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      1 /*
      2  * Copyright (c) 2003-2005  Tom Wu
      3  * All Rights Reserved.
      4  *
      5  * Permission is hereby granted, free of charge, to any person obtaining
      6  * a copy of this software and associated documentation files (the
      7  * "Software"), to deal in the Software without restriction, including
      8  * without limitation the rights to use, copy, modify, merge, publish,
      9  * distribute, sublicense, and/or sell copies of the Software, and to
     10  * permit persons to whom the Software is furnished to do so, subject to
     11  * the following conditions:
     12  *
     13  * The above copyright notice and this permission notice shall be
     14  * included in all copies or substantial portions of the Software.
     15  *
     16  * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
     17  * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
     18  * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
     19  *
     20  * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
     21  * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
     22  * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
     23  * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
     24  * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
     25  *
     26  * In addition, the following condition applies:
     27  *
     28  * All redistributions must retain an intact copy of this copyright notice
     29  * and disclaimer.
     30  */
     31 
     32 // Basic JavaScript BN library - subset useful for RSA encryption.
     33 
     34 // Bits per digit
     35 var dbits;
     36 var BI_DB;
     37 var BI_DM;
     38 var BI_DV;
     39 
     40 var BI_FP;
     41 var BI_FV;
     42 var BI_F1;
     43 var BI_F2;
     44 
     45 // JavaScript engine analysis
     46 var canary = 0xdeadbeefcafe;
     47 var j_lm = ((canary&0xffffff)==0xefcafe);
     48 
     49 // (public) Constructor
     50 function BigInteger(a,b,c) {
     51   this.array = new Array();
     52   if(a != null)
     53     if("number" == typeof a) this.fromNumber(a,b,c);
     54     else if(b == null && "string" != typeof a) this.fromString(a,256);
     55     else this.fromString(a,b);
     56 }
     57 
     58 // return new, unset BigInteger
     59 function nbi() { return new BigInteger(null); }
     60 
     61 // am: Compute w_j += (x*this_i), propagate carries,
     62 // c is initial carry, returns final carry.
     63 // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
     64 // We need to select the fastest one that works in this environment.
     65 
     66 // am1: use a single mult and divide to get the high bits,
     67 // max digit bits should be 26 because
     68 // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
     69 function am1(i,x,w,j,c,n) {
     70   var this_array = this.array;
     71   var w_array    = w.array;
     72   while(--n >= 0) {
     73     var v = x*this_array[i++]+w_array[j]+c;
     74     c = Math.floor(v/0x4000000);
     75     w_array[j++] = v&0x3ffffff;
     76   }
     77   return c;
     78 }
     79 
     80 // am2 avoids a big mult-and-extract completely.
     81 // Max digit bits should be <= 30 because we do bitwise ops
     82 // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
     83 function am2(i,x,w,j,c,n) {
     84   var this_array = this.array;
     85   var w_array    = w.array;
     86   var xl = x&0x7fff, xh = x>>15;
     87   while(--n >= 0) {
     88     var l = this_array[i]&0x7fff;
     89     var h = this_array[i++]>>15;
     90     var m = xh*l+h*xl;
     91     l = xl*l+((m&0x7fff)<<15)+w_array[j]+(c&0x3fffffff);
     92     c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
     93     w_array[j++] = l&0x3fffffff;
     94   }
     95   return c;
     96 }
     97 
     98 // Alternately, set max digit bits to 28 since some
     99 // browsers slow down when dealing with 32-bit numbers.
    100 function am3(i,x,w,j,c,n) {
    101   var this_array = this.array;
    102   var w_array    = w.array;
    103 
    104   var xl = x&0x3fff, xh = x>>14;
    105   while(--n >= 0) {
    106     var l = this_array[i]&0x3fff;
    107     var h = this_array[i++]>>14;
    108     var m = xh*l+h*xl;
    109     l = xl*l+((m&0x3fff)<<14)+w_array[j]+c;
    110     c = (l>>28)+(m>>14)+xh*h;
    111     w_array[j++] = l&0xfffffff;
    112   }
    113   return c;
    114 }
    115 
    116 // This is tailored to VMs with 2-bit tagging. It makes sure
    117 // that all the computations stay within the 29 bits available.
    118 function am4(i,x,w,j,c,n) {
    119   var this_array = this.array;
    120   var w_array    = w.array;
    121 
    122   var xl = x&0x1fff, xh = x>>13;
    123   while(--n >= 0) {
    124     var l = this_array[i]&0x1fff;
    125     var h = this_array[i++]>>13;
    126     var m = xh*l+h*xl;
    127     l = xl*l+((m&0x1fff)<<13)+w_array[j]+c;
    128     c = (l>>26)+(m>>13)+xh*h;
    129     w_array[j++] = l&0x3ffffff;
    130   }
    131   return c;
    132 }
    133 
    134 // am3/28 is best for SM, Rhino, but am4/26 is best for v8.
    135 // Kestrel (Opera 9.5) gets its best result with am4/26.
    136 // IE7 does 9% better with am3/28 than with am4/26.
    137 // Firefox (SM) gets 10% faster with am3/28 than with am4/26.
    138 
    139 setupEngine = function(fn, bits) {
    140   BigInteger.prototype.am = fn;
    141   dbits = bits;
    142 
    143   BI_DB = dbits;
    144   BI_DM = ((1<<dbits)-1);
    145   BI_DV = (1<<dbits);
    146 
    147   BI_FP = 52;
    148   BI_FV = Math.pow(2,BI_FP);
    149   BI_F1 = BI_FP-dbits;
    150   BI_F2 = 2*dbits-BI_FP;
    151 }
    152 
    153 
    154 // Digit conversions
    155 var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
    156 var BI_RC = new Array();
    157 var rr,vv;
    158 rr = "0".charCodeAt(0);
    159 for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
    160 rr = "a".charCodeAt(0);
    161 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
    162 rr = "A".charCodeAt(0);
    163 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
    164 
    165 function int2char(n) { return BI_RM.charAt(n); }
    166 function intAt(s,i) {
    167   var c = BI_RC[s.charCodeAt(i)];
    168   return (c==null)?-1:c;
    169 }
    170 
    171 // (protected) copy this to r
    172 function bnpCopyTo(r) {
    173   var this_array = this.array;
    174   var r_array    = r.array;
    175 
    176   for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i];
    177   r.t = this.t;
    178   r.s = this.s;
    179 }
    180 
    181 // (protected) set from integer value x, -DV <= x < DV
    182 function bnpFromInt(x) {
    183   var this_array = this.array;
    184   this.t = 1;
    185   this.s = (x<0)?-1:0;
    186   if(x > 0) this_array[0] = x;
    187   else if(x < -1) this_array[0] = x+DV;
    188   else this.t = 0;
    189 }
    190 
    191 // return bigint initialized to value
    192 function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
    193 
    194 // (protected) set from string and radix
    195 function bnpFromString(s,b) {
    196   var this_array = this.array;
    197   var k;
    198   if(b == 16) k = 4;
    199   else if(b == 8) k = 3;
    200   else if(b == 256) k = 8; // byte array
    201   else if(b == 2) k = 1;
    202   else if(b == 32) k = 5;
    203   else if(b == 4) k = 2;
    204   else { this.fromRadix(s,b); return; }
    205   this.t = 0;
    206   this.s = 0;
    207   var i = s.length, mi = false, sh = 0;
    208   while(--i >= 0) {
    209     var x = (k==8)?s[i]&0xff:intAt(s,i);
    210     if(x < 0) {
    211       if(s.charAt(i) == "-") mi = true;
    212       continue;
    213     }
    214     mi = false;
    215     if(sh == 0)
    216       this_array[this.t++] = x;
    217     else if(sh+k > BI_DB) {
    218       this_array[this.t-1] |= (x&((1<<(BI_DB-sh))-1))<<sh;
    219       this_array[this.t++] = (x>>(BI_DB-sh));
    220     }
    221     else
    222       this_array[this.t-1] |= x<<sh;
    223     sh += k;
    224     if(sh >= BI_DB) sh -= BI_DB;
    225   }
    226   if(k == 8 && (s[0]&0x80) != 0) {
    227     this.s = -1;
    228     if(sh > 0) this_array[this.t-1] |= ((1<<(BI_DB-sh))-1)<<sh;
    229   }
    230   this.clamp();
    231   if(mi) BigInteger.ZERO.subTo(this,this);
    232 }
    233 
    234 // (protected) clamp off excess high words
    235 function bnpClamp() {
    236   var this_array = this.array;
    237   var c = this.s&BI_DM;
    238   while(this.t > 0 && this_array[this.t-1] == c) --this.t;
    239 }
    240 
    241 // (public) return string representation in given radix
    242 function bnToString(b) {
    243   var this_array = this.array;
    244   if(this.s < 0) return "-"+this.negate().toString(b);
    245   var k;
    246   if(b == 16) k = 4;
    247   else if(b == 8) k = 3;
    248   else if(b == 2) k = 1;
    249   else if(b == 32) k = 5;
    250   else if(b == 4) k = 2;
    251   else return this.toRadix(b);
    252   var km = (1<<k)-1, d, m = false, r = "", i = this.t;
    253   var p = BI_DB-(i*BI_DB)%k;
    254   if(i-- > 0) {
    255     if(p < BI_DB && (d = this_array[i]>>p) > 0) { m = true; r = int2char(d); }
    256     while(i >= 0) {
    257       if(p < k) {
    258         d = (this_array[i]&((1<<p)-1))<<(k-p);
    259         d |= this_array[--i]>>(p+=BI_DB-k);
    260       }
    261       else {
    262         d = (this_array[i]>>(p-=k))&km;
    263         if(p <= 0) { p += BI_DB; --i; }
    264       }
    265       if(d > 0) m = true;
    266       if(m) r += int2char(d);
    267     }
    268   }
    269   return m?r:"0";
    270 }
    271 
    272 // (public) -this
    273 function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
    274 
    275 // (public) |this|
    276 function bnAbs() { return (this.s<0)?this.negate():this; }
    277 
    278 // (public) return + if this > a, - if this < a, 0 if equal
    279 function bnCompareTo(a) {
    280   var this_array = this.array;
    281   var a_array = a.array;
    282 
    283   var r = this.s-a.s;
    284   if(r != 0) return r;
    285   var i = this.t;
    286   r = i-a.t;
    287   if(r != 0) return r;
    288   while(--i >= 0) if((r=this_array[i]-a_array[i]) != 0) return r;
    289   return 0;
    290 }
    291 
    292 // returns bit length of the integer x
    293 function nbits(x) {
    294   var r = 1, t;
    295   if((t=x>>>16) != 0) { x = t; r += 16; }
    296   if((t=x>>8) != 0) { x = t; r += 8; }
    297   if((t=x>>4) != 0) { x = t; r += 4; }
    298   if((t=x>>2) != 0) { x = t; r += 2; }
    299   if((t=x>>1) != 0) { x = t; r += 1; }
    300   return r;
    301 }
    302 
    303 // (public) return the number of bits in "this"
    304 function bnBitLength() {
    305   var this_array = this.array;
    306   if(this.t <= 0) return 0;
    307   return BI_DB*(this.t-1)+nbits(this_array[this.t-1]^(this.s&BI_DM));
    308 }
    309 
    310 // (protected) r = this << n*DB
    311 function bnpDLShiftTo(n,r) {
    312   var this_array = this.array;
    313   var r_array = r.array;
    314   var i;
    315   for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i];
    316   for(i = n-1; i >= 0; --i) r_array[i] = 0;
    317   r.t = this.t+n;
    318   r.s = this.s;
    319 }
    320 
    321 // (protected) r = this >> n*DB
    322 function bnpDRShiftTo(n,r) {
    323   var this_array = this.array;
    324   var r_array = r.array;
    325   for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i];
    326   r.t = Math.max(this.t-n,0);
    327   r.s = this.s;
    328 }
    329 
    330 // (protected) r = this << n
    331 function bnpLShiftTo(n,r) {
    332   var this_array = this.array;
    333   var r_array = r.array;
    334   var bs = n%BI_DB;
    335   var cbs = BI_DB-bs;
    336   var bm = (1<<cbs)-1;
    337   var ds = Math.floor(n/BI_DB), c = (this.s<<bs)&BI_DM, i;
    338   for(i = this.t-1; i >= 0; --i) {
    339     r_array[i+ds+1] = (this_array[i]>>cbs)|c;
    340     c = (this_array[i]&bm)<<bs;
    341   }
    342   for(i = ds-1; i >= 0; --i) r_array[i] = 0;
    343   r_array[ds] = c;
    344   r.t = this.t+ds+1;
    345   r.s = this.s;
    346   r.clamp();
    347 }
    348 
    349 // (protected) r = this >> n
    350 function bnpRShiftTo(n,r) {
    351   var this_array = this.array;
    352   var r_array = r.array;
    353   r.s = this.s;
    354   var ds = Math.floor(n/BI_DB);
    355   if(ds >= this.t) { r.t = 0; return; }
    356   var bs = n%BI_DB;
    357   var cbs = BI_DB-bs;
    358   var bm = (1<<bs)-1;
    359   r_array[0] = this_array[ds]>>bs;
    360   for(var i = ds+1; i < this.t; ++i) {
    361     r_array[i-ds-1] |= (this_array[i]&bm)<<cbs;
    362     r_array[i-ds] = this_array[i]>>bs;
    363   }
    364   if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs;
    365   r.t = this.t-ds;
    366   r.clamp();
    367 }
    368 
    369 // (protected) r = this - a
    370 function bnpSubTo(a,r) {
    371   var this_array = this.array;
    372   var r_array = r.array;
    373   var a_array = a.array;
    374   var i = 0, c = 0, m = Math.min(a.t,this.t);
    375   while(i < m) {
    376     c += this_array[i]-a_array[i];
    377     r_array[i++] = c&BI_DM;
    378     c >>= BI_DB;
    379   }
    380   if(a.t < this.t) {
    381     c -= a.s;
    382     while(i < this.t) {
    383       c += this_array[i];
    384       r_array[i++] = c&BI_DM;
    385       c >>= BI_DB;
    386     }
    387     c += this.s;
    388   }
    389   else {
    390     c += this.s;
    391     while(i < a.t) {
    392       c -= a_array[i];
    393       r_array[i++] = c&BI_DM;
    394       c >>= BI_DB;
    395     }
    396     c -= a.s;
    397   }
    398   r.s = (c<0)?-1:0;
    399   if(c < -1) r_array[i++] = BI_DV+c;
    400   else if(c > 0) r_array[i++] = c;
    401   r.t = i;
    402   r.clamp();
    403 }
    404 
    405 // (protected) r = this * a, r != this,a (HAC 14.12)
    406 // "this" should be the larger one if appropriate.
    407 function bnpMultiplyTo(a,r) {
    408   var this_array = this.array;
    409   var r_array = r.array;
    410   var x = this.abs(), y = a.abs();
    411   var y_array = y.array;
    412 
    413   var i = x.t;
    414   r.t = i+y.t;
    415   while(--i >= 0) r_array[i] = 0;
    416   for(i = 0; i < y.t; ++i) r_array[i+x.t] = x.am(0,y_array[i],r,i,0,x.t);
    417   r.s = 0;
    418   r.clamp();
    419   if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
    420 }
    421 
    422 // (protected) r = this^2, r != this (HAC 14.16)
    423 function bnpSquareTo(r) {
    424   var x = this.abs();
    425   var x_array = x.array;
    426   var r_array = r.array;
    427 
    428   var i = r.t = 2*x.t;
    429   while(--i >= 0) r_array[i] = 0;
    430   for(i = 0; i < x.t-1; ++i) {
    431     var c = x.am(i,x_array[i],r,2*i,0,1);
    432     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) {
    433       r_array[i+x.t] -= BI_DV;
    434       r_array[i+x.t+1] = 1;
    435     }
    436   }
    437   if(r.t > 0) r_array[r.t-1] += x.am(i,x_array[i],r,2*i,0,1);
    438   r.s = 0;
    439   r.clamp();
    440 }
    441 
    442 // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
    443 // r != q, this != m.  q or r may be null.
    444 function bnpDivRemTo(m,q,r) {
    445   var pm = m.abs();
    446   if(pm.t <= 0) return;
    447   var pt = this.abs();
    448   if(pt.t < pm.t) {
    449     if(q != null) q.fromInt(0);
    450     if(r != null) this.copyTo(r);
    451     return;
    452   }
    453   if(r == null) r = nbi();
    454   var y = nbi(), ts = this.s, ms = m.s;
    455   var pm_array = pm.array;
    456   var nsh = BI_DB-nbits(pm_array[pm.t-1]);	// normalize modulus
    457   if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
    458   else { pm.copyTo(y); pt.copyTo(r); }
    459   var ys = y.t;
    460 
    461   var y_array = y.array;
    462   var y0 = y_array[ys-1];
    463   if(y0 == 0) return;
    464   var yt = y0*(1<<BI_F1)+((ys>1)?y_array[ys-2]>>BI_F2:0);
    465   var d1 = BI_FV/yt, d2 = (1<<BI_F1)/yt, e = 1<<BI_F2;
    466   var i = r.t, j = i-ys, t = (q==null)?nbi():q;
    467   y.dlShiftTo(j,t);
    468 
    469   var r_array = r.array;
    470   if(r.compareTo(t) >= 0) {
    471     r_array[r.t++] = 1;
    472     r.subTo(t,r);
    473   }
    474   BigInteger.ONE.dlShiftTo(ys,t);
    475   t.subTo(y,y);	// "negative" y so we can replace sub with am later
    476   while(y.t < ys) y_array[y.t++] = 0;
    477   while(--j >= 0) {
    478     // Estimate quotient digit
    479     var qd = (r_array[--i]==y0)?BI_DM:Math.floor(r_array[i]*d1+(r_array[i-1]+e)*d2);
    480     if((r_array[i]+=y.am(0,qd,r,j,0,ys)) < qd) {	// Try it out
    481       y.dlShiftTo(j,t);
    482       r.subTo(t,r);
    483       while(r_array[i] < --qd) r.subTo(t,r);
    484     }
    485   }
    486   if(q != null) {
    487     r.drShiftTo(ys,q);
    488     if(ts != ms) BigInteger.ZERO.subTo(q,q);
    489   }
    490   r.t = ys;
    491   r.clamp();
    492   if(nsh > 0) r.rShiftTo(nsh,r);	// Denormalize remainder
    493   if(ts < 0) BigInteger.ZERO.subTo(r,r);
    494 }
    495 
    496 // (public) this mod a
    497 function bnMod(a) {
    498   var r = nbi();
    499   this.abs().divRemTo(a,null,r);
    500   if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
    501   return r;
    502 }
    503 
    504 // Modular reduction using "classic" algorithm
    505 function Classic(m) { this.m = m; }
    506 function cConvert(x) {
    507   if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
    508   else return x;
    509 }
    510 function cRevert(x) { return x; }
    511 function cReduce(x) { x.divRemTo(this.m,null,x); }
    512 function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
    513 function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
    514 
    515 Classic.prototype.convert = cConvert;
    516 Classic.prototype.revert = cRevert;
    517 Classic.prototype.reduce = cReduce;
    518 Classic.prototype.mulTo = cMulTo;
    519 Classic.prototype.sqrTo = cSqrTo;
    520 
    521 // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
    522 // justification:
    523 //         xy == 1 (mod m)
    524 //         xy =  1+km
    525 //   xy(2-xy) = (1+km)(1-km)
    526 // x[y(2-xy)] = 1-k^2m^2
    527 // x[y(2-xy)] == 1 (mod m^2)
    528 // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
    529 // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
    530 // JS multiply "overflows" differently from C/C++, so care is needed here.
    531 function bnpInvDigit() {
    532   var this_array = this.array;
    533   if(this.t < 1) return 0;
    534   var x = this_array[0];
    535   if((x&1) == 0) return 0;
    536   var y = x&3;		// y == 1/x mod 2^2
    537   y = (y*(2-(x&0xf)*y))&0xf;	// y == 1/x mod 2^4
    538   y = (y*(2-(x&0xff)*y))&0xff;	// y == 1/x mod 2^8
    539   y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;	// y == 1/x mod 2^16
    540   // last step - calculate inverse mod DV directly;
    541   // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
    542   y = (y*(2-x*y%BI_DV))%BI_DV;		// y == 1/x mod 2^dbits
    543   // we really want the negative inverse, and -DV < y < DV
    544   return (y>0)?BI_DV-y:-y;
    545 }
    546 
    547 // Montgomery reduction
    548 function Montgomery(m) {
    549   this.m = m;
    550   this.mp = m.invDigit();
    551   this.mpl = this.mp&0x7fff;
    552   this.mph = this.mp>>15;
    553   this.um = (1<<(BI_DB-15))-1;
    554   this.mt2 = 2*m.t;
    555 }
    556 
    557 // xR mod m
    558 function montConvert(x) {
    559   var r = nbi();
    560   x.abs().dlShiftTo(this.m.t,r);
    561   r.divRemTo(this.m,null,r);
    562   if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
    563   return r;
    564 }
    565 
    566 // x/R mod m
    567 function montRevert(x) {
    568   var r = nbi();
    569   x.copyTo(r);
    570   this.reduce(r);
    571   return r;
    572 }
    573 
    574 // x = x/R mod m (HAC 14.32)
    575 function montReduce(x) {
    576   var x_array = x.array;
    577   while(x.t <= this.mt2)	// pad x so am has enough room later
    578     x_array[x.t++] = 0;
    579   for(var i = 0; i < this.m.t; ++i) {
    580     // faster way of calculating u0 = x[i]*mp mod DV
    581     var j = x_array[i]&0x7fff;
    582     var u0 = (j*this.mpl+(((j*this.mph+(x_array[i]>>15)*this.mpl)&this.um)<<15))&BI_DM;
    583     // use am to combine the multiply-shift-add into one call
    584     j = i+this.m.t;
    585     x_array[j] += this.m.am(0,u0,x,i,0,this.m.t);
    586     // propagate carry
    587     while(x_array[j] >= BI_DV) { x_array[j] -= BI_DV; x_array[++j]++; }
    588   }
    589   x.clamp();
    590   x.drShiftTo(this.m.t,x);
    591   if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
    592 }
    593 
    594 // r = "x^2/R mod m"; x != r
    595 function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
    596 
    597 // r = "xy/R mod m"; x,y != r
    598 function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
    599 
    600 Montgomery.prototype.convert = montConvert;
    601 Montgomery.prototype.revert = montRevert;
    602 Montgomery.prototype.reduce = montReduce;
    603 Montgomery.prototype.mulTo = montMulTo;
    604 Montgomery.prototype.sqrTo = montSqrTo;
    605 
    606 // (protected) true iff this is even
    607 function bnpIsEven() {
    608   var this_array = this.array;
    609   return ((this.t>0)?(this_array[0]&1):this.s) == 0;
    610 }
    611 
    612 // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
    613 function bnpExp(e,z) {
    614   if(e > 0xffffffff || e < 1) return BigInteger.ONE;
    615   var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
    616   g.copyTo(r);
    617   while(--i >= 0) {
    618     z.sqrTo(r,r2);
    619     if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
    620     else { var t = r; r = r2; r2 = t; }
    621   }
    622   return z.revert(r);
    623 }
    624 
    625 // (public) this^e % m, 0 <= e < 2^32
    626 function bnModPowInt(e,m) {
    627   var z;
    628   if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
    629   return this.exp(e,z);
    630 }
    631 
    632 // protected
    633 BigInteger.prototype.copyTo = bnpCopyTo;
    634 BigInteger.prototype.fromInt = bnpFromInt;
    635 BigInteger.prototype.fromString = bnpFromString;
    636 BigInteger.prototype.clamp = bnpClamp;
    637 BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
    638 BigInteger.prototype.drShiftTo = bnpDRShiftTo;
    639 BigInteger.prototype.lShiftTo = bnpLShiftTo;
    640 BigInteger.prototype.rShiftTo = bnpRShiftTo;
    641 BigInteger.prototype.subTo = bnpSubTo;
    642 BigInteger.prototype.multiplyTo = bnpMultiplyTo;
    643 BigInteger.prototype.squareTo = bnpSquareTo;
    644 BigInteger.prototype.divRemTo = bnpDivRemTo;
    645 BigInteger.prototype.invDigit = bnpInvDigit;
    646 BigInteger.prototype.isEven = bnpIsEven;
    647 BigInteger.prototype.exp = bnpExp;
    648 
    649 // public
    650 BigInteger.prototype.toString = bnToString;
    651 BigInteger.prototype.negate = bnNegate;
    652 BigInteger.prototype.abs = bnAbs;
    653 BigInteger.prototype.compareTo = bnCompareTo;
    654 BigInteger.prototype.bitLength = bnBitLength;
    655 BigInteger.prototype.mod = bnMod;
    656 BigInteger.prototype.modPowInt = bnModPowInt;
    657 
    658 // "constants"
    659 BigInteger.ZERO = nbv(0);
    660 BigInteger.ONE = nbv(1);
    661 // Copyright (c) 2005  Tom Wu
    662 // All Rights Reserved.
    663 // See "LICENSE" for details.
    664 
    665 // Extended JavaScript BN functions, required for RSA private ops.
    666 
    667 // (public)
    668 function bnClone() { var r = nbi(); this.copyTo(r); return r; }
    669 
    670 // (public) return value as integer
    671 function bnIntValue() {
    672   var this_array = this.array;
    673   if(this.s < 0) {
    674     if(this.t == 1) return this_array[0]-BI_DV;
    675     else if(this.t == 0) return -1;
    676   }
    677   else if(this.t == 1) return this_array[0];
    678   else if(this.t == 0) return 0;
    679   // assumes 16 < DB < 32
    680   return ((this_array[1]&((1<<(32-BI_DB))-1))<<BI_DB)|this_array[0];
    681 }
    682 
    683 // (public) return value as byte
    684 function bnByteValue() {
    685   var this_array = this.array;
    686   return (this.t==0)?this.s:(this_array[0]<<24)>>24;
    687 }
    688 
    689 // (public) return value as short (assumes DB>=16)
    690 function bnShortValue() {
    691   var this_array = this.array;
    692   return (this.t==0)?this.s:(this_array[0]<<16)>>16;
    693 }
    694 
    695 // (protected) return x s.t. r^x < DV
    696 function bnpChunkSize(r) { return Math.floor(Math.LN2*BI_DB/Math.log(r)); }
    697 
    698 // (public) 0 if this == 0, 1 if this > 0
    699 function bnSigNum() {
    700   var this_array = this.array;
    701   if(this.s < 0) return -1;
    702   else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) return 0;
    703   else return 1;
    704 }
    705 
    706 // (protected) convert to radix string
    707 function bnpToRadix(b) {
    708   if(b == null) b = 10;
    709   if(this.signum() == 0 || b < 2 || b > 36) return "0";
    710   var cs = this.chunkSize(b);
    711   var a = Math.pow(b,cs);
    712   var d = nbv(a), y = nbi(), z = nbi(), r = "";
    713   this.divRemTo(d,y,z);
    714   while(y.signum() > 0) {
    715     r = (a+z.intValue()).toString(b).substr(1) + r;
    716     y.divRemTo(d,y,z);
    717   }
    718   return z.intValue().toString(b) + r;
    719 }
    720 
    721 // (protected) convert from radix string
    722 function bnpFromRadix(s,b) {
    723   this.fromInt(0);
    724   if(b == null) b = 10;
    725   var cs = this.chunkSize(b);
    726   var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
    727   for(var i = 0; i < s.length; ++i) {
    728     var x = intAt(s,i);
    729     if(x < 0) {
    730       if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
    731       continue;
    732     }
    733     w = b*w+x;
    734     if(++j >= cs) {
    735       this.dMultiply(d);
    736       this.dAddOffset(w,0);
    737       j = 0;
    738       w = 0;
    739     }
    740   }
    741   if(j > 0) {
    742     this.dMultiply(Math.pow(b,j));
    743     this.dAddOffset(w,0);
    744   }
    745   if(mi) BigInteger.ZERO.subTo(this,this);
    746 }
    747 
    748 // (protected) alternate constructor
    749 function bnpFromNumber(a,b,c) {
    750   if("number" == typeof b) {
    751     // new BigInteger(int,int,RNG)
    752     if(a < 2) this.fromInt(1);
    753     else {
    754       this.fromNumber(a,c);
    755       if(!this.testBit(a-1))	// force MSB set
    756         this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
    757       if(this.isEven()) this.dAddOffset(1,0); // force odd
    758       while(!this.isProbablePrime(b)) {
    759         this.dAddOffset(2,0);
    760         if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
    761       }
    762     }
    763   }
    764   else {
    765     // new BigInteger(int,RNG)
    766     var x = new Array(), t = a&7;
    767     x.length = (a>>3)+1;
    768     b.nextBytes(x);
    769     if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
    770     this.fromString(x,256);
    771   }
    772 }
    773 
    774 // (public) convert to bigendian byte array
    775 function bnToByteArray() {
    776   var this_array = this.array;
    777   var i = this.t, r = new Array();
    778   r[0] = this.s;
    779   var p = BI_DB-(i*BI_DB)%8, d, k = 0;
    780   if(i-- > 0) {
    781     if(p < BI_DB && (d = this_array[i]>>p) != (this.s&BI_DM)>>p)
    782       r[k++] = d|(this.s<<(BI_DB-p));
    783     while(i >= 0) {
    784       if(p < 8) {
    785         d = (this_array[i]&((1<<p)-1))<<(8-p);
    786         d |= this_array[--i]>>(p+=BI_DB-8);
    787       }
    788       else {
    789         d = (this_array[i]>>(p-=8))&0xff;
    790         if(p <= 0) { p += BI_DB; --i; }
    791       }
    792       if((d&0x80) != 0) d |= -256;
    793       if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
    794       if(k > 0 || d != this.s) r[k++] = d;
    795     }
    796   }
    797   return r;
    798 }
    799 
    800 function bnEquals(a) { return(this.compareTo(a)==0); }
    801 function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
    802 function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
    803 
    804 // (protected) r = this op a (bitwise)
    805 function bnpBitwiseTo(a,op,r) {
    806   var this_array = this.array;
    807   var a_array    = a.array;
    808   var r_array    = r.array;
    809   var i, f, m = Math.min(a.t,this.t);
    810   for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]);
    811   if(a.t < this.t) {
    812     f = a.s&BI_DM;
    813     for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f);
    814     r.t = this.t;
    815   }
    816   else {
    817     f = this.s&BI_DM;
    818     for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]);
    819     r.t = a.t;
    820   }
    821   r.s = op(this.s,a.s);
    822   r.clamp();
    823 }
    824 
    825 // (public) this & a
    826 function op_and(x,y) { return x&y; }
    827 function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
    828 
    829 // (public) this | a
    830 function op_or(x,y) { return x|y; }
    831 function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
    832 
    833 // (public) this ^ a
    834 function op_xor(x,y) { return x^y; }
    835 function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
    836 
    837 // (public) this & ~a
    838 function op_andnot(x,y) { return x&~y; }
    839 function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
    840 
    841 // (public) ~this
    842 function bnNot() {
    843   var this_array = this.array;
    844   var r = nbi();
    845   var r_array = r.array;
    846 
    847   for(var i = 0; i < this.t; ++i) r_array[i] = BI_DM&~this_array[i];
    848   r.t = this.t;
    849   r.s = ~this.s;
    850   return r;
    851 }
    852 
    853 // (public) this << n
    854 function bnShiftLeft(n) {
    855   var r = nbi();
    856   if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
    857   return r;
    858 }
    859 
    860 // (public) this >> n
    861 function bnShiftRight(n) {
    862   var r = nbi();
    863   if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
    864   return r;
    865 }
    866 
    867 // return index of lowest 1-bit in x, x < 2^31
    868 function lbit(x) {
    869   if(x == 0) return -1;
    870   var r = 0;
    871   if((x&0xffff) == 0) { x >>= 16; r += 16; }
    872   if((x&0xff) == 0) { x >>= 8; r += 8; }
    873   if((x&0xf) == 0) { x >>= 4; r += 4; }
    874   if((x&3) == 0) { x >>= 2; r += 2; }
    875   if((x&1) == 0) ++r;
    876   return r;
    877 }
    878 
    879 // (public) returns index of lowest 1-bit (or -1 if none)
    880 function bnGetLowestSetBit() {
    881   var this_array = this.array;
    882   for(var i = 0; i < this.t; ++i)
    883     if(this_array[i] != 0) return i*BI_DB+lbit(this_array[i]);
    884   if(this.s < 0) return this.t*BI_DB;
    885   return -1;
    886 }
    887 
    888 // return number of 1 bits in x
    889 function cbit(x) {
    890   var r = 0;
    891   while(x != 0) { x &= x-1; ++r; }
    892   return r;
    893 }
    894 
    895 // (public) return number of set bits
    896 function bnBitCount() {
    897   var r = 0, x = this.s&BI_DM;
    898   for(var i = 0; i < this.t; ++i) r += cbit(this_array[i]^x);
    899   return r;
    900 }
    901 
    902 // (public) true iff nth bit is set
    903 function bnTestBit(n) {
    904   var this_array = this.array;
    905   var j = Math.floor(n/BI_DB);
    906   if(j >= this.t) return(this.s!=0);
    907   return((this_array[j]&(1<<(n%BI_DB)))!=0);
    908 }
    909 
    910 // (protected) this op (1<<n)
    911 function bnpChangeBit(n,op) {
    912   var r = BigInteger.ONE.shiftLeft(n);
    913   this.bitwiseTo(r,op,r);
    914   return r;
    915 }
    916 
    917 // (public) this | (1<<n)
    918 function bnSetBit(n) { return this.changeBit(n,op_or); }
    919 
    920 // (public) this & ~(1<<n)
    921 function bnClearBit(n) { return this.changeBit(n,op_andnot); }
    922 
    923 // (public) this ^ (1<<n)
    924 function bnFlipBit(n) { return this.changeBit(n,op_xor); }
    925 
    926 // (protected) r = this + a
    927 function bnpAddTo(a,r) {
    928   var this_array = this.array;
    929   var a_array = a.array;
    930   var r_array = r.array;
    931   var i = 0, c = 0, m = Math.min(a.t,this.t);
    932   while(i < m) {
    933     c += this_array[i]+a_array[i];
    934     r_array[i++] = c&BI_DM;
    935     c >>= BI_DB;
    936   }
    937   if(a.t < this.t) {
    938     c += a.s;
    939     while(i < this.t) {
    940       c += this_array[i];
    941       r_array[i++] = c&BI_DM;
    942       c >>= BI_DB;
    943     }
    944     c += this.s;
    945   }
    946   else {
    947     c += this.s;
    948     while(i < a.t) {
    949       c += a_array[i];
    950       r_array[i++] = c&BI_DM;
    951       c >>= BI_DB;
    952     }
    953     c += a.s;
    954   }
    955   r.s = (c<0)?-1:0;
    956   if(c > 0) r_array[i++] = c;
    957   else if(c < -1) r_array[i++] = BI_DV+c;
    958   r.t = i;
    959   r.clamp();
    960 }
    961 
    962 // (public) this + a
    963 function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
    964 
    965 // (public) this - a
    966 function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
    967 
    968 // (public) this * a
    969 function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
    970 
    971 // (public) this / a
    972 function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
    973 
    974 // (public) this % a
    975 function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
    976 
    977 // (public) [this/a,this%a]
    978 function bnDivideAndRemainder(a) {
    979   var q = nbi(), r = nbi();
    980   this.divRemTo(a,q,r);
    981   return new Array(q,r);
    982 }
    983 
    984 // (protected) this *= n, this >= 0, 1 < n < DV
    985 function bnpDMultiply(n) {
    986   var this_array = this.array;
    987   this_array[this.t] = this.am(0,n-1,this,0,0,this.t);
    988   ++this.t;
    989   this.clamp();
    990 }
    991 
    992 // (protected) this += n << w words, this >= 0
    993 function bnpDAddOffset(n,w) {
    994   var this_array = this.array;
    995   while(this.t <= w) this_array[this.t++] = 0;
    996   this_array[w] += n;
    997   while(this_array[w] >= BI_DV) {
    998     this_array[w] -= BI_DV;
    999     if(++w >= this.t) this_array[this.t++] = 0;
   1000     ++this_array[w];
   1001   }
   1002 }
   1003 
   1004 // A "null" reducer
   1005 function NullExp() {}
   1006 function nNop(x) { return x; }
   1007 function nMulTo(x,y,r) { x.multiplyTo(y,r); }
   1008 function nSqrTo(x,r) { x.squareTo(r); }
   1009 
   1010 NullExp.prototype.convert = nNop;
   1011 NullExp.prototype.revert = nNop;
   1012 NullExp.prototype.mulTo = nMulTo;
   1013 NullExp.prototype.sqrTo = nSqrTo;
   1014 
   1015 // (public) this^e
   1016 function bnPow(e) { return this.exp(e,new NullExp()); }
   1017 
   1018 // (protected) r = lower n words of "this * a", a.t <= n
   1019 // "this" should be the larger one if appropriate.
   1020 function bnpMultiplyLowerTo(a,n,r) {
   1021   var r_array = r.array;
   1022   var a_array = a.array;
   1023   var i = Math.min(this.t+a.t,n);
   1024   r.s = 0; // assumes a,this >= 0
   1025   r.t = i;
   1026   while(i > 0) r_array[--i] = 0;
   1027   var j;
   1028   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);
   1029   for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a_array[i],r,i,0,n-i);
   1030   r.clamp();
   1031 }
   1032 
   1033 // (protected) r = "this * a" without lower n words, n > 0
   1034 // "this" should be the larger one if appropriate.
   1035 function bnpMultiplyUpperTo(a,n,r) {
   1036   var r_array = r.array;
   1037   var a_array = a.array;
   1038   --n;
   1039   var i = r.t = this.t+a.t-n;
   1040   r.s = 0; // assumes a,this >= 0
   1041   while(--i >= 0) r_array[i] = 0;
   1042   for(i = Math.max(n-this.t,0); i < a.t; ++i)
   1043     r_array[this.t+i-n] = this.am(n-i,a_array[i],r,0,0,this.t+i-n);
   1044   r.clamp();
   1045   r.drShiftTo(1,r);
   1046 }
   1047 
   1048 // Barrett modular reduction
   1049 function Barrett(m) {
   1050   // setup Barrett
   1051   this.r2 = nbi();
   1052   this.q3 = nbi();
   1053   BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
   1054   this.mu = this.r2.divide(m);
   1055   this.m = m;
   1056 }
   1057 
   1058 function barrettConvert(x) {
   1059   if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
   1060   else if(x.compareTo(this.m) < 0) return x;
   1061   else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
   1062 }
   1063 
   1064 function barrettRevert(x) { return x; }
   1065 
   1066 // x = x mod m (HAC 14.42)
   1067 function barrettReduce(x) {
   1068   x.drShiftTo(this.m.t-1,this.r2);
   1069   if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
   1070   this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
   1071   this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
   1072   while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
   1073   x.subTo(this.r2,x);
   1074   while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
   1075 }
   1076 
   1077 // r = x^2 mod m; x != r
   1078 function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
   1079 
   1080 // r = x*y mod m; x,y != r
   1081 function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
   1082 
   1083 Barrett.prototype.convert = barrettConvert;
   1084 Barrett.prototype.revert = barrettRevert;
   1085 Barrett.prototype.reduce = barrettReduce;
   1086 Barrett.prototype.mulTo = barrettMulTo;
   1087 Barrett.prototype.sqrTo = barrettSqrTo;
   1088 
   1089 // (public) this^e % m (HAC 14.85)
   1090 function bnModPow(e,m) {
   1091   var e_array = e.array;
   1092   var i = e.bitLength(), k, r = nbv(1), z;
   1093   if(i <= 0) return r;
   1094   else if(i < 18) k = 1;
   1095   else if(i < 48) k = 3;
   1096   else if(i < 144) k = 4;
   1097   else if(i < 768) k = 5;
   1098   else k = 6;
   1099   if(i < 8)
   1100     z = new Classic(m);
   1101   else if(m.isEven())
   1102     z = new Barrett(m);
   1103   else
   1104     z = new Montgomery(m);
   1105 
   1106   // precomputation
   1107   var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
   1108   g[1] = z.convert(this);
   1109   if(k > 1) {
   1110     var g2 = nbi();
   1111     z.sqrTo(g[1],g2);
   1112     while(n <= km) {
   1113       g[n] = nbi();
   1114       z.mulTo(g2,g[n-2],g[n]);
   1115       n += 2;
   1116     }
   1117   }
   1118 
   1119   var j = e.t-1, w, is1 = true, r2 = nbi(), t;
   1120   i = nbits(e_array[j])-1;
   1121   while(j >= 0) {
   1122     if(i >= k1) w = (e_array[j]>>(i-k1))&km;
   1123     else {
   1124       w = (e_array[j]&((1<<(i+1))-1))<<(k1-i);
   1125       if(j > 0) w |= e_array[j-1]>>(BI_DB+i-k1);
   1126     }
   1127 
   1128     n = k;
   1129     while((w&1) == 0) { w >>= 1; --n; }
   1130     if((i -= n) < 0) { i += BI_DB; --j; }
   1131     if(is1) {	// ret == 1, don't bother squaring or multiplying it
   1132       g[w].copyTo(r);
   1133       is1 = false;
   1134     }
   1135     else {
   1136       while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
   1137       if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
   1138       z.mulTo(r2,g[w],r);
   1139     }
   1140 
   1141     while(j >= 0 && (e_array[j]&(1<<i)) == 0) {
   1142       z.sqrTo(r,r2); t = r; r = r2; r2 = t;
   1143       if(--i < 0) { i = BI_DB-1; --j; }
   1144     }
   1145   }
   1146   return z.revert(r);
   1147 }
   1148 
   1149 // (public) gcd(this,a) (HAC 14.54)
   1150 function bnGCD(a) {
   1151   var x = (this.s<0)?this.negate():this.clone();
   1152   var y = (a.s<0)?a.negate():a.clone();
   1153   if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
   1154   var i = x.getLowestSetBit(), g = y.getLowestSetBit();
   1155   if(g < 0) return x;
   1156   if(i < g) g = i;
   1157   if(g > 0) {
   1158     x.rShiftTo(g,x);
   1159     y.rShiftTo(g,y);
   1160   }
   1161   while(x.signum() > 0) {
   1162     if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
   1163     if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
   1164     if(x.compareTo(y) >= 0) {
   1165       x.subTo(y,x);
   1166       x.rShiftTo(1,x);
   1167     }
   1168     else {
   1169       y.subTo(x,y);
   1170       y.rShiftTo(1,y);
   1171     }
   1172   }
   1173   if(g > 0) y.lShiftTo(g,y);
   1174   return y;
   1175 }
   1176 
   1177 // (protected) this % n, n < 2^26
   1178 function bnpModInt(n) {
   1179   var this_array = this.array;
   1180   if(n <= 0) return 0;
   1181   var d = BI_DV%n, r = (this.s<0)?n-1:0;
   1182   if(this.t > 0)
   1183     if(d == 0) r = this_array[0]%n;
   1184     else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n;
   1185   return r;
   1186 }
   1187 
   1188 // (public) 1/this % m (HAC 14.61)
   1189 function bnModInverse(m) {
   1190   var ac = m.isEven();
   1191   if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
   1192   var u = m.clone(), v = this.clone();
   1193   var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
   1194   while(u.signum() != 0) {
   1195     while(u.isEven()) {
   1196       u.rShiftTo(1,u);
   1197       if(ac) {
   1198         if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
   1199         a.rShiftTo(1,a);
   1200       }
   1201       else if(!b.isEven()) b.subTo(m,b);
   1202       b.rShiftTo(1,b);
   1203     }
   1204     while(v.isEven()) {
   1205       v.rShiftTo(1,v);
   1206       if(ac) {
   1207         if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
   1208         c.rShiftTo(1,c);
   1209       }
   1210       else if(!d.isEven()) d.subTo(m,d);
   1211       d.rShiftTo(1,d);
   1212     }
   1213     if(u.compareTo(v) >= 0) {
   1214       u.subTo(v,u);
   1215       if(ac) a.subTo(c,a);
   1216       b.subTo(d,b);
   1217     }
   1218     else {
   1219       v.subTo(u,v);
   1220       if(ac) c.subTo(a,c);
   1221       d.subTo(b,d);
   1222     }
   1223   }
   1224   if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
   1225   if(d.compareTo(m) >= 0) return d.subtract(m);
   1226   if(d.signum() < 0) d.addTo(m,d); else return d;
   1227   if(d.signum() < 0) return d.add(m); else return d;
   1228 }
   1229 
   1230 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];
   1231 var lplim = (1<<26)/lowprimes[lowprimes.length-1];
   1232 
   1233 // (public) test primality with certainty >= 1-.5^t
   1234 function bnIsProbablePrime(t) {
   1235   var i, x = this.abs();
   1236   var x_array = x.array;
   1237   if(x.t == 1 && x_array[0] <= lowprimes[lowprimes.length-1]) {
   1238     for(i = 0; i < lowprimes.length; ++i)
   1239       if(x_array[0] == lowprimes[i]) return true;
   1240     return false;
   1241   }
   1242   if(x.isEven()) return false;
   1243   i = 1;
   1244   while(i < lowprimes.length) {
   1245     var m = lowprimes[i], j = i+1;
   1246     while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
   1247     m = x.modInt(m);
   1248     while(i < j) if(m%lowprimes[i++] == 0) return false;
   1249   }
   1250   return x.millerRabin(t);
   1251 }
   1252 
   1253 // (protected) true if probably prime (HAC 4.24, Miller-Rabin)
   1254 function bnpMillerRabin(t) {
   1255   var n1 = this.subtract(BigInteger.ONE);
   1256   var k = n1.getLowestSetBit();
   1257   if(k <= 0) return false;
   1258   var r = n1.shiftRight(k);
   1259   t = (t+1)>>1;
   1260   if(t > lowprimes.length) t = lowprimes.length;
   1261   var a = nbi();
   1262   for(var i = 0; i < t; ++i) {
   1263     a.fromInt(lowprimes[i]);
   1264     var y = a.modPow(r,this);
   1265     if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
   1266       var j = 1;
   1267       while(j++ < k && y.compareTo(n1) != 0) {
   1268         y = y.modPowInt(2,this);
   1269         if(y.compareTo(BigInteger.ONE) == 0) return false;
   1270       }
   1271       if(y.compareTo(n1) != 0) return false;
   1272     }
   1273   }
   1274   return true;
   1275 }
   1276 
   1277 // protected
   1278 BigInteger.prototype.chunkSize = bnpChunkSize;
   1279 BigInteger.prototype.toRadix = bnpToRadix;
   1280 BigInteger.prototype.fromRadix = bnpFromRadix;
   1281 BigInteger.prototype.fromNumber = bnpFromNumber;
   1282 BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
   1283 BigInteger.prototype.changeBit = bnpChangeBit;
   1284 BigInteger.prototype.addTo = bnpAddTo;
   1285 BigInteger.prototype.dMultiply = bnpDMultiply;
   1286 BigInteger.prototype.dAddOffset = bnpDAddOffset;
   1287 BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
   1288 BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
   1289 BigInteger.prototype.modInt = bnpModInt;
   1290 BigInteger.prototype.millerRabin = bnpMillerRabin;
   1291 
   1292 // public
   1293 BigInteger.prototype.clone = bnClone;
   1294 BigInteger.prototype.intValue = bnIntValue;
   1295 BigInteger.prototype.byteValue = bnByteValue;
   1296 BigInteger.prototype.shortValue = bnShortValue;
   1297 BigInteger.prototype.signum = bnSigNum;
   1298 BigInteger.prototype.toByteArray = bnToByteArray;
   1299 BigInteger.prototype.equals = bnEquals;
   1300 BigInteger.prototype.min = bnMin;
   1301 BigInteger.prototype.max = bnMax;
   1302 BigInteger.prototype.and = bnAnd;
   1303 BigInteger.prototype.or = bnOr;
   1304 BigInteger.prototype.xor = bnXor;
   1305 BigInteger.prototype.andNot = bnAndNot;
   1306 BigInteger.prototype.not = bnNot;
   1307 BigInteger.prototype.shiftLeft = bnShiftLeft;
   1308 BigInteger.prototype.shiftRight = bnShiftRight;
   1309 BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
   1310 BigInteger.prototype.bitCount = bnBitCount;
   1311 BigInteger.prototype.testBit = bnTestBit;
   1312 BigInteger.prototype.setBit = bnSetBit;
   1313 BigInteger.prototype.clearBit = bnClearBit;
   1314 BigInteger.prototype.flipBit = bnFlipBit;
   1315 BigInteger.prototype.add = bnAdd;
   1316 BigInteger.prototype.subtract = bnSubtract;
   1317 BigInteger.prototype.multiply = bnMultiply;
   1318 BigInteger.prototype.divide = bnDivide;
   1319 BigInteger.prototype.remainder = bnRemainder;
   1320 BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
   1321 BigInteger.prototype.modPow = bnModPow;
   1322 BigInteger.prototype.modInverse = bnModInverse;
   1323 BigInteger.prototype.pow = bnPow;
   1324 BigInteger.prototype.gcd = bnGCD;
   1325 BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
   1326 
   1327 // BigInteger interfaces not implemented in jsbn:
   1328 
   1329 // BigInteger(int signum, byte[] magnitude)
   1330 // double doubleValue()
   1331 // float floatValue()
   1332 // int hashCode()
   1333 // long longValue()
   1334 // static BigInteger valueOf(long val)
   1335 // prng4.js - uses Arcfour as a PRNG
   1336 
   1337 function Arcfour() {
   1338   this.i = 0;
   1339   this.j = 0;
   1340   this.S = new Array();
   1341 }
   1342 
   1343 // Initialize arcfour context from key, an array of ints, each from [0..255]
   1344 function ARC4init(key) {
   1345   var i, j, t;
   1346   for(i = 0; i < 256; ++i)
   1347     this.S[i] = i;
   1348   j = 0;
   1349   for(i = 0; i < 256; ++i) {
   1350     j = (j + this.S[i] + key[i % key.length]) & 255;
   1351     t = this.S[i];
   1352     this.S[i] = this.S[j];
   1353     this.S[j] = t;
   1354   }
   1355   this.i = 0;
   1356   this.j = 0;
   1357 }
   1358 
   1359 function ARC4next() {
   1360   var t;
   1361   this.i = (this.i + 1) & 255;
   1362   this.j = (this.j + this.S[this.i]) & 255;
   1363   t = this.S[this.i];
   1364   this.S[this.i] = this.S[this.j];
   1365   this.S[this.j] = t;
   1366   return this.S[(t + this.S[this.i]) & 255];
   1367 }
   1368 
   1369 Arcfour.prototype.init = ARC4init;
   1370 Arcfour.prototype.next = ARC4next;
   1371 
   1372 // Plug in your RNG constructor here
   1373 function prng_newstate() {
   1374   return new Arcfour();
   1375 }
   1376 
   1377 // Pool size must be a multiple of 4 and greater than 32.
   1378 // An array of bytes the size of the pool will be passed to init()
   1379 var rng_psize = 256;
   1380 // Random number generator - requires a PRNG backend, e.g. prng4.js
   1381 
   1382 // For best results, put code like
   1383 // <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
   1384 // in your main HTML document.
   1385 
   1386 var rng_state;
   1387 var rng_pool;
   1388 var rng_pptr;
   1389 
   1390 // Mix in a 32-bit integer into the pool
   1391 function rng_seed_int(x) {
   1392   rng_pool[rng_pptr++] ^= x & 255;
   1393   rng_pool[rng_pptr++] ^= (x >> 8) & 255;
   1394   rng_pool[rng_pptr++] ^= (x >> 16) & 255;
   1395   rng_pool[rng_pptr++] ^= (x >> 24) & 255;
   1396   if(rng_pptr >= rng_psize) rng_pptr -= rng_psize;
   1397 }
   1398 
   1399 // Mix in the current time (w/milliseconds) into the pool
   1400 function rng_seed_time() {
   1401   // Use pre-computed date to avoid making the benchmark
   1402   // results dependent on the current date.
   1403   rng_seed_int(1122926989487);
   1404 }
   1405 
   1406 // Initialize the pool with junk if needed.
   1407 if(rng_pool == null) {
   1408   rng_pool = new Array();
   1409   rng_pptr = 0;
   1410   var t;
   1411   while(rng_pptr < rng_psize) {  // extract some randomness from Math.random()
   1412     t = Math.floor(65536 * Math.random());
   1413     rng_pool[rng_pptr++] = t >>> 8;
   1414     rng_pool[rng_pptr++] = t & 255;
   1415   }
   1416   rng_pptr = 0;
   1417   rng_seed_time();
   1418   //rng_seed_int(window.screenX);
   1419   //rng_seed_int(window.screenY);
   1420 }
   1421 
   1422 function rng_get_byte() {
   1423   if(rng_state == null) {
   1424     rng_seed_time();
   1425     rng_state = prng_newstate();
   1426     rng_state.init(rng_pool);
   1427     for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
   1428       rng_pool[rng_pptr] = 0;
   1429     rng_pptr = 0;
   1430     //rng_pool = null;
   1431   }
   1432   // TODO: allow reseeding after first request
   1433   return rng_state.next();
   1434 }
   1435 
   1436 function rng_get_bytes(ba) {
   1437   var i;
   1438   for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
   1439 }
   1440 
   1441 function SecureRandom() {}
   1442 
   1443 SecureRandom.prototype.nextBytes = rng_get_bytes;
   1444 // Depends on jsbn.js and rng.js
   1445 
   1446 // convert a (hex) string to a bignum object
   1447 function parseBigInt(str,r) {
   1448   return new BigInteger(str,r);
   1449 }
   1450 
   1451 function linebrk(s,n) {
   1452   var ret = "";
   1453   var i = 0;
   1454   while(i + n < s.length) {
   1455     ret += s.substring(i,i+n) + "\n";
   1456     i += n;
   1457   }
   1458   return ret + s.substring(i,s.length);
   1459 }
   1460 
   1461 function byte2Hex(b) {
   1462   if(b < 0x10)
   1463     return "0" + b.toString(16);
   1464   else
   1465     return b.toString(16);
   1466 }
   1467 
   1468 // PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
   1469 function pkcs1pad2(s,n) {
   1470   if(n < s.length + 11) {
   1471     alert("Message too long for RSA");
   1472     return null;
   1473   }
   1474   var ba = new Array();
   1475   var i = s.length - 1;
   1476   while(i >= 0 && n > 0) ba[--n] = s.charCodeAt(i--);
   1477   ba[--n] = 0;
   1478   var rng = new SecureRandom();
   1479   var x = new Array();
   1480   while(n > 2) { // random non-zero pad
   1481     x[0] = 0;
   1482     while(x[0] == 0) rng.nextBytes(x);
   1483     ba[--n] = x[0];
   1484   }
   1485   ba[--n] = 2;
   1486   ba[--n] = 0;
   1487   return new BigInteger(ba);
   1488 }
   1489 
   1490 // "empty" RSA key constructor
   1491 function RSAKey() {
   1492   this.n = null;
   1493   this.e = 0;
   1494   this.d = null;
   1495   this.p = null;
   1496   this.q = null;
   1497   this.dmp1 = null;
   1498   this.dmq1 = null;
   1499   this.coeff = null;
   1500 }
   1501 
   1502 // Set the public key fields N and e from hex strings
   1503 function RSASetPublic(N,E) {
   1504   if(N != null && E != null && N.length > 0 && E.length > 0) {
   1505     this.n = parseBigInt(N,16);
   1506     this.e = parseInt(E,16);
   1507   }
   1508   else
   1509     alert("Invalid RSA public key");
   1510 }
   1511 
   1512 // Perform raw public operation on "x": return x^e (mod n)
   1513 function RSADoPublic(x) {
   1514   return x.modPowInt(this.e, this.n);
   1515 }
   1516 
   1517 // Return the PKCS#1 RSA encryption of "text" as an even-length hex string
   1518 function RSAEncrypt(text) {
   1519   var m = pkcs1pad2(text,(this.n.bitLength()+7)>>3);
   1520   if(m == null) return null;
   1521   var c = this.doPublic(m);
   1522   if(c == null) return null;
   1523   var h = c.toString(16);
   1524   if((h.length & 1) == 0) return h; else return "0" + h;
   1525 }
   1526 
   1527 // Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
   1528 //function RSAEncryptB64(text) {
   1529 //  var h = this.encrypt(text);
   1530 //  if(h) return hex2b64(h); else return null;
   1531 //}
   1532 
   1533 // protected
   1534 RSAKey.prototype.doPublic = RSADoPublic;
   1535 
   1536 // public
   1537 RSAKey.prototype.setPublic = RSASetPublic;
   1538 RSAKey.prototype.encrypt = RSAEncrypt;
   1539 //RSAKey.prototype.encrypt_b64 = RSAEncryptB64;
   1540 // Depends on rsa.js and jsbn2.js
   1541 
   1542 // Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
   1543 function pkcs1unpad2(d,n) {
   1544   var b = d.toByteArray();
   1545   var i = 0;
   1546   while(i < b.length && b[i] == 0) ++i;
   1547   if(b.length-i != n-1 || b[i] != 2)
   1548     return null;
   1549   ++i;
   1550   while(b[i] != 0)
   1551     if(++i >= b.length) return null;
   1552   var ret = "";
   1553   while(++i < b.length)
   1554     ret += String.fromCharCode(b[i]);
   1555   return ret;
   1556 }
   1557 
   1558 // Set the private key fields N, e, and d from hex strings
   1559 function RSASetPrivate(N,E,D) {
   1560   if(N != null && E != null && N.length > 0 && E.length > 0) {
   1561     this.n = parseBigInt(N,16);
   1562     this.e = parseInt(E,16);
   1563     this.d = parseBigInt(D,16);
   1564   }
   1565   else
   1566     alert("Invalid RSA private key");
   1567 }
   1568 
   1569 // Set the private key fields N, e, d and CRT params from hex strings
   1570 function RSASetPrivateEx(N,E,D,P,Q,DP,DQ,C) {
   1571   if(N != null && E != null && N.length > 0 && E.length > 0) {
   1572     this.n = parseBigInt(N,16);
   1573     this.e = parseInt(E,16);
   1574     this.d = parseBigInt(D,16);
   1575     this.p = parseBigInt(P,16);
   1576     this.q = parseBigInt(Q,16);
   1577     this.dmp1 = parseBigInt(DP,16);
   1578     this.dmq1 = parseBigInt(DQ,16);
   1579     this.coeff = parseBigInt(C,16);
   1580   }
   1581   else
   1582     alert("Invalid RSA private key");
   1583 }
   1584 
   1585 // Generate a new random private key B bits long, using public expt E
   1586 function RSAGenerate(B,E) {
   1587   var rng = new SecureRandom();
   1588   var qs = B>>1;
   1589   this.e = parseInt(E,16);
   1590   var ee = new BigInteger(E,16);
   1591   for(;;) {
   1592     for(;;) {
   1593       this.p = new BigInteger(B-qs,1,rng);
   1594       if(this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break;
   1595     }
   1596     for(;;) {
   1597       this.q = new BigInteger(qs,1,rng);
   1598       if(this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break;
   1599     }
   1600     if(this.p.compareTo(this.q) <= 0) {
   1601       var t = this.p;
   1602       this.p = this.q;
   1603       this.q = t;
   1604     }
   1605     var p1 = this.p.subtract(BigInteger.ONE);
   1606     var q1 = this.q.subtract(BigInteger.ONE);
   1607     var phi = p1.multiply(q1);
   1608     if(phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
   1609       this.n = this.p.multiply(this.q);
   1610       this.d = ee.modInverse(phi);
   1611       this.dmp1 = this.d.mod(p1);
   1612       this.dmq1 = this.d.mod(q1);
   1613       this.coeff = this.q.modInverse(this.p);
   1614       break;
   1615     }
   1616   }
   1617 }
   1618 
   1619 // Perform raw private operation on "x": return x^d (mod n)
   1620 function RSADoPrivate(x) {
   1621   if(this.p == null || this.q == null)
   1622     return x.modPow(this.d, this.n);
   1623 
   1624   // TODO: re-calculate any missing CRT params
   1625   var xp = x.mod(this.p).modPow(this.dmp1, this.p);
   1626   var xq = x.mod(this.q).modPow(this.dmq1, this.q);
   1627 
   1628   while(xp.compareTo(xq) < 0)
   1629     xp = xp.add(this.p);
   1630   return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq);
   1631 }
   1632 
   1633 // Return the PKCS#1 RSA decryption of "ctext".
   1634 // "ctext" is an even-length hex string and the output is a plain string.
   1635 function RSADecrypt(ctext) {
   1636   var c = parseBigInt(ctext, 16);
   1637   var m = this.doPrivate(c);
   1638   if(m == null) return null;
   1639   return pkcs1unpad2(m, (this.n.bitLength()+7)>>3);
   1640 }
   1641 
   1642 // Return the PKCS#1 RSA decryption of "ctext".
   1643 // "ctext" is a Base64-encoded string and the output is a plain string.
   1644 //function RSAB64Decrypt(ctext) {
   1645 //  var h = b64tohex(ctext);
   1646 //  if(h) return this.decrypt(h); else return null;
   1647 //}
   1648 
   1649 // protected
   1650 RSAKey.prototype.doPrivate = RSADoPrivate;
   1651 
   1652 // public
   1653 RSAKey.prototype.setPrivate = RSASetPrivate;
   1654 RSAKey.prototype.setPrivateEx = RSASetPrivateEx;
   1655 RSAKey.prototype.generate = RSAGenerate;
   1656 RSAKey.prototype.decrypt = RSADecrypt;
   1657 //RSAKey.prototype.b64_decrypt = RSAB64Decrypt;
   1658 
   1659 
   1660 nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3";
   1661 eValue="10001";
   1662 dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161";
   1663 pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d";
   1664 qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f";
   1665 dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25";
   1666 dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd";
   1667 coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250";
   1668 
   1669 setupEngine(am3, 28);
   1670 
   1671 var TEXT = "The quick brown fox jumped over the extremely lazy frog! " +
   1672     "Now is the time for all good men to come to the party.";
   1673 var encrypted;
   1674 
   1675 function encrypt() {
   1676   var RSA = new RSAKey();
   1677   RSA.setPublic(nValue, eValue);
   1678   RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
   1679   encrypted = RSA.encrypt(TEXT);
   1680 }
   1681 
   1682 function decrypt() {
   1683   var RSA = new RSAKey();
   1684   RSA.setPublic(nValue, eValue);
   1685   RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
   1686   var decrypted = RSA.decrypt(encrypted);
   1687   if (decrypted != TEXT) {
   1688     throw new Error("Crypto operation failed");
   1689   }
   1690 }
   1691 
   1692 for (var i = 0; i < 8; ++i) {
   1693   encrypt();
   1694   decrypt();
   1695 }
   1696