tor-browser

check-crypto.js (49390B)

---

// |jit-test| slow;
// This test times out in rooting analyis builds, and so is marked slow so that
// it's not run as part of the rooting analysis tests on tinderbox.

/*
* 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', 203037, [
//  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);

// This is the best random number generator available to mankind ;)
var MyMath = {
   curr: 0,
   random: function() {
       this.curr = this.curr + 1;
       return this.curr;
   },
};


// (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 * MyMath.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);

// So that v8 understands assertEq()
if (assertEq == undefined)
{
   function assertEq(to_check, expected) {
       if ( to_check !== expected )
       {
           print( "Error: Assertion failed: got \"" + to_check + "\", expected \"" + expected + "\"" );
       }
   }
}

function check_correctness(text, hash) {
 var RSA = new RSAKey();
 RSA.setPublic(nValue, eValue);
 RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
 var encrypted = RSA.encrypt(text);
 var decrypted = RSA.decrypt(encrypted);
 assertEq( encrypted, hash );
 assertEq( decrypted, text );
}

// All 'correct' hashes here come from v8's javascript shell built off of tag 2.3.4
check_correctness("Hello! I am some text.", "142b19b40fee712ab9468be296447d38c7dfe81a7850f11ae6aa21e49396a4e90bd6ba4aa385105e15960a59f95447dfad89671da6e08ed42229939583753be84d07558abb4feee4d46a92fd31d962679a1a5f4bf0fb7af414b9a756e18df7e6d1e96971cc66769f3b27d61ad932f2211373e0de388dc040557d4c3c3fe74320");
check_correctness("PLEASE ENCRYPT ME. I AM TEXT. I AM DIEING TO BE ENCRYPTED. OH WHY WONT YOU ENCRYPT ME!?", "490c1fae87d7046296e4b34b357912a72cb7c38c0da3198f1ac3aad3489662ce02663ec5ea1be58ae73a275f3096b16c491f3520ebf822df6c65cc95e28be1cc0a4454dfba3fdd402c3a9de0db2f308989bfc1a7fada0dd680db76d24b2d96bd6b7e7d7e7f962deb953038bae06092f7bb9bcb40bba4ec92e040df32f98e035e");
check_correctness("x","46c1b7cf202171b1b588e9ecf250e768dcf3b300490e859d508f708e702ef799bc496b9fac7634d60a82644653c5fd25b808393b234567116b8890d5f119c7c74dae7c97c8e40ba78ca2dc3e3d78ce859a7fa3815f42c27d0607eafc3940896abb6019cc28b2ff875531ed581a6351728a8df0d607b7c2c26265bf3dddbe4f84");