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index.js (41819B)


      1 (function(){
      2 
      3     // Copyright (c) 2005  Tom Wu
      4     // All Rights Reserved.
      5     // See "LICENSE" for details.
      6 
      7     // Basic JavaScript BN library - subset useful for RSA encryption.
      8 
      9     // Bits per digit
     10     var dbits;
     11 
     12     // JavaScript engine analysis
     13     var canary = 0xdeadbeefcafe;
     14     var j_lm = ((canary&0xffffff)==0xefcafe);
     15 
     16     // (public) Constructor
     17     function BigInteger(a,b,c) {
     18       if(a != null)
     19         if("number" == typeof a) this.fromNumber(a,b,c);
     20         else if(b == null && "string" != typeof a) this.fromString(a,256);
     21         else this.fromString(a,b);
     22     }
     23 
     24     // return new, unset BigInteger
     25     function nbi() { return new BigInteger(null); }
     26 
     27     // am: Compute w_j += (x*this_i), propagate carries,
     28     // c is initial carry, returns final carry.
     29     // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
     30     // We need to select the fastest one that works in this environment.
     31 
     32     // am1: use a single mult and divide to get the high bits,
     33     // max digit bits should be 26 because
     34     // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
     35     function am1(i,x,w,j,c,n) {
     36       while(--n >= 0) {
     37         var v = x*this[i++]+w[j]+c;
     38         c = Math.floor(v/0x4000000);
     39         w[j++] = v&0x3ffffff;
     40       }
     41       return c;
     42     }
     43     // am2 avoids a big mult-and-extract completely.
     44     // Max digit bits should be <= 30 because we do bitwise ops
     45     // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
     46     function am2(i,x,w,j,c,n) {
     47       var xl = x&0x7fff, xh = x>>15;
     48       while(--n >= 0) {
     49         var l = this[i]&0x7fff;
     50         var h = this[i++]>>15;
     51         var m = xh*l+h*xl;
     52         l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
     53         c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
     54         w[j++] = l&0x3fffffff;
     55       }
     56       return c;
     57     }
     58     // Alternately, set max digit bits to 28 since some
     59     // browsers slow down when dealing with 32-bit numbers.
     60     function am3(i,x,w,j,c,n) {
     61       var xl = x&0x3fff, xh = x>>14;
     62       while(--n >= 0) {
     63         var l = this[i]&0x3fff;
     64         var h = this[i++]>>14;
     65         var m = xh*l+h*xl;
     66         l = xl*l+((m&0x3fff)<<14)+w[j]+c;
     67         c = (l>>28)+(m>>14)+xh*h;
     68         w[j++] = l&0xfffffff;
     69       }
     70       return c;
     71     }
     72     var inBrowser = typeof navigator !== "undefined";
     73     if(inBrowser && j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
     74       BigInteger.prototype.am = am2;
     75       dbits = 30;
     76     }
     77     else if(inBrowser && j_lm && (navigator.appName != "Netscape")) {
     78       BigInteger.prototype.am = am1;
     79       dbits = 26;
     80     }
     81     else { // Mozilla/Netscape seems to prefer am3
     82       BigInteger.prototype.am = am3;
     83       dbits = 28;
     84     }
     85 
     86     BigInteger.prototype.DB = dbits;
     87     BigInteger.prototype.DM = ((1<<dbits)-1);
     88     BigInteger.prototype.DV = (1<<dbits);
     89 
     90     var BI_FP = 52;
     91     BigInteger.prototype.FV = Math.pow(2,BI_FP);
     92     BigInteger.prototype.F1 = BI_FP-dbits;
     93     BigInteger.prototype.F2 = 2*dbits-BI_FP;
     94 
     95     // Digit conversions
     96     var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
     97     var BI_RC = new Array();
     98     var rr,vv;
     99     rr = "0".charCodeAt(0);
    100     for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
    101     rr = "a".charCodeAt(0);
    102     for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
    103     rr = "A".charCodeAt(0);
    104     for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
    105 
    106     function int2char(n) { return BI_RM.charAt(n); }
    107     function intAt(s,i) {
    108       var c = BI_RC[s.charCodeAt(i)];
    109       return (c==null)?-1:c;
    110     }
    111 
    112     // (protected) copy this to r
    113     function bnpCopyTo(r) {
    114       for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
    115       r.t = this.t;
    116       r.s = this.s;
    117     }
    118 
    119     // (protected) set from integer value x, -DV <= x < DV
    120     function bnpFromInt(x) {
    121       this.t = 1;
    122       this.s = (x<0)?-1:0;
    123       if(x > 0) this[0] = x;
    124       else if(x < -1) this[0] = x+this.DV;
    125       else this.t = 0;
    126     }
    127 
    128     // return bigint initialized to value
    129     function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
    130 
    131     // (protected) set from string and radix
    132     function bnpFromString(s,b) {
    133       var k;
    134       if(b == 16) k = 4;
    135       else if(b == 8) k = 3;
    136       else if(b == 256) k = 8; // byte array
    137       else if(b == 2) k = 1;
    138       else if(b == 32) k = 5;
    139       else if(b == 4) k = 2;
    140       else { this.fromRadix(s,b); return; }
    141       this.t = 0;
    142       this.s = 0;
    143       var i = s.length, mi = false, sh = 0;
    144       while(--i >= 0) {
    145         var x = (k==8)?s[i]&0xff:intAt(s,i);
    146         if(x < 0) {
    147           if(s.charAt(i) == "-") mi = true;
    148           continue;
    149         }
    150         mi = false;
    151         if(sh == 0)
    152           this[this.t++] = x;
    153         else if(sh+k > this.DB) {
    154           this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
    155           this[this.t++] = (x>>(this.DB-sh));
    156         }
    157         else
    158           this[this.t-1] |= x<<sh;
    159         sh += k;
    160         if(sh >= this.DB) sh -= this.DB;
    161       }
    162       if(k == 8 && (s[0]&0x80) != 0) {
    163         this.s = -1;
    164         if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
    165       }
    166       this.clamp();
    167       if(mi) BigInteger.ZERO.subTo(this,this);
    168     }
    169 
    170     // (protected) clamp off excess high words
    171     function bnpClamp() {
    172       var c = this.s&this.DM;
    173       while(this.t > 0 && this[this.t-1] == c) --this.t;
    174     }
    175 
    176     // (public) return string representation in given radix
    177     function bnToString(b) {
    178       if(this.s < 0) return "-"+this.negate().toString(b);
    179       var k;
    180       if(b == 16) k = 4;
    181       else if(b == 8) k = 3;
    182       else if(b == 2) k = 1;
    183       else if(b == 32) k = 5;
    184       else if(b == 4) k = 2;
    185       else return this.toRadix(b);
    186       var km = (1<<k)-1, d, m = false, r = "", i = this.t;
    187       var p = this.DB-(i*this.DB)%k;
    188       if(i-- > 0) {
    189         if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
    190         while(i >= 0) {
    191           if(p < k) {
    192             d = (this[i]&((1<<p)-1))<<(k-p);
    193             d |= this[--i]>>(p+=this.DB-k);
    194           }
    195           else {
    196             d = (this[i]>>(p-=k))&km;
    197             if(p <= 0) { p += this.DB; --i; }
    198           }
    199           if(d > 0) m = true;
    200           if(m) r += int2char(d);
    201         }
    202       }
    203       return m?r:"0";
    204     }
    205 
    206     // (public) -this
    207     function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
    208 
    209     // (public) |this|
    210     function bnAbs() { return (this.s<0)?this.negate():this; }
    211 
    212     // (public) return + if this > a, - if this < a, 0 if equal
    213     function bnCompareTo(a) {
    214       var r = this.s-a.s;
    215       if(r != 0) return r;
    216       var i = this.t;
    217       r = i-a.t;
    218       if(r != 0) return (this.s<0)?-r:r;
    219       while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
    220       return 0;
    221     }
    222 
    223     // returns bit length of the integer x
    224     function nbits(x) {
    225       var r = 1, t;
    226       if((t=x>>>16) != 0) { x = t; r += 16; }
    227       if((t=x>>8) != 0) { x = t; r += 8; }
    228       if((t=x>>4) != 0) { x = t; r += 4; }
    229       if((t=x>>2) != 0) { x = t; r += 2; }
    230       if((t=x>>1) != 0) { x = t; r += 1; }
    231       return r;
    232     }
    233 
    234     // (public) return the number of bits in "this"
    235     function bnBitLength() {
    236       if(this.t <= 0) return 0;
    237       return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
    238     }
    239 
    240     // (protected) r = this << n*DB
    241     function bnpDLShiftTo(n,r) {
    242       var i;
    243       for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
    244       for(i = n-1; i >= 0; --i) r[i] = 0;
    245       r.t = this.t+n;
    246       r.s = this.s;
    247     }
    248 
    249     // (protected) r = this >> n*DB
    250     function bnpDRShiftTo(n,r) {
    251       for(var i = n; i < this.t; ++i) r[i-n] = this[i];
    252       r.t = Math.max(this.t-n,0);
    253       r.s = this.s;
    254     }
    255 
    256     // (protected) r = this << n
    257     function bnpLShiftTo(n,r) {
    258       var bs = n%this.DB;
    259       var cbs = this.DB-bs;
    260       var bm = (1<<cbs)-1;
    261       var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
    262       for(i = this.t-1; i >= 0; --i) {
    263         r[i+ds+1] = (this[i]>>cbs)|c;
    264         c = (this[i]&bm)<<bs;
    265       }
    266       for(i = ds-1; i >= 0; --i) r[i] = 0;
    267       r[ds] = c;
    268       r.t = this.t+ds+1;
    269       r.s = this.s;
    270       r.clamp();
    271     }
    272 
    273     // (protected) r = this >> n
    274     function bnpRShiftTo(n,r) {
    275       r.s = this.s;
    276       var ds = Math.floor(n/this.DB);
    277       if(ds >= this.t) { r.t = 0; return; }
    278       var bs = n%this.DB;
    279       var cbs = this.DB-bs;
    280       var bm = (1<<bs)-1;
    281       r[0] = this[ds]>>bs;
    282       for(var i = ds+1; i < this.t; ++i) {
    283         r[i-ds-1] |= (this[i]&bm)<<cbs;
    284         r[i-ds] = this[i]>>bs;
    285       }
    286       if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
    287       r.t = this.t-ds;
    288       r.clamp();
    289     }
    290 
    291     // (protected) r = this - a
    292     function bnpSubTo(a,r) {
    293       var i = 0, c = 0, m = Math.min(a.t,this.t);
    294       while(i < m) {
    295         c += this[i]-a[i];
    296         r[i++] = c&this.DM;
    297         c >>= this.DB;
    298       }
    299       if(a.t < this.t) {
    300         c -= a.s;
    301         while(i < this.t) {
    302           c += this[i];
    303           r[i++] = c&this.DM;
    304           c >>= this.DB;
    305         }
    306         c += this.s;
    307       }
    308       else {
    309         c += this.s;
    310         while(i < a.t) {
    311           c -= a[i];
    312           r[i++] = c&this.DM;
    313           c >>= this.DB;
    314         }
    315         c -= a.s;
    316       }
    317       r.s = (c<0)?-1:0;
    318       if(c < -1) r[i++] = this.DV+c;
    319       else if(c > 0) r[i++] = c;
    320       r.t = i;
    321       r.clamp();
    322     }
    323 
    324     // (protected) r = this * a, r != this,a (HAC 14.12)
    325     // "this" should be the larger one if appropriate.
    326     function bnpMultiplyTo(a,r) {
    327       var x = this.abs(), y = a.abs();
    328       var i = x.t;
    329       r.t = i+y.t;
    330       while(--i >= 0) r[i] = 0;
    331       for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
    332       r.s = 0;
    333       r.clamp();
    334       if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
    335     }
    336 
    337     // (protected) r = this^2, r != this (HAC 14.16)
    338     function bnpSquareTo(r) {
    339       var x = this.abs();
    340       var i = r.t = 2*x.t;
    341       while(--i >= 0) r[i] = 0;
    342       for(i = 0; i < x.t-1; ++i) {
    343         var c = x.am(i,x[i],r,2*i,0,1);
    344         if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
    345           r[i+x.t] -= x.DV;
    346           r[i+x.t+1] = 1;
    347         }
    348       }
    349       if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
    350       r.s = 0;
    351       r.clamp();
    352     }
    353 
    354     // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
    355     // r != q, this != m.  q or r may be null.
    356     function bnpDivRemTo(m,q,r) {
    357       var pm = m.abs();
    358       if(pm.t <= 0) return;
    359       var pt = this.abs();
    360       if(pt.t < pm.t) {
    361         if(q != null) q.fromInt(0);
    362         if(r != null) this.copyTo(r);
    363         return;
    364       }
    365       if(r == null) r = nbi();
    366       var y = nbi(), ts = this.s, ms = m.s;
    367       var nsh = this.DB-nbits(pm[pm.t-1]);   // normalize modulus
    368       if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
    369       else { pm.copyTo(y); pt.copyTo(r); }
    370       var ys = y.t;
    371       var y0 = y[ys-1];
    372       if(y0 == 0) return;
    373       var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
    374       var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
    375       var i = r.t, j = i-ys, t = (q==null)?nbi():q;
    376       y.dlShiftTo(j,t);
    377       if(r.compareTo(t) >= 0) {
    378         r[r.t++] = 1;
    379         r.subTo(t,r);
    380       }
    381       BigInteger.ONE.dlShiftTo(ys,t);
    382       t.subTo(y,y);  // "negative" y so we can replace sub with am later
    383       while(y.t < ys) y[y.t++] = 0;
    384       while(--j >= 0) {
    385         // Estimate quotient digit
    386         var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
    387         if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) {   // Try it out
    388           y.dlShiftTo(j,t);
    389           r.subTo(t,r);
    390           while(r[i] < --qd) r.subTo(t,r);
    391         }
    392       }
    393       if(q != null) {
    394         r.drShiftTo(ys,q);
    395         if(ts != ms) BigInteger.ZERO.subTo(q,q);
    396       }
    397       r.t = ys;
    398       r.clamp();
    399       if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
    400       if(ts < 0) BigInteger.ZERO.subTo(r,r);
    401     }
    402 
    403     // (public) this mod a
    404     function bnMod(a) {
    405       var r = nbi();
    406       this.abs().divRemTo(a,null,r);
    407       if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
    408       return r;
    409     }
    410 
    411     // Modular reduction using "classic" algorithm
    412     function Classic(m) { this.m = m; }
    413     function cConvert(x) {
    414       if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
    415       else return x;
    416     }
    417     function cRevert(x) { return x; }
    418     function cReduce(x) { x.divRemTo(this.m,null,x); }
    419     function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
    420     function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
    421 
    422     Classic.prototype.convert = cConvert;
    423     Classic.prototype.revert = cRevert;
    424     Classic.prototype.reduce = cReduce;
    425     Classic.prototype.mulTo = cMulTo;
    426     Classic.prototype.sqrTo = cSqrTo;
    427 
    428     // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
    429     // justification:
    430     //         xy == 1 (mod m)
    431     //         xy =  1+km
    432     //   xy(2-xy) = (1+km)(1-km)
    433     // x[y(2-xy)] = 1-k^2m^2
    434     // x[y(2-xy)] == 1 (mod m^2)
    435     // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
    436     // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
    437     // JS multiply "overflows" differently from C/C++, so care is needed here.
    438     function bnpInvDigit() {
    439       if(this.t < 1) return 0;
    440       var x = this[0];
    441       if((x&1) == 0) return 0;
    442       var y = x&3;       // y == 1/x mod 2^2
    443       y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
    444       y = (y*(2-(x&0xff)*y))&0xff;   // y == 1/x mod 2^8
    445       y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;    // y == 1/x mod 2^16
    446       // last step - calculate inverse mod DV directly;
    447       // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
    448       y = (y*(2-x*y%this.DV))%this.DV;       // y == 1/x mod 2^dbits
    449       // we really want the negative inverse, and -DV < y < DV
    450       return (y>0)?this.DV-y:-y;
    451     }
    452 
    453     // Montgomery reduction
    454     function Montgomery(m) {
    455       this.m = m;
    456       this.mp = m.invDigit();
    457       this.mpl = this.mp&0x7fff;
    458       this.mph = this.mp>>15;
    459       this.um = (1<<(m.DB-15))-1;
    460       this.mt2 = 2*m.t;
    461     }
    462 
    463     // xR mod m
    464     function montConvert(x) {
    465       var r = nbi();
    466       x.abs().dlShiftTo(this.m.t,r);
    467       r.divRemTo(this.m,null,r);
    468       if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
    469       return r;
    470     }
    471 
    472     // x/R mod m
    473     function montRevert(x) {
    474       var r = nbi();
    475       x.copyTo(r);
    476       this.reduce(r);
    477       return r;
    478     }
    479 
    480     // x = x/R mod m (HAC 14.32)
    481     function montReduce(x) {
    482       while(x.t <= this.mt2) // pad x so am has enough room later
    483         x[x.t++] = 0;
    484       for(var i = 0; i < this.m.t; ++i) {
    485         // faster way of calculating u0 = x[i]*mp mod DV
    486         var j = x[i]&0x7fff;
    487         var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
    488         // use am to combine the multiply-shift-add into one call
    489         j = i+this.m.t;
    490         x[j] += this.m.am(0,u0,x,i,0,this.m.t);
    491         // propagate carry
    492         while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
    493       }
    494       x.clamp();
    495       x.drShiftTo(this.m.t,x);
    496       if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
    497     }
    498 
    499     // r = "x^2/R mod m"; x != r
    500     function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
    501 
    502     // r = "xy/R mod m"; x,y != r
    503     function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
    504 
    505     Montgomery.prototype.convert = montConvert;
    506     Montgomery.prototype.revert = montRevert;
    507     Montgomery.prototype.reduce = montReduce;
    508     Montgomery.prototype.mulTo = montMulTo;
    509     Montgomery.prototype.sqrTo = montSqrTo;
    510 
    511     // (protected) true iff this is even
    512     function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
    513 
    514     // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
    515     function bnpExp(e,z) {
    516       if(e > 0xffffffff || e < 1) return BigInteger.ONE;
    517       var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
    518       g.copyTo(r);
    519       while(--i >= 0) {
    520         z.sqrTo(r,r2);
    521         if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
    522         else { var t = r; r = r2; r2 = t; }
    523       }
    524       return z.revert(r);
    525     }
    526 
    527     // (public) this^e % m, 0 <= e < 2^32
    528     function bnModPowInt(e,m) {
    529       var z;
    530       if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
    531       return this.exp(e,z);
    532     }
    533 
    534     // protected
    535     BigInteger.prototype.copyTo = bnpCopyTo;
    536     BigInteger.prototype.fromInt = bnpFromInt;
    537     BigInteger.prototype.fromString = bnpFromString;
    538     BigInteger.prototype.clamp = bnpClamp;
    539     BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
    540     BigInteger.prototype.drShiftTo = bnpDRShiftTo;
    541     BigInteger.prototype.lShiftTo = bnpLShiftTo;
    542     BigInteger.prototype.rShiftTo = bnpRShiftTo;
    543     BigInteger.prototype.subTo = bnpSubTo;
    544     BigInteger.prototype.multiplyTo = bnpMultiplyTo;
    545     BigInteger.prototype.squareTo = bnpSquareTo;
    546     BigInteger.prototype.divRemTo = bnpDivRemTo;
    547     BigInteger.prototype.invDigit = bnpInvDigit;
    548     BigInteger.prototype.isEven = bnpIsEven;
    549     BigInteger.prototype.exp = bnpExp;
    550 
    551     // public
    552     BigInteger.prototype.toString = bnToString;
    553     BigInteger.prototype.negate = bnNegate;
    554     BigInteger.prototype.abs = bnAbs;
    555     BigInteger.prototype.compareTo = bnCompareTo;
    556     BigInteger.prototype.bitLength = bnBitLength;
    557     BigInteger.prototype.mod = bnMod;
    558     BigInteger.prototype.modPowInt = bnModPowInt;
    559 
    560     // "constants"
    561     BigInteger.ZERO = nbv(0);
    562     BigInteger.ONE = nbv(1);
    563 
    564     // Copyright (c) 2005-2009  Tom Wu
    565     // All Rights Reserved.
    566     // See "LICENSE" for details.
    567 
    568     // Extended JavaScript BN functions, required for RSA private ops.
    569 
    570     // Version 1.1: new BigInteger("0", 10) returns "proper" zero
    571     // Version 1.2: square() API, isProbablePrime fix
    572 
    573     // (public)
    574     function bnClone() { var r = nbi(); this.copyTo(r); return r; }
    575 
    576     // (public) return value as integer
    577     function bnIntValue() {
    578       if(this.s < 0) {
    579         if(this.t == 1) return this[0]-this.DV;
    580         else if(this.t == 0) return -1;
    581       }
    582       else if(this.t == 1) return this[0];
    583       else if(this.t == 0) return 0;
    584       // assumes 16 < DB < 32
    585       return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
    586     }
    587 
    588     // (public) return value as byte
    589     function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
    590 
    591     // (public) return value as short (assumes DB>=16)
    592     function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
    593 
    594     // (protected) return x s.t. r^x < DV
    595     function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }
    596 
    597     // (public) 0 if this == 0, 1 if this > 0
    598     function bnSigNum() {
    599       if(this.s < 0) return -1;
    600       else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
    601       else return 1;
    602     }
    603 
    604     // (protected) convert to radix string
    605     function bnpToRadix(b) {
    606       if(b == null) b = 10;
    607       if(this.signum() == 0 || b < 2 || b > 36) return "0";
    608       var cs = this.chunkSize(b);
    609       var a = Math.pow(b,cs);
    610       var d = nbv(a), y = nbi(), z = nbi(), r = "";
    611       this.divRemTo(d,y,z);
    612       while(y.signum() > 0) {
    613         r = (a+z.intValue()).toString(b).substr(1) + r;
    614         y.divRemTo(d,y,z);
    615       }
    616       return z.intValue().toString(b) + r;
    617     }
    618 
    619     // (protected) convert from radix string
    620     function bnpFromRadix(s,b) {
    621       this.fromInt(0);
    622       if(b == null) b = 10;
    623       var cs = this.chunkSize(b);
    624       var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
    625       for(var i = 0; i < s.length; ++i) {
    626         var x = intAt(s,i);
    627         if(x < 0) {
    628           if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
    629           continue;
    630         }
    631         w = b*w+x;
    632         if(++j >= cs) {
    633           this.dMultiply(d);
    634           this.dAddOffset(w,0);
    635           j = 0;
    636           w = 0;
    637         }
    638       }
    639       if(j > 0) {
    640         this.dMultiply(Math.pow(b,j));
    641         this.dAddOffset(w,0);
    642       }
    643       if(mi) BigInteger.ZERO.subTo(this,this);
    644     }
    645 
    646     // (protected) alternate constructor
    647     function bnpFromNumber(a,b,c) {
    648       if("number" == typeof b) {
    649         // new BigInteger(int,int,RNG)
    650         if(a < 2) this.fromInt(1);
    651         else {
    652           this.fromNumber(a,c);
    653           if(!this.testBit(a-1))	// force MSB set
    654             this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
    655           if(this.isEven()) this.dAddOffset(1,0); // force odd
    656           while(!this.isProbablePrime(b)) {
    657             this.dAddOffset(2,0);
    658             if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
    659           }
    660         }
    661       }
    662       else {
    663         // new BigInteger(int,RNG)
    664         var x = new Array(), t = a&7;
    665         x.length = (a>>3)+1;
    666         b.nextBytes(x);
    667         if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
    668         this.fromString(x,256);
    669       }
    670     }
    671 
    672     // (public) convert to bigendian byte array
    673     function bnToByteArray() {
    674       var i = this.t, r = new Array();
    675       r[0] = this.s;
    676       var p = this.DB-(i*this.DB)%8, d, k = 0;
    677       if(i-- > 0) {
    678         if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
    679           r[k++] = d|(this.s<<(this.DB-p));
    680         while(i >= 0) {
    681           if(p < 8) {
    682             d = (this[i]&((1<<p)-1))<<(8-p);
    683             d |= this[--i]>>(p+=this.DB-8);
    684           }
    685           else {
    686             d = (this[i]>>(p-=8))&0xff;
    687             if(p <= 0) { p += this.DB; --i; }
    688           }
    689           if((d&0x80) != 0) d |= -256;
    690           if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
    691           if(k > 0 || d != this.s) r[k++] = d;
    692         }
    693       }
    694       return r;
    695     }
    696 
    697     function bnEquals(a) { return(this.compareTo(a)==0); }
    698     function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
    699     function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
    700 
    701     // (protected) r = this op a (bitwise)
    702     function bnpBitwiseTo(a,op,r) {
    703       var i, f, m = Math.min(a.t,this.t);
    704       for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
    705       if(a.t < this.t) {
    706         f = a.s&this.DM;
    707         for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
    708         r.t = this.t;
    709       }
    710       else {
    711         f = this.s&this.DM;
    712         for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
    713         r.t = a.t;
    714       }
    715       r.s = op(this.s,a.s);
    716       r.clamp();
    717     }
    718 
    719     // (public) this & a
    720     function op_and(x,y) { return x&y; }
    721     function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
    722 
    723     // (public) this | a
    724     function op_or(x,y) { return x|y; }
    725     function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
    726 
    727     // (public) this ^ a
    728     function op_xor(x,y) { return x^y; }
    729     function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
    730 
    731     // (public) this & ~a
    732     function op_andnot(x,y) { return x&~y; }
    733     function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
    734 
    735     // (public) ~this
    736     function bnNot() {
    737       var r = nbi();
    738       for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
    739       r.t = this.t;
    740       r.s = ~this.s;
    741       return r;
    742     }
    743 
    744     // (public) this << n
    745     function bnShiftLeft(n) {
    746       var r = nbi();
    747       if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
    748       return r;
    749     }
    750 
    751     // (public) this >> n
    752     function bnShiftRight(n) {
    753       var r = nbi();
    754       if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
    755       return r;
    756     }
    757 
    758     // return index of lowest 1-bit in x, x < 2^31
    759     function lbit(x) {
    760       if(x == 0) return -1;
    761       var r = 0;
    762       if((x&0xffff) == 0) { x >>= 16; r += 16; }
    763       if((x&0xff) == 0) { x >>= 8; r += 8; }
    764       if((x&0xf) == 0) { x >>= 4; r += 4; }
    765       if((x&3) == 0) { x >>= 2; r += 2; }
    766       if((x&1) == 0) ++r;
    767       return r;
    768     }
    769 
    770     // (public) returns index of lowest 1-bit (or -1 if none)
    771     function bnGetLowestSetBit() {
    772       for(var i = 0; i < this.t; ++i)
    773         if(this[i] != 0) return i*this.DB+lbit(this[i]);
    774       if(this.s < 0) return this.t*this.DB;
    775       return -1;
    776     }
    777 
    778     // return number of 1 bits in x
    779     function cbit(x) {
    780       var r = 0;
    781       while(x != 0) { x &= x-1; ++r; }
    782       return r;
    783     }
    784 
    785     // (public) return number of set bits
    786     function bnBitCount() {
    787       var r = 0, x = this.s&this.DM;
    788       for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
    789       return r;
    790     }
    791 
    792     // (public) true iff nth bit is set
    793     function bnTestBit(n) {
    794       var j = Math.floor(n/this.DB);
    795       if(j >= this.t) return(this.s!=0);
    796       return((this[j]&(1<<(n%this.DB)))!=0);
    797     }
    798 
    799     // (protected) this op (1<<n)
    800     function bnpChangeBit(n,op) {
    801       var r = BigInteger.ONE.shiftLeft(n);
    802       this.bitwiseTo(r,op,r);
    803       return r;
    804     }
    805 
    806     // (public) this | (1<<n)
    807     function bnSetBit(n) { return this.changeBit(n,op_or); }
    808 
    809     // (public) this & ~(1<<n)
    810     function bnClearBit(n) { return this.changeBit(n,op_andnot); }
    811 
    812     // (public) this ^ (1<<n)
    813     function bnFlipBit(n) { return this.changeBit(n,op_xor); }
    814 
    815     // (protected) r = this + a
    816     function bnpAddTo(a,r) {
    817       var i = 0, c = 0, m = Math.min(a.t,this.t);
    818       while(i < m) {
    819         c += this[i]+a[i];
    820         r[i++] = c&this.DM;
    821         c >>= this.DB;
    822       }
    823       if(a.t < this.t) {
    824         c += a.s;
    825         while(i < this.t) {
    826           c += this[i];
    827           r[i++] = c&this.DM;
    828           c >>= this.DB;
    829         }
    830         c += this.s;
    831       }
    832       else {
    833         c += this.s;
    834         while(i < a.t) {
    835           c += a[i];
    836           r[i++] = c&this.DM;
    837           c >>= this.DB;
    838         }
    839         c += a.s;
    840       }
    841       r.s = (c<0)?-1:0;
    842       if(c > 0) r[i++] = c;
    843       else if(c < -1) r[i++] = this.DV+c;
    844       r.t = i;
    845       r.clamp();
    846     }
    847 
    848     // (public) this + a
    849     function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
    850 
    851     // (public) this - a
    852     function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
    853 
    854     // (public) this * a
    855     function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
    856 
    857     // (public) this^2
    858     function bnSquare() { var r = nbi(); this.squareTo(r); return r; }
    859 
    860     // (public) this / a
    861     function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
    862 
    863     // (public) this % a
    864     function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
    865 
    866     // (public) [this/a,this%a]
    867     function bnDivideAndRemainder(a) {
    868       var q = nbi(), r = nbi();
    869       this.divRemTo(a,q,r);
    870       return new Array(q,r);
    871     }
    872 
    873     // (protected) this *= n, this >= 0, 1 < n < DV
    874     function bnpDMultiply(n) {
    875       this[this.t] = this.am(0,n-1,this,0,0,this.t);
    876       ++this.t;
    877       this.clamp();
    878     }
    879 
    880     // (protected) this += n << w words, this >= 0
    881     function bnpDAddOffset(n,w) {
    882       if(n == 0) return;
    883       while(this.t <= w) this[this.t++] = 0;
    884       this[w] += n;
    885       while(this[w] >= this.DV) {
    886         this[w] -= this.DV;
    887         if(++w >= this.t) this[this.t++] = 0;
    888         ++this[w];
    889       }
    890     }
    891 
    892     // A "null" reducer
    893     function NullExp() {}
    894     function nNop(x) { return x; }
    895     function nMulTo(x,y,r) { x.multiplyTo(y,r); }
    896     function nSqrTo(x,r) { x.squareTo(r); }
    897 
    898     NullExp.prototype.convert = nNop;
    899     NullExp.prototype.revert = nNop;
    900     NullExp.prototype.mulTo = nMulTo;
    901     NullExp.prototype.sqrTo = nSqrTo;
    902 
    903     // (public) this^e
    904     function bnPow(e) { return this.exp(e,new NullExp()); }
    905 
    906     // (protected) r = lower n words of "this * a", a.t <= n
    907     // "this" should be the larger one if appropriate.
    908     function bnpMultiplyLowerTo(a,n,r) {
    909       var i = Math.min(this.t+a.t,n);
    910       r.s = 0; // assumes a,this >= 0
    911       r.t = i;
    912       while(i > 0) r[--i] = 0;
    913       var j;
    914       for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
    915       for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
    916       r.clamp();
    917     }
    918 
    919     // (protected) r = "this * a" without lower n words, n > 0
    920     // "this" should be the larger one if appropriate.
    921     function bnpMultiplyUpperTo(a,n,r) {
    922       --n;
    923       var i = r.t = this.t+a.t-n;
    924       r.s = 0; // assumes a,this >= 0
    925       while(--i >= 0) r[i] = 0;
    926       for(i = Math.max(n-this.t,0); i < a.t; ++i)
    927         r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
    928       r.clamp();
    929       r.drShiftTo(1,r);
    930     }
    931 
    932     // Barrett modular reduction
    933     function Barrett(m) {
    934       // setup Barrett
    935       this.r2 = nbi();
    936       this.q3 = nbi();
    937       BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
    938       this.mu = this.r2.divide(m);
    939       this.m = m;
    940     }
    941 
    942     function barrettConvert(x) {
    943       if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
    944       else if(x.compareTo(this.m) < 0) return x;
    945       else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
    946     }
    947 
    948     function barrettRevert(x) { return x; }
    949 
    950     // x = x mod m (HAC 14.42)
    951     function barrettReduce(x) {
    952       x.drShiftTo(this.m.t-1,this.r2);
    953       if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
    954       this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
    955       this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
    956       while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
    957       x.subTo(this.r2,x);
    958       while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
    959     }
    960 
    961     // r = x^2 mod m; x != r
    962     function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
    963 
    964     // r = x*y mod m; x,y != r
    965     function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
    966 
    967     Barrett.prototype.convert = barrettConvert;
    968     Barrett.prototype.revert = barrettRevert;
    969     Barrett.prototype.reduce = barrettReduce;
    970     Barrett.prototype.mulTo = barrettMulTo;
    971     Barrett.prototype.sqrTo = barrettSqrTo;
    972 
    973     // (public) this^e % m (HAC 14.85)
    974     function bnModPow(e,m) {
    975       var i = e.bitLength(), k, r = nbv(1), z;
    976       if(i <= 0) return r;
    977       else if(i < 18) k = 1;
    978       else if(i < 48) k = 3;
    979       else if(i < 144) k = 4;
    980       else if(i < 768) k = 5;
    981       else k = 6;
    982       if(i < 8)
    983         z = new Classic(m);
    984       else if(m.isEven())
    985         z = new Barrett(m);
    986       else
    987         z = new Montgomery(m);
    988 
    989       // precomputation
    990       var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
    991       g[1] = z.convert(this);
    992       if(k > 1) {
    993         var g2 = nbi();
    994         z.sqrTo(g[1],g2);
    995         while(n <= km) {
    996           g[n] = nbi();
    997           z.mulTo(g2,g[n-2],g[n]);
    998           n += 2;
    999         }
   1000       }
   1001 
   1002       var j = e.t-1, w, is1 = true, r2 = nbi(), t;
   1003       i = nbits(e[j])-1;
   1004       while(j >= 0) {
   1005         if(i >= k1) w = (e[j]>>(i-k1))&km;
   1006         else {
   1007           w = (e[j]&((1<<(i+1))-1))<<(k1-i);
   1008           if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
   1009         }
   1010 
   1011         n = k;
   1012         while((w&1) == 0) { w >>= 1; --n; }
   1013         if((i -= n) < 0) { i += this.DB; --j; }
   1014         if(is1) {	// ret == 1, don't bother squaring or multiplying it
   1015           g[w].copyTo(r);
   1016           is1 = false;
   1017         }
   1018         else {
   1019           while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
   1020           if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
   1021           z.mulTo(r2,g[w],r);
   1022         }
   1023 
   1024         while(j >= 0 && (e[j]&(1<<i)) == 0) {
   1025           z.sqrTo(r,r2); t = r; r = r2; r2 = t;
   1026           if(--i < 0) { i = this.DB-1; --j; }
   1027         }
   1028       }
   1029       return z.revert(r);
   1030     }
   1031 
   1032     // (public) gcd(this,a) (HAC 14.54)
   1033     function bnGCD(a) {
   1034       var x = (this.s<0)?this.negate():this.clone();
   1035       var y = (a.s<0)?a.negate():a.clone();
   1036       if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
   1037       var i = x.getLowestSetBit(), g = y.getLowestSetBit();
   1038       if(g < 0) return x;
   1039       if(i < g) g = i;
   1040       if(g > 0) {
   1041         x.rShiftTo(g,x);
   1042         y.rShiftTo(g,y);
   1043       }
   1044       while(x.signum() > 0) {
   1045         if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
   1046         if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
   1047         if(x.compareTo(y) >= 0) {
   1048           x.subTo(y,x);
   1049           x.rShiftTo(1,x);
   1050         }
   1051         else {
   1052           y.subTo(x,y);
   1053           y.rShiftTo(1,y);
   1054         }
   1055       }
   1056       if(g > 0) y.lShiftTo(g,y);
   1057       return y;
   1058     }
   1059 
   1060     // (protected) this % n, n < 2^26
   1061     function bnpModInt(n) {
   1062       if(n <= 0) return 0;
   1063       var d = this.DV%n, r = (this.s<0)?n-1:0;
   1064       if(this.t > 0)
   1065         if(d == 0) r = this[0]%n;
   1066         else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
   1067       return r;
   1068     }
   1069 
   1070     // (public) 1/this % m (HAC 14.61)
   1071     function bnModInverse(m) {
   1072       var ac = m.isEven();
   1073       if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
   1074       var u = m.clone(), v = this.clone();
   1075       var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
   1076       while(u.signum() != 0) {
   1077         while(u.isEven()) {
   1078           u.rShiftTo(1,u);
   1079           if(ac) {
   1080             if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
   1081             a.rShiftTo(1,a);
   1082           }
   1083           else if(!b.isEven()) b.subTo(m,b);
   1084           b.rShiftTo(1,b);
   1085         }
   1086         while(v.isEven()) {
   1087           v.rShiftTo(1,v);
   1088           if(ac) {
   1089             if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
   1090             c.rShiftTo(1,c);
   1091           }
   1092           else if(!d.isEven()) d.subTo(m,d);
   1093           d.rShiftTo(1,d);
   1094         }
   1095         if(u.compareTo(v) >= 0) {
   1096           u.subTo(v,u);
   1097           if(ac) a.subTo(c,a);
   1098           b.subTo(d,b);
   1099         }
   1100         else {
   1101           v.subTo(u,v);
   1102           if(ac) c.subTo(a,c);
   1103           d.subTo(b,d);
   1104         }
   1105       }
   1106       if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
   1107       if(d.compareTo(m) >= 0) return d.subtract(m);
   1108       if(d.signum() < 0) d.addTo(m,d); else return d;
   1109       if(d.signum() < 0) return d.add(m); else return d;
   1110     }
   1111 
   1112     var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997];
   1113     var lplim = (1<<26)/lowprimes[lowprimes.length-1];
   1114 
   1115     // (public) test primality with certainty >= 1-.5^t
   1116     function bnIsProbablePrime(t) {
   1117       var i, x = this.abs();
   1118       if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
   1119         for(i = 0; i < lowprimes.length; ++i)
   1120           if(x[0] == lowprimes[i]) return true;
   1121         return false;
   1122       }
   1123       if(x.isEven()) return false;
   1124       i = 1;
   1125       while(i < lowprimes.length) {
   1126         var m = lowprimes[i], j = i+1;
   1127         while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
   1128         m = x.modInt(m);
   1129         while(i < j) if(m%lowprimes[i++] == 0) return false;
   1130       }
   1131       return x.millerRabin(t);
   1132     }
   1133 
   1134     // (protected) true if probably prime (HAC 4.24, Miller-Rabin)
   1135     function bnpMillerRabin(t) {
   1136       var n1 = this.subtract(BigInteger.ONE);
   1137       var k = n1.getLowestSetBit();
   1138       if(k <= 0) return false;
   1139       var r = n1.shiftRight(k);
   1140       t = (t+1)>>1;
   1141       if(t > lowprimes.length) t = lowprimes.length;
   1142       var a = nbi();
   1143       for(var i = 0; i < t; ++i) {
   1144         //Pick bases at random, instead of starting at 2
   1145         a.fromInt(lowprimes[Math.floor(Math.random()*lowprimes.length)]);
   1146         var y = a.modPow(r,this);
   1147         if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
   1148           var j = 1;
   1149           while(j++ < k && y.compareTo(n1) != 0) {
   1150             y = y.modPowInt(2,this);
   1151             if(y.compareTo(BigInteger.ONE) == 0) return false;
   1152           }
   1153           if(y.compareTo(n1) != 0) return false;
   1154         }
   1155       }
   1156       return true;
   1157     }
   1158 
   1159     // protected
   1160     BigInteger.prototype.chunkSize = bnpChunkSize;
   1161     BigInteger.prototype.toRadix = bnpToRadix;
   1162     BigInteger.prototype.fromRadix = bnpFromRadix;
   1163     BigInteger.prototype.fromNumber = bnpFromNumber;
   1164     BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
   1165     BigInteger.prototype.changeBit = bnpChangeBit;
   1166     BigInteger.prototype.addTo = bnpAddTo;
   1167     BigInteger.prototype.dMultiply = bnpDMultiply;
   1168     BigInteger.prototype.dAddOffset = bnpDAddOffset;
   1169     BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
   1170     BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
   1171     BigInteger.prototype.modInt = bnpModInt;
   1172     BigInteger.prototype.millerRabin = bnpMillerRabin;
   1173 
   1174     // public
   1175     BigInteger.prototype.clone = bnClone;
   1176     BigInteger.prototype.intValue = bnIntValue;
   1177     BigInteger.prototype.byteValue = bnByteValue;
   1178     BigInteger.prototype.shortValue = bnShortValue;
   1179     BigInteger.prototype.signum = bnSigNum;
   1180     BigInteger.prototype.toByteArray = bnToByteArray;
   1181     BigInteger.prototype.equals = bnEquals;
   1182     BigInteger.prototype.min = bnMin;
   1183     BigInteger.prototype.max = bnMax;
   1184     BigInteger.prototype.and = bnAnd;
   1185     BigInteger.prototype.or = bnOr;
   1186     BigInteger.prototype.xor = bnXor;
   1187     BigInteger.prototype.andNot = bnAndNot;
   1188     BigInteger.prototype.not = bnNot;
   1189     BigInteger.prototype.shiftLeft = bnShiftLeft;
   1190     BigInteger.prototype.shiftRight = bnShiftRight;
   1191     BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
   1192     BigInteger.prototype.bitCount = bnBitCount;
   1193     BigInteger.prototype.testBit = bnTestBit;
   1194     BigInteger.prototype.setBit = bnSetBit;
   1195     BigInteger.prototype.clearBit = bnClearBit;
   1196     BigInteger.prototype.flipBit = bnFlipBit;
   1197     BigInteger.prototype.add = bnAdd;
   1198     BigInteger.prototype.subtract = bnSubtract;
   1199     BigInteger.prototype.multiply = bnMultiply;
   1200     BigInteger.prototype.divide = bnDivide;
   1201     BigInteger.prototype.remainder = bnRemainder;
   1202     BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
   1203     BigInteger.prototype.modPow = bnModPow;
   1204     BigInteger.prototype.modInverse = bnModInverse;
   1205     BigInteger.prototype.pow = bnPow;
   1206     BigInteger.prototype.gcd = bnGCD;
   1207     BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
   1208 
   1209     // JSBN-specific extension
   1210     BigInteger.prototype.square = bnSquare;
   1211 
   1212     // Expose the Barrett function
   1213     BigInteger.prototype.Barrett = Barrett
   1214 
   1215     // BigInteger interfaces not implemented in jsbn:
   1216 
   1217     // BigInteger(int signum, byte[] magnitude)
   1218     // double doubleValue()
   1219     // float floatValue()
   1220     // int hashCode()
   1221     // long longValue()
   1222     // static BigInteger valueOf(long val)
   1223 
   1224 	// Random number generator - requires a PRNG backend, e.g. prng4.js
   1225 
   1226 	// For best results, put code like
   1227 	// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
   1228 	// in your main HTML document.
   1229 
   1230 	var rng_state;
   1231 	var rng_pool;
   1232 	var rng_pptr;
   1233 
   1234 	// Mix in a 32-bit integer into the pool
   1235 	function rng_seed_int(x) {
   1236 	  rng_pool[rng_pptr++] ^= x & 255;
   1237 	  rng_pool[rng_pptr++] ^= (x >> 8) & 255;
   1238 	  rng_pool[rng_pptr++] ^= (x >> 16) & 255;
   1239 	  rng_pool[rng_pptr++] ^= (x >> 24) & 255;
   1240 	  if(rng_pptr >= rng_psize) rng_pptr -= rng_psize;
   1241 	}
   1242 
   1243 	// Mix in the current time (w/milliseconds) into the pool
   1244 	function rng_seed_time() {
   1245 	  rng_seed_int(new Date().getTime());
   1246 	}
   1247 
   1248 	// Initialize the pool with junk if needed.
   1249 	if(rng_pool == null) {
   1250 	  rng_pool = new Array();
   1251 	  rng_pptr = 0;
   1252 	  var t;
   1253 	  if(typeof window !== "undefined" && window.crypto) {
   1254 		if (window.crypto.getRandomValues) {
   1255 		  // Use webcrypto if available
   1256 		  var ua = new Uint8Array(32);
   1257 		  window.crypto.getRandomValues(ua);
   1258 		  for(t = 0; t < 32; ++t)
   1259 			rng_pool[rng_pptr++] = ua[t];
   1260 		}
   1261 		else if(navigator.appName == "Netscape" && navigator.appVersion < "5") {
   1262 		  // Extract entropy (256 bits) from NS4 RNG if available
   1263 		  var z = window.crypto.random(32);
   1264 		  for(t = 0; t < z.length; ++t)
   1265 			rng_pool[rng_pptr++] = z.charCodeAt(t) & 255;
   1266 		}
   1267 	  }
   1268 	  while(rng_pptr < rng_psize) {  // extract some randomness from Math.random()
   1269 		t = Math.floor(65536 * Math.random());
   1270 		rng_pool[rng_pptr++] = t >>> 8;
   1271 		rng_pool[rng_pptr++] = t & 255;
   1272 	  }
   1273 	  rng_pptr = 0;
   1274 	  rng_seed_time();
   1275 	  //rng_seed_int(window.screenX);
   1276 	  //rng_seed_int(window.screenY);
   1277 	}
   1278 
   1279 	function rng_get_byte() {
   1280 	  if(rng_state == null) {
   1281 		rng_seed_time();
   1282 		rng_state = prng_newstate();
   1283 		rng_state.init(rng_pool);
   1284 		for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
   1285 		  rng_pool[rng_pptr] = 0;
   1286 		rng_pptr = 0;
   1287 		//rng_pool = null;
   1288 	  }
   1289 	  // TODO: allow reseeding after first request
   1290 	  return rng_state.next();
   1291 	}
   1292 
   1293 	function rng_get_bytes(ba) {
   1294 	  var i;
   1295 	  for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
   1296 	}
   1297 
   1298 	function SecureRandom() {}
   1299 
   1300 	SecureRandom.prototype.nextBytes = rng_get_bytes;
   1301 
   1302 	// prng4.js - uses Arcfour as a PRNG
   1303 
   1304 	function Arcfour() {
   1305 	  this.i = 0;
   1306 	  this.j = 0;
   1307 	  this.S = new Array();
   1308 	}
   1309 
   1310 	// Initialize arcfour context from key, an array of ints, each from [0..255]
   1311 	function ARC4init(key) {
   1312 	  var i, j, t;
   1313 	  for(i = 0; i < 256; ++i)
   1314 		this.S[i] = i;
   1315 	  j = 0;
   1316 	  for(i = 0; i < 256; ++i) {
   1317 		j = (j + this.S[i] + key[i % key.length]) & 255;
   1318 		t = this.S[i];
   1319 		this.S[i] = this.S[j];
   1320 		this.S[j] = t;
   1321 	  }
   1322 	  this.i = 0;
   1323 	  this.j = 0;
   1324 	}
   1325 
   1326 	function ARC4next() {
   1327 	  var t;
   1328 	  this.i = (this.i + 1) & 255;
   1329 	  this.j = (this.j + this.S[this.i]) & 255;
   1330 	  t = this.S[this.i];
   1331 	  this.S[this.i] = this.S[this.j];
   1332 	  this.S[this.j] = t;
   1333 	  return this.S[(t + this.S[this.i]) & 255];
   1334 	}
   1335 
   1336 	Arcfour.prototype.init = ARC4init;
   1337 	Arcfour.prototype.next = ARC4next;
   1338 
   1339 	// Plug in your RNG constructor here
   1340 	function prng_newstate() {
   1341 	  return new Arcfour();
   1342 	}
   1343 
   1344 	// Pool size must be a multiple of 4 and greater than 32.
   1345 	// An array of bytes the size of the pool will be passed to init()
   1346 	var rng_psize = 256;
   1347 
   1348   BigInteger.SecureRandom = SecureRandom;
   1349   BigInteger.BigInteger = BigInteger;
   1350   if (typeof exports !== 'undefined') {
   1351     exports = module.exports = BigInteger;
   1352   } else {
   1353     this.BigInteger = BigInteger;
   1354     this.SecureRandom = SecureRandom;
   1355   }
   1356 
   1357 }).call(this);