The Tor Browser: js/src/v8/crypto.js@129ffea94266 (annotated)

js/src/v8/crypto.js@129ffea94266 (annotated)

js/src/v8/crypto.js

Sat, 03 Jan 2015 20:18:00 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Sat, 03 Jan 2015 20:18:00 +0100
branch: TOR_BUG_3246
changeset 7: 129ffea94266
permissions: -rw-r--r--

Conditionally enable double key logic according to:
private browsing mode or privacy.thirdparty.isolate preference and
implement in GetCookieStringCommon and FindCookie where it counts...
With some reservations of how to convince FindCookie users to test
condition and pass a nullptr when disabling double key logic.

 /*
  * 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");
   }
 }