The Tor Browser: comparison js/src/jit-test/tests/v8-v5/check-crypto.js

comparison: js/src/jit-test/tests/v8-v5/check-crypto.js

js/src/jit-test/tests/v8-v5/check-crypto.js

changeset 0: 6474c204b198

equal deleted inserted replaced

--1:000000000000
+:f06fbb0e1481
+// |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");