/js/src/v8/crypto.js

   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
  33// The code has been adapted for use as a benchmark by Google.
  34var Crypto = new BenchmarkSuite('Crypto', 266181, [
  35  new Benchmark("Encrypt", encrypt),
  36  new Benchmark("Decrypt", decrypt)
  37]);
  38
  39
  40// Basic JavaScript BN library - subset useful for RSA encryption.
  41
  42// Bits per digit
  43var dbits;
  44var BI_DB;
  45var BI_DM;
  46var BI_DV;
  47
  48var BI_FP;
  49var BI_FV;
  50var BI_F1;
  51var BI_F2;
  52
  53// JavaScript engine analysis
  54var canary = 0xdeadbeefcafe;
  55var j_lm = ((canary&0xffffff)==0xefcafe);
  56
  57// (public) Constructor
  58function BigInteger(a,b,c) {
  59  this.array = new Array();
  60  if(a != null)
  61    if("number" == typeof a) this.fromNumber(a,b,c);
  62    else if(b == null && "string" != typeof a) this.fromString(a,256);
  63    else this.fromString(a,b);
  64}
  65
  66// return new, unset BigInteger
  67function nbi() { return new BigInteger(null); }
  68
  69// am: Compute w_j += (x*this_i), propagate carries,
  70// c is initial carry, returns final carry.
  71// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
  72// We need to select the fastest one that works in this environment.
  73
  74// am1: use a single mult and divide to get the high bits,
  75// max digit bits should be 26 because
  76// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
  77function am1(i,x,w,j,c,n) {
  78  var this_array = this.array;
  79  var w_array    = w.array;
  80  while(--n >= 0) {
  81    var v = x*this_array[i++]+w_array[j]+c;
  82    c = Math.floor(v/0x4000000);
  83    w_array[j++] = v&0x3ffffff;
  84  }
  85  return c;
  86}
  87
  88// am2 avoids a big mult-and-extract completely.
  89// Max digit bits should be <= 30 because we do bitwise ops
  90// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
  91function am2(i,x,w,j,c,n) {
  92  var this_array = this.array;
  93  var w_array    = w.array;
  94  var xl = x&0x7fff, xh = x>>15;
  95  while(--n >= 0) {
  96    var l = this_array[i]&0x7fff;
  97    var h = this_array[i++]>>15;
  98    var m = xh*l+h*xl;
  99    l = xl*l+((m&0x7fff)<<15)+w_array[j]+(c&0x3fffffff);
 100    c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
 101    w_array[j++] = l&0x3fffffff;
 102  }
 103  return c;
 104}
 105
 106// Alternately, set max digit bits to 28 since some
 107// browsers slow down when dealing with 32-bit numbers.
 108function am3(i,x,w,j,c,n) {
 109  var this_array = this.array;
 110  var w_array    = w.array;
 111
 112  var xl = x&0x3fff, xh = x>>14;
 113  while(--n >= 0) {
 114    var l = this_array[i]&0x3fff;
 115    var h = this_array[i++]>>14;
 116    var m = xh*l+h*xl;
 117    l = xl*l+((m&0x3fff)<<14)+w_array[j]+c;
 118    c = (l>>28)+(m>>14)+xh*h;
 119    w_array[j++] = l&0xfffffff;
 120  }
 121  return c;
 122}
 123
 124// This is tailored to VMs with 2-bit tagging. It makes sure
 125// that all the computations stay within the 29 bits available.
 126function am4(i,x,w,j,c,n) {
 127  var this_array = this.array;
 128  var w_array    = w.array;
 129
 130  var xl = x&0x1fff, xh = x>>13;
 131  while(--n >= 0) {
 132    var l = this_array[i]&0x1fff;
 133    var h = this_array[i++]>>13;
 134    var m = xh*l+h*xl;
 135    l = xl*l+((m&0x1fff)<<13)+w_array[j]+c;
 136    c = (l>>26)+(m>>13)+xh*h;
 137    w_array[j++] = l&0x3ffffff;
 138  }
 139  return c;
 140}
 141
 142// am3/28 is best for SM, Rhino, but am4/26 is best for v8.
 143// Kestrel (Opera 9.5) gets its best result with am4/26.
 144// IE7 does 9% better with am3/28 than with am4/26.
 145// Firefox (SM) gets 10% faster with am3/28 than with am4/26.
 146
 147setupEngine = function(fn, bits) {
 148  BigInteger.prototype.am = fn;
 149  dbits = bits;
 150
 151  BI_DB = dbits;
 152  BI_DM = ((1<<dbits)-1);
 153  BI_DV = (1<<dbits);
 154
 155  BI_FP = 52;
 156  BI_FV = Math.pow(2,BI_FP);
 157  BI_F1 = BI_FP-dbits;
 158  BI_F2 = 2*dbits-BI_FP;
 159}
 160
 161
 162// Digit conversions
 163var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
 164var BI_RC = new Array();
 165var rr,vv;
 166rr = "0".charCodeAt(0);
 167for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
 168rr = "a".charCodeAt(0);
 169for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
 170rr = "A".charCodeAt(0);
 171for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
 172
 173function int2char(n) { return BI_RM.charAt(n); }
 174function intAt(s,i) {
 175  var c = BI_RC[s.charCodeAt(i)];
 176  return (c==null)?-1:c;
 177}
 178
 179// (protected) copy this to r
 180function bnpCopyTo(r) {
 181  var this_array = this.array;
 182  var r_array    = r.array;
 183
 184  for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i];
 185  r.t = this.t;
 186  r.s = this.s;
 187}
 188
 189// (protected) set from integer value x, -DV <= x < DV
 190function bnpFromInt(x) {
 191  var this_array = this.array;
 192  this.t = 1;
 193  this.s = (x<0)?-1:0;
 194  if(x > 0) this_array[0] = x;
 195  else if(x < -1) this_array[0] = x+DV;
 196  else this.t = 0;
 197}
 198
 199// return bigint initialized to value
 200function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
 201
 202// (protected) set from string and radix
 203function bnpFromString(s,b) {
 204  var this_array = this.array;
 205  var k;
 206  if(b == 16) k = 4;
 207  else if(b == 8) k = 3;
 208  else if(b == 256) k = 8; // byte array
 209  else if(b == 2) k = 1;
 210  else if(b == 32) k = 5;
 211  else if(b == 4) k = 2;
 212  else { this.fromRadix(s,b); return; }
 213  this.t = 0;
 214  this.s = 0;
 215  var i = s.length, mi = false, sh = 0;
 216  while(--i >= 0) {
 217    var x = (k==8)?s[i]&0xff:intAt(s,i);
 218    if(x < 0) {
 219      if(s.charAt(i) == "-") mi = true;
 220      continue;
 221    }
 222    mi = false;
 223    if(sh == 0)
 224      this_array[this.t++] = x;
 225    else if(sh+k > BI_DB) {
 226      this_array[this.t-1] |= (x&((1<<(BI_DB-sh))-1))<<sh;
 227      this_array[this.t++] = (x>>(BI_DB-sh));
 228    }
 229    else
 230      this_array[this.t-1] |= x<<sh;
 231    sh += k;
 232    if(sh >= BI_DB) sh -= BI_DB;
 233  }
 234  if(k == 8 && (s[0]&0x80) != 0) {
 235    this.s = -1;
 236    if(sh > 0) this_array[this.t-1] |= ((1<<(BI_DB-sh))-1)<<sh;
 237  }
 238  this.clamp();
 239  if(mi) BigInteger.ZERO.subTo(this,this);
 240}
 241
 242// (protected) clamp off excess high words
 243function bnpClamp() {
 244  var this_array = this.array;
 245  var c = this.s&BI_DM;
 246  while(this.t > 0 && this_array[this.t-1] == c) --this.t;
 247}
 248
 249// (public) return string representation in given radix
 250function bnToString(b) {
 251  var this_array = this.array;
 252  if(this.s < 0) return "-"+this.negate().toString(b);
 253  var k;
 254  if(b == 16) k = 4;
 255  else if(b == 8) k = 3;
 256  else if(b == 2) k = 1;
 257  else if(b == 32) k = 5;
 258  else if(b == 4) k = 2;
 259  else return this.toRadix(b);
 260  var km = (1<<k)-1, d, m = false, r = "", i = this.t;
 261  var p = BI_DB-(i*BI_DB)%k;
 262  if(i-- > 0) {
 263    if(p < BI_DB && (d = this_array[i]>>p) > 0) { m = true; r = int2char(d); }
 264    while(i >= 0) {
 265      if(p < k) {
 266        d = (this_array[i]&((1<<p)-1))<<(k-p);
 267        d |= this_array[--i]>>(p+=BI_DB-k);
 268      }
 269      else {
 270        d = (this_array[i]>>(p-=k))&km;
 271        if(p <= 0) { p += BI_DB; --i; }
 272      }
 273      if(d > 0) m = true;
 274      if(m) r += int2char(d);
 275    }
 276  }
 277  return m?r:"0";
 278}
 279
 280// (public) -this
 281function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
 282
 283// (public) |this|
 284function bnAbs() { return (this.s<0)?this.negate():this; }
 285
 286// (public) return + if this > a, - if this < a, 0 if equal
 287function bnCompareTo(a) {
 288  var this_array = this.array;
 289  var a_array = a.array;
 290
 291  var r = this.s-a.s;
 292  if(r != 0) return r;
 293  var i = this.t;
 294  r = i-a.t;
 295  if(r != 0) return r;
 296  while(--i >= 0) if((r=this_array[i]-a_array[i]) != 0) return r;
 297  return 0;
 298}
 299
 300// returns bit length of the integer x
 301function nbits(x) {
 302  var r = 1, t;
 303  if((t=x>>>16) != 0) { x = t; r += 16; }
 304  if((t=x>>8) != 0) { x = t; r += 8; }
 305  if((t=x>>4) != 0) { x = t; r += 4; }
 306  if((t=x>>2) != 0) { x = t; r += 2; }
 307  if((t=x>>1) != 0) { x = t; r += 1; }
 308  return r;
 309}
 310
 311// (public) return the number of bits in "this"
 312function bnBitLength() {
 313  var this_array = this.array;
 314  if(this.t <= 0) return 0;
 315  return BI_DB*(this.t-1)+nbits(this_array[this.t-1]^(this.s&BI_DM));
 316}
 317
 318// (protected) r = this << n*DB
 319function bnpDLShiftTo(n,r) {
 320  var this_array = this.array;
 321  var r_array = r.array;
 322  var i;
 323  for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i];
 324  for(i = n-1; i >= 0; --i) r_array[i] = 0;
 325  r.t = this.t+n;
 326  r.s = this.s;
 327}
 328
 329// (protected) r = this >> n*DB
 330function bnpDRShiftTo(n,r) {
 331  var this_array = this.array;
 332  var r_array = r.array;
 333  for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i];
 334  r.t = Math.max(this.t-n,0);
 335  r.s = this.s;
 336}
 337
 338// (protected) r = this << n
 339function bnpLShiftTo(n,r) {
 340  var this_array = this.array;
 341  var r_array = r.array;
 342  var bs = n%BI_DB;
 343  var cbs = BI_DB-bs;
 344  var bm = (1<<cbs)-1;
 345  var ds = Math.floor(n/BI_DB), c = (this.s<<bs)&BI_DM, i;
 346  for(i = this.t-1; i >= 0; --i) {
 347    r_array[i+ds+1] = (this_array[i]>>cbs)|c;
 348    c = (this_array[i]&bm)<<bs;
 349  }
 350  for(i = ds-1; i >= 0; --i) r_array[i] = 0;
 351  r_array[ds] = c;
 352  r.t = this.t+ds+1;
 353  r.s = this.s;
 354  r.clamp();
 355}
 356
 357// (protected) r = this >> n
 358function bnpRShiftTo(n,r) {
 359  var this_array = this.array;
 360  var r_array = r.array;
 361  r.s = this.s;
 362  var ds = Math.floor(n/BI_DB);
 363  if(ds >= this.t) { r.t = 0; return; }
 364  var bs = n%BI_DB;
 365  var cbs = BI_DB-bs;
 366  var bm = (1<<bs)-1;
 367  r_array[0] = this_array[ds]>>bs;
 368  for(var i = ds+1; i < this.t; ++i) {
 369    r_array[i-ds-1] |= (this_array[i]&bm)<<cbs;
 370    r_array[i-ds] = this_array[i]>>bs;
 371  }
 372  if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs;
 373  r.t = this.t-ds;
 374  r.clamp();
 375}
 376
 377// (protected) r = this - a
 378function bnpSubTo(a,r) {
 379  var this_array = this.array;
 380  var r_array = r.array;
 381  var a_array = a.array;
 382  var i = 0, c = 0, m = Math.min(a.t,this.t);
 383  while(i < m) {
 384    c += this_array[i]-a_array[i];
 385    r_array[i++] = c&BI_DM;
 386    c >>= BI_DB;
 387  }
 388  if(a.t < this.t) {
 389    c -= a.s;
 390    while(i < this.t) {
 391      c += this_array[i];
 392      r_array[i++] = c&BI_DM;
 393      c >>= BI_DB;
 394    }
 395    c += this.s;
 396  }
 397  else {
 398    c += this.s;
 399    while(i < a.t) {
 400      c -= a_array[i];
 401      r_array[i++] = c&BI_DM;
 402      c >>= BI_DB;
 403    }
 404    c -= a.s;
 405  }
 406  r.s = (c<0)?-1:0;
 407  if(c < -1) r_array[i++] = BI_DV+c;
 408  else if(c > 0) r_array[i++] = c;
 409  r.t = i;
 410  r.clamp();
 411}
 412
 413// (protected) r = this * a, r != this,a (HAC 14.12)
 414// "this" should be the larger one if appropriate.
 415function bnpMultiplyTo(a,r) {
 416  var this_array = this.array;
 417  var r_array = r.array;
 418  var x = this.abs(), y = a.abs();
 419  var y_array = y.array;
 420
 421  var i = x.t;
 422  r.t = i+y.t;
 423  while(--i >= 0) r_array[i] = 0;
 424  for(i = 0; i < y.t; ++i) r_array[i+x.t] = x.am(0,y_array[i],r,i,0,x.t);
 425  r.s = 0;
 426  r.clamp();
 427  if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
 428}
 429
 430// (protected) r = this^2, r != this (HAC 14.16)
 431function bnpSquareTo(r) {
 432  var x = this.abs();
 433  var x_array = x.array;
 434  var r_array = r.array;
 435
 436  var i = r.t = 2*x.t;
 437  while(--i >= 0) r_array[i] = 0;
 438  for(i = 0; i < x.t-1; ++i) {
 439    var c = x.am(i,x_array[i],r,2*i,0,1);
 440    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) {
 441      r_array[i+x.t] -= BI_DV;
 442      r_array[i+x.t+1] = 1;
 443    }
 444  }
 445  if(r.t > 0) r_array[r.t-1] += x.am(i,x_array[i],r,2*i,0,1);
 446  r.s = 0;
 447  r.clamp();
 448}
 449
 450// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
 451// r != q, this != m.  q or r may be null.
 452function bnpDivRemTo(m,q,r) {
 453  var pm = m.abs();
 454  if(pm.t <= 0) return;
 455  var pt = this.abs();
 456  if(pt.t < pm.t) {
 457    if(q != null) q.fromInt(0);
 458    if(r != null) this.copyTo(r);
 459    return;
 460  }
 461  if(r == null) r = nbi();
 462  var y = nbi(), ts = this.s, ms = m.s;
 463  var pm_array = pm.array;
 464  var nsh = BI_DB-nbits(pm_array[pm.t-1]);	// normalize modulus
 465  if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
 466  else { pm.copyTo(y); pt.copyTo(r); }
 467  var ys = y.t;
 468
 469  var y_array = y.array;
 470  var y0 = y_array[ys-1];
 471  if(y0 == 0) return;
 472  var yt = y0*(1<<BI_F1)+((ys>1)?y_array[ys-2]>>BI_F2:0);
 473  var d1 = BI_FV/yt, d2 = (1<<BI_F1)/yt, e = 1<<BI_F2;
 474  var i = r.t, j = i-ys, t = (q==null)?nbi():q;
 475  y.dlShiftTo(j,t);
 476
 477  var r_array = r.array;
 478  if(r.compareTo(t) >= 0) {
 479    r_array[r.t++] = 1;
 480    r.subTo(t,r);
 481  }
 482  BigInteger.ONE.dlShiftTo(ys,t);
 483  t.subTo(y,y);	// "negative" y so we can replace sub with am later
 484  while(y.t < ys) y_array[y.t++] = 0;
 485  while(--j >= 0) {
 486    // Estimate quotient digit
 487    var qd = (r_array[--i]==y0)?BI_DM:Math.floor(r_array[i]*d1+(r_array[i-1]+e)*d2);
 488    if((r_array[i]+=y.am(0,qd,r,j,0,ys)) < qd) {	// Try it out
 489      y.dlShiftTo(j,t);
 490      r.subTo(t,r);
 491      while(r_array[i] < --qd) r.subTo(t,r);
 492    }
 493  }
 494  if(q != null) {
 495    r.drShiftTo(ys,q);
 496    if(ts != ms) BigInteger.ZERO.subTo(q,q);
 497  }
 498  r.t = ys;
 499  r.clamp();
 500  if(nsh > 0) r.rShiftTo(nsh,r);	// Denormalize remainder
 501  if(ts < 0) BigInteger.ZERO.subTo(r,r);
 502}
 503
 504// (public) this mod a
 505function bnMod(a) {
 506  var r = nbi();
 507  this.abs().divRemTo(a,null,r);
 508  if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
 509  return r;
 510}
 511
 512// Modular reduction using "classic" algorithm
 513function Classic(m) { this.m = m; }
 514function cConvert(x) {
 515  if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
 516  else return x;
 517}
 518function cRevert(x) { return x; }
 519function cReduce(x) { x.divRemTo(this.m,null,x); }
 520function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
 521function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
 522
 523Classic.prototype.convert = cConvert;
 524Classic.prototype.revert = cRevert;
 525Classic.prototype.reduce = cReduce;
 526Classic.prototype.mulTo = cMulTo;
 527Classic.prototype.sqrTo = cSqrTo;
 528
 529// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
 530// justification:
 531//         xy == 1 (mod m)
 532//         xy =  1+km
 533//   xy(2-xy) = (1+km)(1-km)
 534// x[y(2-xy)] = 1-k^2m^2
 535// x[y(2-xy)] == 1 (mod m^2)
 536// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
 537// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
 538// JS multiply "overflows" differently from C/C++, so care is needed here.
 539function bnpInvDigit() {
 540  var this_array = this.array;
 541  if(this.t < 1) return 0;
 542  var x = this_array[0];
 543  if((x&1) == 0) return 0;
 544  var y = x&3;		// y == 1/x mod 2^2
 545  y = (y*(2-(x&0xf)*y))&0xf;	// y == 1/x mod 2^4
 546  y = (y*(2-(x&0xff)*y))&0xff;	// y == 1/x mod 2^8
 547  y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;	// y == 1/x mod 2^16
 548  // last step - calculate inverse mod DV directly;
 549  // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
 550  y = (y*(2-x*y%BI_DV))%BI_DV;		// y == 1/x mod 2^dbits
 551  // we really want the negative inverse, and -DV < y < DV
 552  return (y>0)?BI_DV-y:-y;
 553}
 554
 555// Montgomery reduction
 556function Montgomery(m) {
 557  this.m = m;
 558  this.mp = m.invDigit();
 559  this.mpl = this.mp&0x7fff;
 560  this.mph = this.mp>>15;
 561  this.um = (1<<(BI_DB-15))-1;
 562  this.mt2 = 2*m.t;
 563}
 564
 565// xR mod m
 566function montConvert(x) {
 567  var r = nbi();
 568  x.abs().dlShiftTo(this.m.t,r);
 569  r.divRemTo(this.m,null,r);
 570  if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
 571  return r;
 572}
 573
 574// x/R mod m
 575function montRevert(x) {
 576  var r = nbi();
 577  x.copyTo(r);
 578  this.reduce(r);
 579  return r;
 580}
 581
 582// x = x/R mod m (HAC 14.32)
 583function montReduce(x) {
 584  var x_array = x.array;
 585  while(x.t <= this.mt2)	// pad x so am has enough room later
 586    x_array[x.t++] = 0;
 587  for(var i = 0; i < this.m.t; ++i) {
 588    // faster way of calculating u0 = x[i]*mp mod DV
 589    var j = x_array[i]&0x7fff;
 590    var u0 = (j*this.mpl+(((j*this.mph+(x_array[i]>>15)*this.mpl)&this.um)<<15))&BI_DM;
 591    // use am to combine the multiply-shift-add into one call
 592    j = i+this.m.t;
 593    x_array[j] += this.m.am(0,u0,x,i,0,this.m.t);
 594    // propagate carry
 595    while(x_array[j] >= BI_DV) { x_array[j] -= BI_DV; x_array[++j]++; }
 596  }
 597  x.clamp();
 598  x.drShiftTo(this.m.t,x);
 599  if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
 600}
 601
 602// r = "x^2/R mod m"; x != r
 603function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
 604
 605// r = "xy/R mod m"; x,y != r
 606function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
 607
 608Montgomery.prototype.convert = montConvert;
 609Montgomery.prototype.revert = montRevert;
 610Montgomery.prototype.reduce = montReduce;
 611Montgomery.prototype.mulTo = montMulTo;
 612Montgomery.prototype.sqrTo = montSqrTo;
 613
 614// (protected) true iff this is even
 615function bnpIsEven() {
 616  var this_array = this.array;
 617  return ((this.t>0)?(this_array[0]&1):this.s) == 0;
 618}
 619
 620// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
 621function bnpExp(e,z) {
 622  if(e > 0xffffffff || e < 1) return BigInteger.ONE;
 623  var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
 624  g.copyTo(r);
 625  while(--i >= 0) {
 626    z.sqrTo(r,r2);
 627    if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
 628    else { var t = r; r = r2; r2 = t; }
 629  }
 630  return z.revert(r);
 631}
 632
 633// (public) this^e % m, 0 <= e < 2^32
 634function bnModPowInt(e,m) {
 635  var z;
 636  if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
 637  return this.exp(e,z);
 638}
 639
 640// protected
 641BigInteger.prototype.copyTo = bnpCopyTo;
 642BigInteger.prototype.fromInt = bnpFromInt;
 643BigInteger.prototype.fromString = bnpFromString;
 644BigInteger.prototype.clamp = bnpClamp;
 645BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
 646BigInteger.prototype.drShiftTo = bnpDRShiftTo;
 647BigInteger.prototype.lShiftTo = bnpLShiftTo;
 648BigInteger.prototype.rShiftTo = bnpRShiftTo;
 649BigInteger.prototype.subTo = bnpSubTo;
 650BigInteger.prototype.multiplyTo = bnpMultiplyTo;
 651BigInteger.prototype.squareTo = bnpSquareTo;
 652BigInteger.prototype.divRemTo = bnpDivRemTo;
 653BigInteger.prototype.invDigit = bnpInvDigit;
 654BigInteger.prototype.isEven = bnpIsEven;
 655BigInteger.prototype.exp = bnpExp;
 656
 657// public
 658BigInteger.prototype.toString = bnToString;
 659BigInteger.prototype.negate = bnNegate;
 660BigInteger.prototype.abs = bnAbs;
 661BigInteger.prototype.compareTo = bnCompareTo;
 662BigInteger.prototype.bitLength = bnBitLength;
 663BigInteger.prototype.mod = bnMod;
 664BigInteger.prototype.modPowInt = bnModPowInt;
 665
 666// "constants"
 667BigInteger.ZERO = nbv(0);
 668BigInteger.ONE = nbv(1);
 669// Copyright (c) 2005  Tom Wu
 670// All Rights Reserved.
 671// See "LICENSE" for details.
 672
 673// Extended JavaScript BN functions, required for RSA private ops.
 674
 675// (public)
 676function bnClone() { var r = nbi(); this.copyTo(r); return r; }
 677
 678// (public) return value as integer
 679function bnIntValue() {
 680  var this_array = this.array;
 681  if(this.s < 0) {
 682    if(this.t == 1) return this_array[0]-BI_DV;
 683    else if(this.t == 0) return -1;
 684  }
 685  else if(this.t == 1) return this_array[0];
 686  else if(this.t == 0) return 0;
 687  // assumes 16 < DB < 32
 688  return ((this_array[1]&((1<<(32-BI_DB))-1))<<BI_DB)|this_array[0];
 689}
 690
 691// (public) return value as byte
 692function bnByteValue() {
 693  var this_array = this.array;
 694  return (this.t==0)?this.s:(this_array[0]<<24)>>24;
 695}
 696
 697// (public) return value as short (assumes DB>=16)
 698function bnShortValue() {
 699  var this_array = this.array;
 700  return (this.t==0)?this.s:(this_array[0]<<16)>>16;
 701}
 702
 703// (protected) return x s.t. r^x < DV
 704function bnpChunkSize(r) { return Math.floor(Math.LN2*BI_DB/Math.log(r)); }
 705
 706// (public) 0 if this == 0, 1 if this > 0
 707function bnSigNum() {
 708  var this_array = this.array;
 709  if(this.s < 0) return -1;
 710  else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) return 0;
 711  else return 1;
 712}
 713
 714// (protected) convert to radix string
 715function bnpToRadix(b) {
 716  if(b == null) b = 10;
 717  if(this.signum() == 0 || b < 2 || b > 36) return "0";
 718  var cs = this.chunkSize(b);
 719  var a = Math.pow(b,cs);
 720  var d = nbv(a), y = nbi(), z = nbi(), r = "";
 721  this.divRemTo(d,y,z);
 722  while(y.signum() > 0) {
 723    r = (a+z.intValue()).toString(b).substr(1) + r;
 724    y.divRemTo(d,y,z);
 725  }
 726  return z.intValue().toString(b) + r;
 727}
 728
 729// (protected) convert from radix string
 730function bnpFromRadix(s,b) {
 731  this.fromInt(0);
 732  if(b == null) b = 10;
 733  var cs = this.chunkSize(b);
 734  var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
 735  for(var i = 0; i < s.length; ++i) {
 736    var x = intAt(s,i);
 737    if(x < 0) {
 738      if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
 739      continue;
 740    }
 741    w = b*w+x;
 742    if(++j >= cs) {
 743      this.dMultiply(d);
 744      this.dAddOffset(w,0);
 745      j = 0;
 746      w = 0;
 747    }
 748  }
 749  if(j > 0) {
 750    this.dMultiply(Math.pow(b,j));
 751    this.dAddOffset(w,0);
 752  }
 753  if(mi) BigInteger.ZERO.subTo(this,this);
 754}
 755
 756// (protected) alternate constructor
 757function bnpFromNumber(a,b,c) {
 758  if("number" == typeof b) {
 759    // new BigInteger(int,int,RNG)
 760    if(a < 2) this.fromInt(1);
 761    else {
 762      this.fromNumber(a,c);
 763      if(!this.testBit(a-1))	// force MSB set
 764        this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
 765      if(this.isEven()) this.dAddOffset(1,0); // force odd
 766      while(!this.isProbablePrime(b)) {
 767        this.dAddOffset(2,0);
 768        if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
 769      }
 770    }
 771  }
 772  else {
 773    // new BigInteger(int,RNG)
 774    var x = new Array(), t = a&7;
 775    x.length = (a>>3)+1;
 776    b.nextBytes(x);
 777    if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
 778    this.fromString(x,256);
 779  }
 780}
 781
 782// (public) convert to bigendian byte array
 783function bnToByteArray() {
 784  var this_array = this.array;
 785  var i = this.t, r = new Array();
 786  r[0] = this.s;
 787  var p = BI_DB-(i*BI_DB)%8, d, k = 0;
 788  if(i-- > 0) {
 789    if(p < BI_DB && (d = this_array[i]>>p) != (this.s&BI_DM)>>p)
 790      r[k++] = d|(this.s<<(BI_DB-p));
 791    while(i >= 0) {
 792      if(p < 8) {
 793        d = (this_array[i]&((1<<p)-1))<<(8-p);
 794        d |= this_array[--i]>>(p+=BI_DB-8);
 795      }
 796      else {
 797        d = (this_array[i]>>(p-=8))&0xff;
 798        if(p <= 0) { p += BI_DB; --i; }
 799      }
 800      if((d&0x80) != 0) d |= -256;
 801      if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
 802      if(k > 0 || d != this.s) r[k++] = d;
 803    }
 804  }
 805  return r;
 806}
 807
 808function bnEquals(a) { return(this.compareTo(a)==0); }
 809function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
 810function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
 811
 812// (protected) r = this op a (bitwise)
 813function bnpBitwiseTo(a,op,r) {
 814  var this_array = this.array;
 815  var a_array    = a.array;
 816  var r_array    = r.array;
 817  var i, f, m = Math.min(a.t,this.t);
 818  for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]);
 819  if(a.t < this.t) {
 820    f = a.s&BI_DM;
 821    for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f);
 822    r.t = this.t;
 823  }
 824  else {
 825    f = this.s&BI_DM;
 826    for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]);
 827    r.t = a.t;
 828  }
 829  r.s = op(this.s,a.s);
 830  r.clamp();
 831}
 832
 833// (public) this & a
 834function op_and(x,y) { return x&y; }
 835function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
 836
 837// (public) this | a
 838function op_or(x,y) { return x|y; }
 839function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
 840
 841// (public) this ^ a
 842function op_xor(x,y) { return x^y; }
 843function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
 844
 845// (public) this & ~a
 846function op_andnot(x,y) { return x&~y; }
 847function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
 848
 849// (public) ~this
 850function bnNot() {
 851  var this_array = this.array;
 852  var r = nbi();
 853  var r_array = r.array;
 854
 855  for(var i = 0; i < this.t; ++i) r_array[i] = BI_DM&~this_array[i];
 856  r.t = this.t;
 857  r.s = ~this.s;
 858  return r;
 859}
 860
 861// (public) this << n
 862function bnShiftLeft(n) {
 863  var r = nbi();
 864  if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
 865  return r;
 866}
 867
 868// (public) this >> n
 869function bnShiftRight(n) {
 870  var r = nbi();
 871  if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
 872  return r;
 873}
 874
 875// return index of lowest 1-bit in x, x < 2^31
 876function lbit(x) {
 877  if(x == 0) return -1;
 878  var r = 0;
 879  if((x&0xffff) == 0) { x >>= 16; r += 16; }
 880  if((x&0xff) == 0) { x >>= 8; r += 8; }
 881  if((x&0xf) == 0) { x >>= 4; r += 4; }
 882  if((x&3) == 0) { x >>= 2; r += 2; }
 883  if((x&1) == 0) ++r;
 884  return r;
 885}
 886
 887// (public) returns index of lowest 1-bit (or -1 if none)
 888function bnGetLowestSetBit() {
 889  var this_array = this.array;
 890  for(var i = 0; i < this.t; ++i)
 891    if(this_array[i] != 0) return i*BI_DB+lbit(this_array[i]);
 892  if(this.s < 0) return this.t*BI_DB;
 893  return -1;
 894}
 895
 896// return number of 1 bits in x
 897function cbit(x) {
 898  var r = 0;
 899  while(x != 0) { x &= x-1; ++r; }
 900  return r;
 901}
 902
 903// (public) return number of set bits
 904function bnBitCount() {
 905  var r = 0, x = this.s&BI_DM;
 906  for(var i = 0; i < this.t; ++i) r += cbit(this_array[i]^x);
 907  return r;
 908}
 909
 910// (public) true iff nth bit is set
 911function bnTestBit(n) {
 912  var this_array = this.array;
 913  var j = Math.floor(n/BI_DB);
 914  if(j >= this.t) return(this.s!=0);
 915  return((this_array[j]&(1<<(n%BI_DB)))!=0);
 916}
 917
 918// (protected) this op (1<<n)
 919function bnpChangeBit(n,op) {
 920  var r = BigInteger.ONE.shiftLeft(n);
 921  this.bitwiseTo(r,op,r);
 922  return r;
 923}
 924
 925// (public) this | (1<<n)
 926function bnSetBit(n) { return this.changeBit(n,op_or); }
 927
 928// (public) this & ~(1<<n)
 929function bnClearBit(n) { return this.changeBit(n,op_andnot); }
 930
 931// (public) this ^ (1<<n)
 932function bnFlipBit(n) { return this.changeBit(n,op_xor); }
 933
 934// (protected) r = this + a
 935function bnpAddTo(a,r) {
 936  var this_array = this.array;
 937  var a_array = a.array;
 938  var r_array = r.array;
 939  var i = 0, c = 0, m = Math.min(a.t,this.t);
 940  while(i < m) {
 941    c += this_array[i]+a_array[i];
 942    r_array[i++] = c&BI_DM;
 943    c >>= BI_DB;
 944  }
 945  if(a.t < this.t) {
 946    c += a.s;
 947    while(i < this.t) {
 948      c += this_array[i];
 949      r_array[i++] = c&BI_DM;
 950      c >>= BI_DB;
 951    }
 952    c += this.s;
 953  }
 954  else {
 955    c += this.s;
 956    while(i < a.t) {
 957      c += a_array[i];
 958      r_array[i++] = c&BI_DM;
 959      c >>= BI_DB;
 960    }
 961    c += a.s;
 962  }
 963  r.s = (c<0)?-1:0;
 964  if(c > 0) r_array[i++] = c;
 965  else if(c < -1) r_array[i++] = BI_DV+c;
 966  r.t = i;
 967  r.clamp();
 968}
 969
 970// (public) this + a
 971function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
 972
 973// (public) this - a
 974function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
 975
 976// (public) this * a
 977function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
 978
 979// (public) this / a
 980function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
 981
 982// (public) this % a
 983function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
 984
 985// (public) [this/a,this%a]
 986function bnDivideAndRemainder(a) {
 987  var q = nbi(), r = nbi();
 988  this.divRemTo(a,q,r);
 989  return new Array(q,r);
 990}
 991
 992// (protected) this *= n, this >= 0, 1 < n < DV
 993function bnpDMultiply(n) {
 994  var this_array = this.array;
 995  this_array[this.t] = this.am(0,n-1,this,0,0,this.t);
 996  ++this.t;
 997  this.clamp();
 998}
 999
1000// (protected) this += n << w words, this >= 0
1001function bnpDAddOffset(n,w) {
1002  var this_array = this.array;
1003  while(this.t <= w) this_array[this.t++] = 0;
1004  this_array[w] += n;
1005  while(this_array[w] >= BI_DV) {
1006    this_array[w] -= BI_DV;
1007    if(++w >= this.t) this_array[this.t++] = 0;
1008    ++this_array[w];
1009  }
1010}
1011
1012// A "null" reducer
1013function NullExp() {}
1014function nNop(x) { return x; }
1015function nMulTo(x,y,r) { x.multiplyTo(y,r); }
1016function nSqrTo(x,r) { x.squareTo(r); }
1017
1018NullExp.prototype.convert = nNop;
1019NullExp.prototype.revert = nNop;
1020NullExp.prototype.mulTo = nMulTo;
1021NullExp.prototype.sqrTo = nSqrTo;
1022
1023// (public) this^e
1024function bnPow(e) { return this.exp(e,new NullExp()); }
1025
1026// (protected) r = lower n words of "this * a", a.t <= n
1027// "this" should be the larger one if appropriate.
1028function bnpMultiplyLowerTo(a,n,r) {
1029  var r_array = r.array;
1030  var a_array = a.array;
1031  var i = Math.min(this.t+a.t,n);
1032  r.s = 0; // assumes a,this >= 0
1033  r.t = i;
1034  while(i > 0) r_array[--i] = 0;
1035  var j;
1036  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);
1037  for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a_array[i],r,i,0,n-i);
1038  r.clamp();
1039}
1040
1041// (protected) r = "this * a" without lower n words, n > 0
1042// "this" should be the larger one if appropriate.
1043function bnpMultiplyUpperTo(a,n,r) {
1044  var r_array = r.array;
1045  var a_array = a.array;
1046  --n;
1047  var i = r.t = this.t+a.t-n;
1048  r.s = 0; // assumes a,this >= 0
1049  while(--i >= 0) r_array[i] = 0;
1050  for(i = Math.max(n-this.t,0); i < a.t; ++i)
1051    r_array[this.t+i-n] = this.am(n-i,a_array[i],r,0,0,this.t+i-n);
1052  r.clamp();
1053  r.drShiftTo(1,r);
1054}
1055
1056// Barrett modular reduction
1057function Barrett(m) {
1058  // setup Barrett
1059  this.r2 = nbi();
1060  this.q3 = nbi();
1061  BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
1062  this.mu = this.r2.divide(m);
1063  this.m = m;
1064}
1065
1066function barrettConvert(x) {
1067  if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
1068  else if(x.compareTo(this.m) < 0) return x;
1069  else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
1070}
1071
1072function barrettRevert(x) { return x; }
1073
1074// x = x mod m (HAC 14.42)
1075function barrettReduce(x) {
1076  x.drShiftTo(this.m.t-1,this.r2);
1077  if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
1078  this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
1079  this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
1080  while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
1081  x.subTo(this.r2,x);
1082  while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
1083}
1084
1085// r = x^2 mod m; x != r
1086function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
1087
1088// r = x*y mod m; x,y != r
1089function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
1090
1091Barrett.prototype.convert = barrettConvert;
1092Barrett.prototype.revert = barrettRevert;
1093Barrett.prototype.reduce = barrettReduce;
1094Barrett.prototype.mulTo = barrettMulTo;
1095Barrett.prototype.sqrTo = barrettSqrTo;
1096
1097// (public) this^e % m (HAC 14.85)
1098function bnModPow(e,m) {
1099  var e_array = e.array;
1100  var i = e.bitLength(), k, r = nbv(1), z;
1101  if(i <= 0) return r;
1102  else if(i < 18) k = 1;
1103  else if(i < 48) k = 3;
1104  else if(i < 144) k = 4;
1105  else if(i < 768) k = 5;
1106  else k = 6;
1107  if(i < 8)
1108    z = new Classic(m);
1109  else if(m.isEven())
1110    z = new Barrett(m);
1111  else
1112    z = new Montgomery(m);
1113
1114  // precomputation
1115  var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
1116  g[1] = z.convert(this);
1117  if(k > 1) {
1118    var g2 = nbi();
1119    z.sqrTo(g[1],g2);
1120    while(n <= km) {
1121      g[n] = nbi();
1122      z.mulTo(g2,g[n-2],g[n]);
1123      n += 2;
1124    }
1125  }
1126
1127  var j = e.t-1, w, is1 = true, r2 = nbi(), t;
1128  i = nbits(e_array[j])-1;
1129  while(j >= 0) {
1130    if(i >= k1) w = (e_array[j]>>(i-k1))&km;
1131    else {
1132      w = (e_array[j]&((1<<(i+1))-1))<<(k1-i);
1133      if(j > 0) w |= e_array[j-1]>>(BI_DB+i-k1);
1134    }
1135
1136    n = k;
1137    while((w&1) == 0) { w >>= 1; --n; }
1138    if((i -= n) < 0) { i += BI_DB; --j; }
1139    if(is1) {	// ret == 1, don't bother squaring or multiplying it
1140      g[w].copyTo(r);
1141      is1 = false;
1142    }
1143    else {
1144      while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
1145      if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
1146      z.mulTo(r2,g[w],r);
1147    }
1148
1149    while(j >= 0 && (e_array[j]&(1<<i)) == 0) {
1150      z.sqrTo(r,r2); t = r; r = r2; r2 = t;
1151      if(--i < 0) { i = BI_DB-1; --j; }
1152    }
1153  }
1154  return z.revert(r);
1155}
1156
1157// (public) gcd(this,a) (HAC 14.54)
1158function bnGCD(a) {
1159  var x = (this.s<0)?this.negate():this.clone();
1160  var y = (a.s<0)?a.negate():a.clone();
1161  if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
1162  var i = x.getLowestSetBit(), g = y.getLowestSetBit();
1163  if(g < 0) return x;
1164  if(i < g) g = i;
1165  if(g > 0) {
1166    x.rShiftTo(g,x);
1167    y.rShiftTo(g,y);
1168  }
1169  while(x.signum() > 0) {
1170    if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
1171    if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
1172    if(x.compareTo(y) >= 0) {
1173      x.subTo(y,x);
1174      x.rShiftTo(1,x);
1175    }
1176    else {
1177      y.subTo(x,y);
1178      y.rShiftTo(1,y);
1179    }
1180  }
1181  if(g > 0) y.lShiftTo(g,y);
1182  return y;
1183}
1184
1185// (protected) this % n, n < 2^26
1186function bnpModInt(n) {
1187  var this_array = this.array;
1188  if(n <= 0) return 0;
1189  var d = BI_DV%n, r = (this.s<0)?n-1:0;
1190  if(this.t > 0)
1191    if(d == 0) r = this_array[0]%n;
1192    else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n;
1193  return r;
1194}
1195
1196// (public) 1/this % m (HAC 14.61)
1197function bnModInverse(m) {
1198  var ac = m.isEven();
1199  if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
1200  var u = m.clone(), v = this.clone();
1201  var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
1202  while(u.signum() != 0) {
1203    while(u.isEven()) {
1204      u.rShiftTo(1,u);
1205      if(ac) {
1206        if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
1207        a.rShiftTo(1,a);
1208      }
1209      else if(!b.isEven()) b.subTo(m,b);
1210      b.rShiftTo(1,b);
1211    }
1212    while(v.isEven()) {
1213      v.rShiftTo(1,v);
1214      if(ac) {
1215        if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
1216        c.rShiftTo(1,c);
1217      }
1218      else if(!d.isEven()) d.subTo(m,d);
1219      d.rShiftTo(1,d);
1220    }
1221    if(u.compareTo(v) >= 0) {
1222      u.subTo(v,u);
1223      if(ac) a.subTo(c,a);
1224      b.subTo(d,b);
1225    }
1226    else {
1227      v.subTo(u,v);
1228      if(ac) c.subTo(a,c);
1229      d.subTo(b,d);
1230    }
1231  }
1232  if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
1233  if(d.compareTo(m) >= 0) return d.subtract(m);
1234  if(d.signum() < 0) d.addTo(m,d); else return d;
1235  if(d.signum() < 0) return d.add(m); else return d;
1236}
1237
1238var 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];
1239var lplim = (1<<26)/lowprimes[lowprimes.length-1];
1240
1241// (public) test primality with certainty >= 1-.5^t
1242function bnIsProbablePrime(t) {
1243  var i, x = this.abs();
1244  var x_array = x.array;
1245  if(x.t == 1 && x_array[0] <= lowprimes[lowprimes.length-1]) {
1246    for(i = 0; i < lowprimes.length; ++i)
1247      if(x_array[0] == lowprimes[i]) return true;
1248    return false;
1249  }
1250  if(x.isEven()) return false;
1251  i = 1;
1252  while(i < lowprimes.length) {
1253    var m = lowprimes[i], j = i+1;
1254    while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
1255    m = x.modInt(m);
1256    while(i < j) if(m%lowprimes[i++] == 0) return false;
1257  }
1258  return x.millerRabin(t);
1259}
1260
1261// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
1262function bnpMillerRabin(t) {
1263  var n1 = this.subtract(BigInteger.ONE);
1264  var k = n1.getLowestSetBit();
1265  if(k <= 0) return false;
1266  var r = n1.shiftRight(k);
1267  t = (t+1)>>1;
1268  if(t > lowprimes.length) t = lowprimes.length;
1269  var a = nbi();
1270  for(var i = 0; i < t; ++i) {
1271    a.fromInt(lowprimes[i]);
1272    var y = a.modPow(r,this);
1273    if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
1274      var j = 1;
1275      while(j++ < k && y.compareTo(n1) != 0) {
1276        y = y.modPowInt(2,this);
1277        if(y.compareTo(BigInteger.ONE) == 0) return false;
1278      }
1279      if(y.compareTo(n1) != 0) return false;
1280    }
1281  }
1282  return true;
1283}
1284
1285// protected
1286BigInteger.prototype.chunkSize = bnpChunkSize;
1287BigInteger.prototype.toRadix = bnpToRadix;
1288BigInteger.prototype.fromRadix = bnpFromRadix;
1289BigInteger.prototype.fromNumber = bnpFromNumber;
1290BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
1291BigInteger.prototype.changeBit = bnpChangeBit;
1292BigInteger.prototype.addTo = bnpAddTo;
1293BigInteger.prototype.dMultiply = bnpDMultiply;
1294BigInteger.prototype.dAddOffset = bnpDAddOffset;
1295BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
1296BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
1297BigInteger.prototype.modInt = bnpModInt;
1298BigInteger.prototype.millerRabin = bnpMillerRabin;
1299
1300// public
1301BigInteger.prototype.clone = bnClone;
1302BigInteger.prototype.intValue = bnIntValue;
1303BigInteger.prototype.byteValue = bnByteValue;
1304BigInteger.prototype.shortValue = bnShortValue;
1305BigInteger.prototype.signum = bnSigNum;
1306BigInteger.prototype.toByteArray = bnToByteArray;
1307BigInteger.prototype.equals = bnEquals;
1308BigInteger.prototype.min = bnMin;
1309BigInteger.prototype.max = bnMax;
1310BigInteger.prototype.and = bnAnd;
1311BigInteger.prototype.or = bnOr;
1312BigInteger.prototype.xor = bnXor;
1313BigInteger.prototype.andNot = bnAndNot;
1314BigInteger.prototype.not = bnNot;
1315BigInteger.prototype.shiftLeft = bnShiftLeft;
1316BigInteger.prototype.shiftRight = bnShiftRight;
1317BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
1318BigInteger.prototype.bitCount = bnBitCount;
1319BigInteger.prototype.testBit = bnTestBit;
1320BigInteger.prototype.setBit = bnSetBit;
1321BigInteger.prototype.clearBit = bnClearBit;
1322BigInteger.prototype.flipBit = bnFlipBit;
1323BigInteger.prototype.add = bnAdd;
1324BigInteger.prototype.subtract = bnSubtract;
1325BigInteger.prototype.multiply = bnMultiply;
1326BigInteger.prototype.divide = bnDivide;
1327BigInteger.prototype.remainder = bnRemainder;
1328BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
1329BigInteger.prototype.modPow = bnModPow;
1330BigInteger.prototype.modInverse = bnModInverse;
1331BigInteger.prototype.pow = bnPow;
1332BigInteger.prototype.gcd = bnGCD;
1333BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
1334
1335// BigInteger interfaces not implemented in jsbn:
1336
1337// BigInteger(int signum, byte[] magnitude)
1338// double doubleValue()
1339// float floatValue()
1340// int hashCode()
1341// long longValue()
1342// static BigInteger valueOf(long val)
1343// prng4.js - uses Arcfour as a PRNG
1344
1345function Arcfour() {
1346  this.i = 0;
1347  this.j = 0;
1348  this.S = new Array();
1349}
1350
1351// Initialize arcfour context from key, an array of ints, each from [0..255]
1352function ARC4init(key) {
1353  var i, j, t;
1354  for(i = 0; i < 256; ++i)
1355    this.S[i] = i;
1356  j = 0;
1357  for(i = 0; i < 256; ++i) {
1358    j = (j + this.S[i] + key[i % key.length]) & 255;
1359    t = this.S[i];
1360    this.S[i] = this.S[j];
1361    this.S[j] = t;
1362  }
1363  this.i = 0;
1364  this.j = 0;
1365}
1366
1367function ARC4next() {
1368  var t;
1369  this.i = (this.i + 1) & 255;
1370  this.j = (this.j + this.S[this.i]) & 255;
1371  t = this.S[this.i];
1372  this.S[this.i] = this.S[this.j];
1373  this.S[this.j] = t;
1374  return this.S[(t + this.S[this.i]) & 255];
1375}
1376
1377Arcfour.prototype.init = ARC4init;
1378Arcfour.prototype.next = ARC4next;
1379
1380// Plug in your RNG constructor here
1381function prng_newstate() {
1382  return new Arcfour();
1383}
1384
1385// Pool size must be a multiple of 4 and greater than 32.
1386// An array of bytes the size of the pool will be passed to init()
1387var rng_psize = 256;
1388// Random number generator - requires a PRNG backend, e.g. prng4.js
1389
1390// For best results, put code like
1391// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
1392// in your main HTML document.
1393
1394var rng_state;
1395var rng_pool;
1396var rng_pptr;
1397
1398// Mix in a 32-bit integer into the pool
1399function rng_seed_int(x) {
1400  rng_pool[rng_pptr++] ^= x & 255;
1401  rng_pool[rng_pptr++] ^= (x >> 8) & 255;
1402  rng_pool[rng_pptr++] ^= (x >> 16) & 255;
1403  rng_pool[rng_pptr++] ^= (x >> 24) & 255;
1404  if(rng_pptr >= rng_psize) rng_pptr -= rng_psize;
1405}
1406
1407// Mix in the current time (w/milliseconds) into the pool
1408function rng_seed_time() {
1409  // Use pre-computed date to avoid making the benchmark 
1410  // results dependent on the current date.
1411  rng_seed_int(1122926989487);
1412}
1413
1414// Initialize the pool with junk if needed.
1415if(rng_pool == null) {
1416  rng_pool = new Array();
1417  rng_pptr = 0;
1418  var t;
1419  while(rng_pptr < rng_psize) {  // extract some randomness from Math.random()
1420    t = Math.floor(65536 * Math.random());
1421    rng_pool[rng_pptr++] = t >>> 8;
1422    rng_pool[rng_pptr++] = t & 255;
1423  }
1424  rng_pptr = 0;
1425  rng_seed_time();
1426  //rng_seed_int(window.screenX);
1427  //rng_seed_int(window.screenY);
1428}
1429
1430function rng_get_byte() {
1431  if(rng_state == null) {
1432    rng_seed_time();
1433    rng_state = prng_newstate();
1434    rng_state.init(rng_pool);
1435    for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
1436      rng_pool[rng_pptr] = 0;
1437    rng_pptr = 0;
1438    //rng_pool = null;
1439  }
1440  // TODO: allow reseeding after first request
1441  return rng_state.next();
1442}
1443
1444function rng_get_bytes(ba) {
1445  var i;
1446  for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
1447}
1448
1449function SecureRandom() {}
1450
1451SecureRandom.prototype.nextBytes = rng_get_bytes;
1452// Depends on jsbn.js and rng.js
1453
1454// convert a (hex) string to a bignum object
1455function parseBigInt(str,r) {
1456  return new BigInteger(str,r);
1457}
1458
1459function linebrk(s,n) {
1460  var ret = "";
1461  var i = 0;
1462  while(i + n < s.length) {
1463    ret += s.substring(i,i+n) + "\n";
1464    i += n;
1465  }
1466  return ret + s.substring(i,s.length);
1467}
1468
1469function byte2Hex(b) {
1470  if(b < 0x10)
1471    return "0" + b.toString(16);
1472  else
1473    return b.toString(16);
1474}
1475
1476// PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
1477function pkcs1pad2(s,n) {
1478  if(n < s.length + 11) {
1479    alert("Message too long for RSA");
1480    return null;
1481  }
1482  var ba = new Array();
1483  var i = s.length - 1;
1484  while(i >= 0 && n > 0) ba[--n] = s.charCodeAt(i--);
1485  ba[--n] = 0;
1486  var rng = new SecureRandom();
1487  var x = new Array();
1488  while(n > 2) { // random non-zero pad
1489    x[0] = 0;
1490    while(x[0] == 0) rng.nextBytes(x);
1491    ba[--n] = x[0];
1492  }
1493  ba[--n] = 2;
1494  ba[--n] = 0;
1495  return new BigInteger(ba);
1496}
1497
1498// "empty" RSA key constructor
1499function RSAKey() {
1500  this.n = null;
1501  this.e = 0;
1502  this.d = null;
1503  this.p = null;
1504  this.q = null;
1505  this.dmp1 = null;
1506  this.dmq1 = null;
1507  this.coeff = null;
1508}
1509
1510// Set the public key fields N and e from hex strings
1511function RSASetPublic(N,E) {
1512  if(N != null && E != null && N.length > 0 && E.length > 0) {
1513    this.n = parseBigInt(N,16);
1514    this.e = parseInt(E,16);
1515  }
1516  else
1517    alert("Invalid RSA public key");
1518}
1519
1520// Perform raw public operation on "x": return x^e (mod n)
1521function RSADoPublic(x) {
1522  return x.modPowInt(this.e, this.n);
1523}
1524
1525// Return the PKCS#1 RSA encryption of "text" as an even-length hex string
1526function RSAEncrypt(text) {
1527  var m = pkcs1pad2(text,(this.n.bitLength()+7)>>3);
1528  if(m == null) return null;
1529  var c = this.doPublic(m);
1530  if(c == null) return null;
1531  var h = c.toString(16);
1532  if((h.length & 1) == 0) return h; else return "0" + h;
1533}
1534
1535// Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
1536//function RSAEncryptB64(text) {
1537//  var h = this.encrypt(text);
1538//  if(h) return hex2b64(h); else return null;
1539//}
1540
1541// protected
1542RSAKey.prototype.doPublic = RSADoPublic;
1543
1544// public
1545RSAKey.prototype.setPublic = RSASetPublic;
1546RSAKey.prototype.encrypt = RSAEncrypt;
1547//RSAKey.prototype.encrypt_b64 = RSAEncryptB64;
1548// Depends on rsa.js and jsbn2.js
1549
1550// Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
1551function pkcs1unpad2(d,n) {
1552  var b = d.toByteArray();
1553  var i = 0;
1554  while(i < b.length && b[i] == 0) ++i;
1555  if(b.length-i != n-1 || b[i] != 2)
1556    return null;
1557  ++i;
1558  while(b[i] != 0)
1559    if(++i >= b.length) return null;
1560  var ret = "";
1561  while(++i < b.length)
1562    ret += String.fromCharCode(b[i]);
1563  return ret;
1564}
1565
1566// Set the private key fields N, e, and d from hex strings
1567function RSASetPrivate(N,E,D) {
1568  if(N != null && E != null && N.length > 0 && E.length > 0) {
1569    this.n = parseBigInt(N,16);
1570    this.e = parseInt(E,16);
1571    this.d = parseBigInt(D,16);
1572  }
1573  else
1574    alert("Invalid RSA private key");
1575}
1576
1577// Set the private key fields N, e, d and CRT params from hex strings
1578function RSASetPrivateEx(N,E,D,P,Q,DP,DQ,C) {
1579  if(N != null && E != null && N.length > 0 && E.length > 0) {
1580    this.n = parseBigInt(N,16);
1581    this.e = parseInt(E,16);
1582    this.d = parseBigInt(D,16);
1583    this.p = parseBigInt(P,16);
1584    this.q = parseBigInt(Q,16);
1585    this.dmp1 = parseBigInt(DP,16);
1586    this.dmq1 = parseBigInt(DQ,16);
1587    this.coeff = parseBigInt(C,16);
1588  }
1589  else
1590    alert("Invalid RSA private key");
1591}
1592
1593// Generate a new random private key B bits long, using public expt E
1594function RSAGenerate(B,E) {
1595  var rng = new SecureRandom();
1596  var qs = B>>1;
1597  this.e = parseInt(E,16);
1598  var ee = new BigInteger(E,16);
1599  for(;;) {
1600    for(;;) {
1601      this.p = new BigInteger(B-qs,1,rng);
1602      if(this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break;
1603    }
1604    for(;;) {
1605      this.q = new BigInteger(qs,1,rng);
1606      if(this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break;
1607    }
1608    if(this.p.compareTo(this.q) <= 0) {
1609      var t = this.p;
1610      this.p = this.q;
1611      this.q = t;
1612    }
1613    var p1 = this.p.subtract(BigInteger.ONE);
1614    var q1 = this.q.subtract(BigInteger.ONE);
1615    var phi = p1.multiply(q1);
1616    if(phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
1617      this.n = this.p.multiply(this.q);
1618      this.d = ee.modInverse(phi);
1619      this.dmp1 = this.d.mod(p1);
1620      this.dmq1 = this.d.mod(q1);
1621      this.coeff = this.q.modInverse(this.p);
1622      break;
1623    }
1624  }
1625}
1626
1627// Perform raw private operation on "x": return x^d (mod n)
1628function RSADoPrivate(x) {
1629  if(this.p == null || this.q == null)
1630    return x.modPow(this.d, this.n);
1631
1632  // TODO: re-calculate any missing CRT params
1633  var xp = x.mod(this.p).modPow(this.dmp1, this.p);
1634  var xq = x.mod(this.q).modPow(this.dmq1, this.q);
1635
1636  while(xp.compareTo(xq) < 0)
1637    xp = xp.add(this.p);
1638  return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq);
1639}
1640
1641// Return the PKCS#1 RSA decryption of "ctext".
1642// "ctext" is an even-length hex string and the output is a plain string.
1643function RSADecrypt(ctext) {
1644  var c = parseBigInt(ctext, 16);
1645  var m = this.doPrivate(c);
1646  if(m == null) return null;
1647  return pkcs1unpad2(m, (this.n.bitLength()+7)>>3);
1648}
1649
1650// Return the PKCS#1 RSA decryption of "ctext".
1651// "ctext" is a Base64-encoded string and the output is a plain string.
1652//function RSAB64Decrypt(ctext) {
1653//  var h = b64tohex(ctext);
1654//  if(h) return this.decrypt(h); else return null;
1655//}
1656
1657// protected
1658RSAKey.prototype.doPrivate = RSADoPrivate;
1659
1660// public
1661RSAKey.prototype.setPrivate = RSASetPrivate;
1662RSAKey.prototype.setPrivateEx = RSASetPrivateEx;
1663RSAKey.prototype.generate = RSAGenerate;
1664RSAKey.prototype.decrypt = RSADecrypt;
1665//RSAKey.prototype.b64_decrypt = RSAB64Decrypt;
1666
1667
1668nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3";
1669eValue="10001";
1670dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161";
1671pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d";
1672qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f";
1673dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25";
1674dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd";
1675coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250";
1676
1677setupEngine(am3, 28);
1678
1679var TEXT = "The quick brown fox jumped over the extremely lazy frog! " +
1680    "Now is the time for all good men to come to the party.";
1681var encrypted;
1682
1683function encrypt() {
1684  var RSA = new RSAKey();
1685  RSA.setPublic(nValue, eValue);
1686  RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
1687  encrypted = RSA.encrypt(TEXT);
1688}
1689
1690function decrypt() {
1691  var RSA = new RSAKey();
1692  RSA.setPublic(nValue, eValue);
1693  RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
1694  var decrypted = RSA.decrypt(encrypted);
1695  if (decrypted != TEXT) {
1696    throw new Error("Crypto operation failed");
1697  }
1698}