The Tor Browser / file revision

 /*

  * 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");

   }

 }