cbit(this_array[i] ^ x);
  return r;
}

// (public) true iff nth bit is set
function bnTestBit(n) {
  var this_array = this.array;
  var j = Math.floor(n / BI_DB);
  if (j >= this.t) return this.s != 0;
  return (this_array[j] & (1 << n % BI_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 this_array = this.array;
  var a_array = a.array;
  var r_array = r.array;
  var i = 0,
    c = 0,
    m = Math.min(a.t, this.t);
  while (i < m) {
    c += this_array[i] + a_array[i];
    r_array[i++] = c & BI_DM;
    c >>= BI_DB;
  }
  if (a.t < this.t) {
    c += a.s;
    while (i < this.t) {
      c += this_array[i];
      r_array[i++] = c & BI_DM;
      c >>= BI_DB;
    }
    c += this.s;
  } else {
    c += this.s;
    while (i < a.t) {
      c += a_array[i];
      r_array[i++] = c & BI_DM;
      c >>= BI_DB;
    }
    c += a.s;
  }
  r.s = c < 0 ? -1 : 0;
  if (c > 0) r_array[i++] = c;
  else if (c < -1) r_array[i++] = BI_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 / 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) {
  var this_array = this.array;
  this_array[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) {
  var this_array = this.array;
  while (this.t <= w) this_array[this.t++] = 0;
  this_array[w] += n;
  while (this_array[w] >= BI_DV) {
    this_array[w] -= BI_DV;
    if (++w >= this.t) this_array[this.t++] = 0;
    ++this_array[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 r_array = r.array;
  var a_array = a.array;
  var i = Math.min(this.t + a.t, n);
  r.s = 0; // assumes a,this >= 0
  r.t = i;
  while (i > 0) r_array[--i] = 0;
  var j;
  for (j = r.t - this.t; i < j; ++i)
    r_array[i + this.t] = this.am(0, a_array[i], r, i, 0, this.t);
  for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a_array[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) {
  var r_array = r.array;
  var a_array = a.array;
  --n;
  var i = (r.t = this.t + a.t - n);
  r.s = 0; // assumes a,this >= 0
  while (--i >= 0) r_array[i] = 0;
  for (i = Math.max(n - this.t, 0); i < a.t; ++i)
    r_array[this.t + i - n] = this.am(
      n - i,
      a_array[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 e_array = e.array;
  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_array[j]) - 1;
  while (j >= 0) {
    if (i >= k1) w = (e_array[j] >> (i - k1)) & km;
    else {
      w = (e_array[j] & ((1 << (i + 1)) - 1)) << (k1 - i);
      if (j > 0) w |= e_array[j - 1] >> (BI_DB + i - k1);
    }

    n = k;
    while ((w & 1) == 0) {
      w >>= 1;
      --n;
    }
    if ((i -= n) < 0) {
      i += BI_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_array[j] & (1 << i)) == 0) {
      z.sqrTo(r, r2);
      t = r;
      r = r2;
      r2 = t;
      if (--i < 0) {
        i = BI_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) {
  var this_array = this.array;
  if (n <= 0) return 0;
  var d = BI_DV % n,
    r = this.s < 0 ? n - 1 : 0;
  if (this.t > 0)
    if (d == 0) r = this_array[0] % n;
    else for (var i = this.t - 1; i >= 0; --i) r = (d * r + this_array[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,
];
var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];

// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
  var i,
    x = this.abs();
  var x_array = x.array;
  if (x.t == 1 && x_array[0] <= lowprimes[lowprimes.length - 1]) {
    for (i = 0; i < lowprimes.length; ++i)
      if (x_array[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);
}

// (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();
  for (var i = 0; i < t; ++i) {
    a.fromInt(lowprimes[i]);
    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;
}

// 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 interfaces not implemented in jsbn:

// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
// prng4.js - uses Arcfour as a PRNG

function Arcfour() {
  this.i = 0;
  this.j = 0;
  this.S = new Array();
}

// Initialize arcfour context from key, an array of ints, each from [0..255]
function ARC4init(key) {
  var i, j, t;
  for (i = 0; i < 256; ++i) this.S[i] = i;
  j = 0;
  for (i = 0; i < 256; ++i) {
    j = (j + this.S[i] + key[i % key.length]) & 255;
    t = this.S[i];
    this.S[i] = this.S[j];
    this.S[j] = t;
  }
  this.i = 0;
  this.j = 0;
}

function ARC4next() {
  var t;
  this.i = (this.i + 1) & 255;
  this.j = (this.j + this.S[this.i]) & 255;
  t = this.S[this.i];
  this.S[this.i] = this.S[this.j];
  this.S[this.j] = t;
  return this.S[(t + this.S[this.i]) & 255];
}

Arcfour.prototype.init = ARC4init;
Arcfour.prototype.next = ARC4next;

// Plug in your RNG constructor here
function prng_newstate() {
  return new Arcfour();
}

// Pool size must be a multiple of 4 and greater than 32.
// An array of bytes the size of the pool will be passed to init()
var rng_psize = 256;
// Random number generator - requires a PRNG backend, e.g. prng4.js

// For best results, put code like
// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
// in your main HTML document.

var rng_state;
var rng_pool;
var rng_pptr;

// Mix in a 32-bit integer into the pool
function rng_seed_int(x) {
  rng_pool[rng_pptr++] ^= x & 255;
  rng_pool[rng_pptr++] ^= (x >> 8) & 255;
  rng_pool[rng_pptr++] ^= (x >> 16) & 255;
  rng_pool[rng_pptr++] ^= (x >> 24) & 255;
  if (rng_pptr >= rng_psize) rng_pptr -= rng_psize;
}

// Mix in the current time (w/milliseconds) into the pool
function rng_seed_time() {
  // Use pre-computed date to avoid making the benchmark
  // results dependent on the current date.
  rng_seed_int(1122926989487);
}

// Initialize the pool with junk if needed.
if (rng_pool == null) {
  rng_pool = new Array();
  rng_pptr = 0;
  var t;
  while (rng_pptr < rng_psize) {
    // extract some randomness from Math.random()
    t = Math.floor(65536 * Math.random());
    rng_pool[rng_pptr++] = t >>> 8;
    rng_pool[rng_pptr++] = t & 255;
  }
  rng_pptr = 0;
  rng_seed_time();
  //rng_seed_int(window.screenX);
  //rng_seed_int(window.screenY);
}

function rng_get_byte() {
  if (rng_state == null) {
    rng_seed_time();
    rng_state = prng_newstate();
    rng_state.init(rng_pool);
    for (rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
      rng_pool[rng_pptr] = 0;
    rng_pptr = 0;
    //rng_pool = null;
  }
  // TODO: allow reseeding after first request
  return rng_state.next();
}

function rng_get_bytes(ba) {
  var i;
  for (i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
}

function SecureRandom() {}

SecureRandom.prototype.nextBytes = rng_get_bytes;
// Depends on jsbn.js and rng.js

// convert a (hex) string to a bignum object
function parseBigInt(str, r) {
  return new BigInteger(str, r);
}

function linebrk(s, n) {
  var ret = "";
  var i = 0;
  while (i + n < s.length) {
    ret += s.substring(i, i + n) + "\n";
    i += n;
  }
  return ret + s.substring(i, s.length);
}

function byte2Hex(b) {
  if (b < 0x10) return "0" + b.toString(16);
  else return b.toString(16);
}

// PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
function pkcs1pad2(s, n) {
  if (n < s.length + 11) {
    alert("Message too long for RSA");
    return null;
  }
  var ba = new Array();
  var i = s.length - 1;
  while (i >= 0 && n > 0) ba[--n] = s.charCodeAt(i--);
  ba[--n] = 0;
  var rng = new SecureRandom();
  var x = new Array();
  while (n > 2) {
    // random non-zero pad
    x[0] = 0;
    while (x[0] == 0) rng.nextBytes(x);
    ba[--n] = x[0];
  }
  ba[--n] = 2;
  ba[--n] = 0;
  return new BigInteger(ba);
}

// "empty" RSA key constructor
function RSAKey() {
  this.n = null;
  this.e = 0;
  this.d = null;
  this.p = null;
  this.q = null;
  this.dmp1 = null;
  this.dmq1 = null;
  this.coeff = null;
}

// Set the public key fields N and e from hex strings
function RSASetPublic(N, E) {
  if (N != null && E != null && N.length > 0 && E.length > 0) {
    this.n = parseBigInt(N, 16);
    this.e = parseInt(E, 16);
  } else alert("Invalid RSA public key");
}

// Perform raw public operation on "x": return x^e (mod n)
function RSADoPublic(x) {
  return x.modPowInt(this.e, this.n);
}

// Return the PKCS#1 RSA encryption of "text" as an even-length hex string
function RSAEncrypt(text) {
  var m = pkcs1pad2(text, (this.n.bitLength() + 7) >> 3);
  if (m == null) return null;
  var c = this.doPublic(m);
  if (c == null) return null;
  var h = c.toString(16);
  if ((h.length & 1) == 0) return h;
  else return "0" + h;
}

// Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
//function RSAEncryptB64(text) {
//  var h = this.encrypt(text);
//  if(h) return hex2b64(h); else return null;
//}

// protected
RSAKey.prototype.doPublic = RSADoPublic;

// public
RSAKey.prototype.setPublic = RSASetPublic;
RSAKey.prototype.encrypt = RSAEncrypt;
//RSAKey.prototype.encrypt_b64 = RSAEncryptB64;
// Depends on rsa.js and jsbn2.js

// Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
function pkcs1unpad2(d, n) {
  var b = d.toByteArray();
  var i = 0;
  while (i < b.length && b[i] == 0) ++i;
  if (b.length - i != n - 1 || b[i] != 2) return null;
  ++i;
  while (b[i] != 0) if (++i >= b.length) return null;
  var ret = "";
  while (++i < b.length) ret += String.fromCharCode(b[i]);
  return ret;
}

// Set the private key fields N, e, and d from hex strings
function RSASetPrivate(N, E, D) {
  if (N != null && E != null && N.length > 0 && E.length > 0) {
    this.n = parseBigInt(N, 16);
    this.e = parseInt(E, 16);
    this.d = parseBigInt(D, 16);
  } else alert("Invalid RSA private key");
}

// Set the private key fields N, e, d and CRT params from hex strings
function RSASetPrivateEx(N, E, D, P, Q, DP, DQ, C) {
  if (N != null && E != null && N.length > 0 && E.length > 0) {
    this.n = parseBigInt(N, 16);
    this.e = parseInt(E, 16);
    this.d = parseBigInt(D, 16);
    this.p = parseBigInt(P, 16);
    this.q = parseBigInt(Q, 16);
    this.dmp1 = parseBigInt(DP, 16);
    this.dmq1 = parseBigInt(DQ, 16);
    this.coeff = parseBigInt(C, 16);
  } else alert("Invalid RSA private key");
}

// Generate a new random private key B bits long, using public expt E
function RSAGenerate(B, E) {
  var rng = new SecureRandom();
  var qs = B >> 1;
  this.e = parseInt(E, 16);
  var ee = new BigInteger(E, 16);
  for (;;) {
    for (;;) {
      this.p = new BigInteger(B - qs, 1, rng);
      if (
        this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) ==
          0 &&
        this.p.isProbablePrime(10)
      )
        break;
    }
    for (;;) {
      this.q = new BigInteger(qs, 1, rng);
      if (
        this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) ==
          0 &&
        this.q.isProbablePrime(10)
      )
        break;
    }
    if (this.p.compareTo(this.q) <= 0) {
      var t = this.p;
      this.p = this.q;
      this.q = t;
    }
    var p1 = this.p.subtract(BigInteger.ONE);
    var q1 = this.q.subtract(BigInteger.ONE);
    var phi = p1.multiply(q1);
    if (phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
      this.n = this.p.multiply(this.q);
      this.d = ee.modInverse(phi);
      this.dmp1 = this.d.mod(p1);
      this.dmq1 = this.d.mod(q1);
      this.coeff = this.q.modInverse(this.p);
      break;
    }
  }
}

// Perform raw private operation on "x": return x^d (mod n)
function RSADoPrivate(x) {
  if (this.p == null || this.q == null) return x.modPow(this.d, this.n);

  // TODO: re-calculate any missing CRT params
  var xp = x.mod(this.p).modPow(this.dmp1, this.p);
  var xq = x.mod(this.q).modPow(this.dmq1, this.q);

  while (xp.compareTo(xq) < 0) xp = xp.add(this.p);
  return xp
    .subtract(xq)
    .multiply(this.coeff)
    .mod(this.p)
    .multiply(this.q)
    .add(xq);
}

// Return the PKCS#1 RSA decryption of "ctext".
// "ctext" is an even-length hex string and the output is a plain string.
function RSADecrypt(ctext) {
  var c = parseBigInt(ctext, 16);
  var m = this.doPrivate(c);
  if (m == null) return null;
  return pkcs1unpad2(m, (this.n.bitLength() + 7) >> 3);
}

// Return the PKCS#1 RSA decryption of "ctext".
// "ctext" is a Base64-encoded string and the output is a plain string.
//function RSAB64Decrypt(ctext) {
//  var h = b64tohex(ctext);
//  if(h) return this.decrypt(h); else return null;
//}

// protected
RSAKey.prototype.doPrivate = RSADoPrivate;

// public
RSAKey.prototype.setPrivate = RSASetPrivate;
RSAKey.prototype.setPrivateEx = RSASetPrivateEx;
RSAKey.prototype.generate = RSAGenerate;
RSAKey.prototype.decrypt = RSADecrypt;
//RSAKey.prototype.b64_decrypt = RSAB64Decrypt;

nValue =
  "a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3";
eValue = "10001";
dValue =
  "8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161";
pValue =
  "d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d";
qValue =
  "cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f";
dmp1Value =
  "1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25";
dmq1Value =
  "3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd";
coeffValue =
  "3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250";

setupEngine(am3, 28);

var TEXT =
  "The quick brown fox jumped over the extremely lazy frog! " +
  "Now is the time for all good men to come to the party.";
var encrypted;

function encrypt() {
  var RSA = new RSAKey();
  RSA.setPublic(nValue, eValue);
  RSA.setPrivateEx(
    nValue,
    eValue,
    dValue,
    pValue,
    qValue,
    dmp1Value,
    dmq1Value,
    coeffValue
  );
  encrypted = RSA.encrypt(TEXT);
}

function decrypt() {
  var RSA = new RSAKey();
  RSA.setPublic(nValue, eValue);
  RSA.setPrivateEx(
    nValue,
    eValue,
    dValue,
    pValue,
    qValue,
    dmp1Value,
    dmq1Value,
    coeffValue
  );
  var decrypted = RSA.decrypt(encrypted);
  if (decrypted != TEXT) {
    throw new Error("Crypto operation failed");
  }
}
