jsbn.js

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

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

/*
Licensing (LICENSE)
-------------------

This software is covered under the following copyright:
*/
/*
 * 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.
 */
/*
Address all questions regarding this license to:

  Tom Wu
  tjw@cs.Stanford.EDU
*/
var forge = require('./forge');

module.exports = forge.jsbn = forge.jsbn || {};

// Bits per digit
var dbits;

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

// (public) Constructor
function BigInteger(a,b,c) {
  this.data = [];
  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);
}
forge.jsbn.BigInteger = BigInteger;

// 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.data[i++]+w.data[j]+c;
    c = Math.floor(v/0x4000000);
    w.data[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.data[i]&0x7fff;
    var h = this.data[i++]>>15;
    var m = xh*l+h*xl;
    l = xl*l+((m&0x7fff)<<15)+w.data[j]+(c&0x3fffffff);
    c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
    w.data[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.data[i]&0x3fff;
    var h = this.data[i++]>>14;
    var m = xh*l+h*xl;
    l = xl*l+((m&0x3fff)<<14)+w.data[j]+c;
    c = (l>>28)+(m>>14)+xh*h;
    w.data[j++] = l&0xfffffff;
  }
  return c;
}

// node.js (no browser)
if(typeof(navigator) === 'undefined')
{
   BigInteger.prototype.am = am3;
   dbits = 28;
} else if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
  BigInteger.prototype.am = am2;
  dbits = 30;
} else if(j_lm && (navigator.appName != "Netscape")) {
  BigInteger.prototype.am = am1;
  dbits = 26;
} else { // Mozilla/Netscape seems to prefer am3
  BigInteger.prototype.am = am3;
  dbits = 28;
}

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

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

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

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

// (protected) copy this to r
function bnpCopyTo(r) {
  for(var i = this.t-1; i >= 0; --i) r.data[i] = this.data[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.data[0] = x;
  else if(x < -1) this.data[0] = x+this.DV;
  else this.t = 0;
}

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

// (protected) set from string and radix
function bnpFromString(s,b) {
  var k;
  if(b == 16) k = 4;
  else if(b == 8) k = 3;
  else if(b == 256) k = 8; // byte array
  else if(b == 2) k = 1;
  else if(b == 32) k = 5;
  else if(b == 4) k = 2;
  else { this.fromRadix(s,b); return; }
  this.t = 0;
  this.s = 0;
  var i = s.length, mi = false, sh = 0;
  while(--i >= 0) {
    var x = (k==8)?s[i]&0xff:intAt(s,i);
    if(x < 0) {
      if(s.charAt(i) == "-") mi = true;
      continue;
    }
    mi = false;
    if(sh == 0)
      this.data[this.t++] = x;
    else if(sh+k > this.DB) {
      this.data[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
      this.data[this.t++] = (x>>(this.DB-sh));
    } else
      this.data[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.data[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.data[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.data[i]>>p) > 0) { m = true; r = int2char(d); }
    while(i >= 0) {
      if(p < k) {
        d = (this.data[i]&((1<<p)-1))<<(k-p);
        d |= this.data[--i]>>(p+=this.DB-k);
      } else {
        d = (this.data[i]>>(p-=k))&km;
        if(p <= 0) { p += this.DB; --i; }
      }
      if(d > 0) m = true;
      if(m) r += int2char(d);
    }
  }
  return m?r:"0";
}

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

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

// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
  var r = this.s-a.s;
  if(r != 0) return r;
  var i = this.t;
  r = i-a.t;
  if(r != 0) return (this.s<0)?-r:r;
  while(--i >= 0) if((r=this.data[i]-a.data[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.data[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.data[i+n] = this.data[i];
  for(i = n-1; i >= 0; --i) r.data[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.data[i-n] = this.data[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.data[i+ds+1] = (this.data[i]>>cbs)|c;
    c = (this.data[i]&bm)<<bs;
  }
  for(i = ds-1; i >= 0; --i) r.data[i] = 0;
  r.data[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.data[0] = this.data[ds]>>bs;
  for(var i = ds+1; i < this.t; ++i) {
    r.data[i-ds-1] |= (this.data[i]&bm)<<cbs;
    r.data[i-ds] = this.data[i]>>bs;
  }
  if(bs > 0) r.data[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.data[i]-a.data[i];
    r.data[i++] = c&this.DM;
    c >>= this.DB;
  }
  if(a.t < this.t) {
    c -= a.s;
    while(i < this.t) {
      c += this.data[i];
      r.data[i++] = c&this.DM;
      c >>= this.DB;
    }
    c += this.s;
  } else {
    c += this.s;
    while(i < a.t) {
      c -= a.data[i];
      r.data[i++] = c&this.DM;
      c >>= this.DB;
    }
    c -= a.s;
  }
  r.s = (c<0)?-1:0;
  if(c < -1) r.data[i++] = this.DV+c;
  else if(c > 0) r.data[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.data[i] = 0;
  for(i = 0; i < y.t; ++i) r.data[i+x.t] = x.am(0,y.data[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.data[i] = 0;
  for(i = 0; i < x.t-1; ++i) {
    var c = x.am(i,x.data[i],r,2*i,0,1);
    if((r.data[i+x.t]+=x.am(i+1,2*x.data[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
      r.data[i+x.t] -= x.DV;
      r.data[i+x.t+1] = 1;
    }
  }
  if(r.t > 0) r.data[r.t-1] += x.am(i,x.data[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.data[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.data[ys-1];
  if(y0 == 0) return;
  var yt = y0*(1<<this.F1)+((ys>1)?y.data[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.data[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.data[y.t++] = 0;
  while(--j >= 0) {
    // Estimate quotient digit
    var qd = (r.data[--i]==y0)?this.DM:Math.floor(r.data[i]*d1+(r.data[i-1]+e)*d2);
    if((r.data[i]+=y.am(0,qd,r,j,0,ys)) < qd) {	// Try it out
      y.dlShiftTo(j,t);
      r.subTo(t,r);
      while(r.data[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.data[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.data[x.t++] = 0;
  for(var i = 0; i < this.m.t; ++i) {
    // faster way of calculating u0 = x.data[i]*mp mod DV
    var j = x.data[i]&0x7fff;
    var u0 = (j*this.mpl+(((j*this.mph+(x.data[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.data[j] += this.m.am(0,u0,x,i,0,this.m.t);
    // propagate carry
    while(x.data[j] >= x.DV) { x.data[j] -= x.DV; x.data[++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.data[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);

// jsbn2 lib

//Copyright (c) 2005-2009  Tom Wu
//All Rights Reserved.
//See "LICENSE" for details (See jsbn.js for LICENSE).

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

//Version 1.1: new BigInteger("0", 10) returns "proper" zero

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

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

//(public) return value as short (assumes DB>=16)
function bnShortValue() { return (this.t==0)?this.s:(this.data[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.data[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.data[i]>>p) != (this.s&this.DM)>>p)
   r[k++] = d|(this.s<<(this.DB-p));
 while(i >= 0) {
   if(p < 8) {
     d = (this.data[i]&((1<<p)-1))<<(8-p);
     d |= this.data[--i]>>(p+=this.DB-8);
   } else {
     d = (this.data[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.data[i] = op(this.data[i],a.data[i]);
if(a.t < this.t) {
 f = a.s&this.DM;
 for(i = m; i < this.t; ++i) r.data[i] = op(this.data[i],f);
 r.t = this.t;
} else {
 f = this.s&this.DM;
 for(i = m; i < a.t; ++i) r.data[i] = op(f,a.data[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.data[i] = this.DM&~this.data[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.data[i] != 0) return i*this.DB+lbit(this.data[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.data[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.data[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.data[i]+a.data[i];
 r.data[i++] = c&this.DM;
 c >>= this.DB;
}
if(a.t < this.t) {
 c += a.s;
 while(i < this.t) {
   c += this.data[i];
   r.data[i++] = c&this.DM;
   c >>= this.DB;
 }
 c += this.s;
} else {
 c += this.s;
 while(i < a.t) {
   c += a.data[i];
   r.data[i++] = c&this.DM;
   c >>= this.DB;
 }
 c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r.data[i++] = c;
else if(c < -1) r.data[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 / 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.data[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.data[this.t++] = 0;
this.data[w] += n;
while(this.data[w] >= this.DV) {
 this.data[w] -= this.DV;
 if(++w >= this.t) this.data[this.t++] = 0;
 ++this.data[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.data[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r.data[i+this.t] = this.am(0,a.data[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a.data[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.data[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
 r.data[this.t+i-n] = this.am(n-i,a.data[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.data[j])-1;
while(j >= 0) {
 if(i >= k1) w = (e.data[j]>>(i-k1))&km;
 else {
   w = (e.data[j]&((1<<(i+1))-1))<<(k1-i);
   if(j > 0) w |= e.data[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.data[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.data[0]%n;
 else for(var i = this.t-1; i >= 0; --i) r = (d*r+this.data[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();
if(x.t == 1 && x.data[0] <= lowprimes[lowprimes.length-1]) {
 for(i = 0; i < lowprimes.length; ++i)
   if(x.data[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);
var prng = bnGetPrng();
var a;
for(var i = 0; i < t; ++i) {
 // select witness 'a' at random from between 1 and n1
 do {
   a = new BigInteger(this.bitLength(), prng);
 }
 while(a.compareTo(BigInteger.ONE) <= 0 || a.compareTo(n1) >= 0);
 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;
}

// get pseudo random number generator
function bnGetPrng() {
  // create prng with api that matches BigInteger secure random
  return {
    // x is an array to fill with bytes
    nextBytes: function(x) {
      for(var i = 0; i < x.length; ++i) {
        x[i] = Math.floor(Math.random() * 0x0100);
      }
    }
  };
}

//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)