chrome/test/data/dromaeo/tests/v8-crypto.html

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   5 /*
   6  * Copyright (c) 2003-2005  Tom Wu
   7  * All Rights Reserved.
   8  *
   9  * Permission is hereby granted, free of charge, to any person obtaining
  10  * a copy of this software and associated documentation files (the
  11  * "Software"), to deal in the Software without restriction, including
  12  * without limitation the rights to use, copy, modify, merge, publish,
  13  * distribute, sublicense, and/or sell copies of the Software, and to
  14  * permit persons to whom the Software is furnished to do so, subject to
  15  * the following conditions:
  16  *
  17  * The above copyright notice and this permission notice shall be
  18  * included in all copies or substantial portions of the Software.
  19  *
  20  * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
  21  * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
  22  * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
  23  *
  24  * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
  25  * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
  26  * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
  27  * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
  28  * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  29  *
  30  * In addition, the following condition applies:
  31  *
  32  * All redistributions must retain an intact copy of this copyright notice
  33  * and disclaimer.
  34  */
  35
  36
  37 // The code has been adapted for use as a benchmark by Google.
  38
  39 // Basic JavaScript BN library - subset useful for RSA encryption.
  40
  41 // Bits per digit
  42 var dbits;
  43 var BI_DB;
  44 var BI_DM;
  45 var BI_DV;
  46
  47 var BI_FP;
  48 var BI_FV;
  49 var BI_F1;
  50 var BI_F2;
  51
  52 // JavaScript engine analysis
  53 var canary = 0xdeadbeefcafe;
  54 var j_lm = ((canary&0xffffff)==0xefcafe);
  55
  56 // (public) Constructor
  57 function BigInteger(a,b,c) {
  58   this.array = new Array();
  59   if(a != null)
  60     if("number" == typeof a) this.fromNumber(a,b,c);
  61     else if(b == null && "string" != typeof a) this.fromString(a,256);
  62     else this.fromString(a,b);
  63 }
  64
  65 // return new, unset BigInteger
  66 function nbi() { return new BigInteger(null); }
  67
  68 // am: Compute w_j += (x*this_i), propagate carries,
  69 // c is initial carry, returns final carry.
  70 // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
  71 // We need to select the fastest one that works in this environment.
  72
  73 // am1: use a single mult and divide to get the high bits,
  74 // max digit bits should be 26 because
  75 // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
  76 function am1(i,x,w,j,c,n) {
  77   var this_array = this.array;
  78   var w_array    = w.array;
  79   while(--n >= 0) {
  80     var v = x*this_array[i++]+w_array[j]+c;
  81     c = Math.floor(v/0x4000000);
  82     w_array[j++] = v&0x3ffffff;
  83   }
  84   return c;
  85 }
  86
  87 // am2 avoids a big mult-and-extract completely.
  88 // Max digit bits should be <= 30 because we do bitwise ops
  89 // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
  90 function am2(i,x,w,j,c,n) {
  91   var this_array = this.array;
  92   var w_array    = w.array;
  93   var xl = x&0x7fff, xh = x>>15;
  94   while(--n >= 0) {
  95     var l = this_array[i]&0x7fff;
  96     var h = this_array[i++]>>15;
  97     var m = xh*l+h*xl;
  98     l = xl*l+((m&0x7fff)<<15)+w_array[j]+(c&0x3fffffff);
  99     c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
 100     w_array[j++] = l&0x3fffffff;
 101   }
 102   return c;
 103 }
 104
 105 // Alternately, set max digit bits to 28 since some
 106 // browsers slow down when dealing with 32-bit numbers.
 107 function am3(i,x,w,j,c,n) {
 108   var this_array = this.array;
 109   var w_array    = w.array;
 110
 111   var xl = x&0x3fff, xh = x>>14;
 112   while(--n >= 0) {
 113     var l = this_array[i]&0x3fff;
 114     var h = this_array[i++]>>14;
 115     var m = xh*l+h*xl;
 116     l = xl*l+((m&0x3fff)<<14)+w_array[j]+c;
 117     c = (l>>28)+(m>>14)+xh*h;
 118     w_array[j++] = l&0xfffffff;
 119   }
 120   return c;
 121 }
 122
 123 // This is tailored to VMs with 2-bit tagging. It makes sure
 124 // that all the computations stay within the 29 bits available.
 125 function am4(i,x,w,j,c,n) {
 126   var this_array = this.array;
 127   var w_array    = w.array;
 128
 129   var xl = x&0x1fff, xh = x>>13;
 130   while(--n >= 0) {
 131     var l = this_array[i]&0x1fff;
 132     var h = this_array[i++]>>13;
 133     var m = xh*l+h*xl;
 134     l = xl*l+((m&0x1fff)<<13)+w_array[j]+c;
 135     c = (l>>26)+(m>>13)+xh*h;
 136     w_array[j++] = l&0x3ffffff;
 137   }
 138   return c;
 139 }
 140
 141 // am3/28 is best for SM, Rhino, but am4/26 is best for v8.
 142 // Kestrel (Opera 9.5) gets its best result with am4/26.
 143 // IE7 does 9% better with am3/28 than with am4/26.
 144 // Firefox (SM) gets 10% faster with am3/28 than with am4/26.
 145
 146 setupEngine = function(fn, bits) {
 147   BigInteger.prototype.am = fn;
 148   dbits = bits;
 149
 150   BI_DB = dbits;
 151   BI_DM = ((1<<dbits)-1);
 152   BI_DV = (1<<dbits);
 153
 154   BI_FP = 52;
 155   BI_FV = Math.pow(2,BI_FP);
 156   BI_F1 = BI_FP-dbits;
 157   BI_F2 = 2*dbits-BI_FP;
 158 }
 159
 160
 161 // Digit conversions
 162 var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
 163 var BI_RC = new Array();
 164 var rr,vv;
 165 rr = "0".charCodeAt(0);
 166 for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
 167 rr = "a".charCodeAt(0);
 168 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
 169 rr = "A".charCodeAt(0);
 170 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
 171
 172 function int2char(n) { return BI_RM.charAt(n); }
 173 function intAt(s,i) {
 174   var c = BI_RC[s.charCodeAt(i)];
 175   return (c==null)?-1:c;
 176 }
 177
 178 // (protected) copy this to r
 179 function bnpCopyTo(r) {
 180   var this_array = this.array;
 181   var r_array    = r.array;
 182
 183   for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i];
 184   r.t = this.t;
 185   r.s = this.s;
 186 }
 187
 188 // (protected) set from integer value x, -DV <= x < DV
 189 function bnpFromInt(x) {
 190   var this_array = this.array;
 191   this.t = 1;
 192   this.s = (x<0)?-1:0;
 193   if(x > 0) this_array[0] = x;
 194   else if(x < -1) this_array[0] = x+DV;
 195   else this.t = 0;
 196 }
 197
 198 // return bigint initialized to value
 199 function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
 200
 201 // (protected) set from string and radix
 202 function bnpFromString(s,b) {
 203   var this_array = this.array;
 204   var k;
 205   if(b == 16) k = 4;
 206   else if(b == 8) k = 3;
 207   else if(b == 256) k = 8; // byte array
 208   else if(b == 2) k = 1;
 209   else if(b == 32) k = 5;
 210   else if(b == 4) k = 2;
 211   else { this.fromRadix(s,b); return; }
 212   this.t = 0;
 213   this.s = 0;
 214   var i = s.length, mi = false, sh = 0;
 215   while(--i >= 0) {
 216     var x = (k==8)?s[i]&0xff:intAt(s,i);
 217     if(x < 0) {
 218       if(s.charAt(i) == "-") mi = true;
 219       continue;
 220     }
 221     mi = false;
 222     if(sh == 0)
 223       this_array[this.t++] = x;
 224     else if(sh+k > BI_DB) {
 225       this_array[this.t-1] |= (x&((1<<(BI_DB-sh))-1))<<sh;
 226       this_array[this.t++] = (x>>(BI_DB-sh));
 227     }
 228     else
 229       this_array[this.t-1] |= x<<sh;
 230     sh += k;
 231     if(sh >= BI_DB) sh -= BI_DB;
 232   }
 233   if(k == 8 && (s[0]&0x80) != 0) {
 234     this.s = -1;
 235     if(sh > 0) this_array[this.t-1] |= ((1<<(BI_DB-sh))-1)<<sh;
 236   }
 237   this.clamp();
 238   if(mi) BigInteger.ZERO.subTo(this,this);
 239 }
 240
 241 // (protected) clamp off excess high words
 242 function bnpClamp() {
 243   var this_array = this.array;
 244   var c = this.s&BI_DM;
 245   while(this.t > 0 && this_array[this.t-1] == c) --this.t;
 246 }
 247
 248 // (public) return string representation in given radix
 249 function bnToString(b) {
 250   var this_array = this.array;
 251   if(this.s < 0) return "-"+this.negate().toString(b);
 252   var k;
 253   if(b == 16) k = 4;
 254   else if(b == 8) k = 3;
 255   else if(b == 2) k = 1;
 256   else if(b == 32) k = 5;
 257   else if(b == 4) k = 2;
 258   else return this.toRadix(b);
 259   var km = (1<<k)-1, d, m = false, r = "", i = this.t;
 260   var p = BI_DB-(i*BI_DB)%k;
 261   if(i-- > 0) {
 262     if(p < BI_DB && (d = this_array[i]>>p) > 0) { m = true; r = int2char(d); }
 263     while(i >= 0) {
 264       if(p < k) {
 265         d = (this_array[i]&((1<<p)-1))<<(k-p);
 266         d |= this_array[--i]>>(p+=BI_DB-k);
 267       }
 268       else {
 269         d = (this_array[i]>>(p-=k))&km;
 270         if(p <= 0) { p += BI_DB; --i; }
 271       }
 272       if(d > 0) m = true;
 273       if(m) r += int2char(d);
 274     }
 275   }
 276   return m?r:"0";
 277 }
 278
 279 // (public) -this
 280 function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
 281
 282 // (public) |this|
 283 function bnAbs() { return (this.s<0)?this.negate():this; }
 284
 285 // (public) return + if this > a, - if this < a, 0 if equal
 286 function bnCompareTo(a) {
 287   var this_array = this.array;
 288   var a_array = a.array;
 289
 290   var r = this.s-a.s;
 291   if(r != 0) return r;
 292   var i = this.t;
 293   r = i-a.t;
 294   if(r != 0) return r;
 295   while(--i >= 0) if((r=this_array[i]-a_array[i]) != 0) return r;
 296   return 0;
 297 }
 298
 299 // returns bit length of the integer x
 300 function nbits(x) {
 301   var r = 1, t;
 302   if((t=x>>>16) != 0) { x = t; r += 16; }
 303   if((t=x>>8) != 0) { x = t; r += 8; }
 304   if((t=x>>4) != 0) { x = t; r += 4; }
 305   if((t=x>>2) != 0) { x = t; r += 2; }
 306   if((t=x>>1) != 0) { x = t; r += 1; }
 307   return r;
 308 }
 309
 310 // (public) return the number of bits in "this"
 311 function bnBitLength() {
 312   var this_array = this.array;
 313   if(this.t <= 0) return 0;
 314   return BI_DB*(this.t-1)+nbits(this_array[this.t-1]^(this.s&BI_DM));
 315 }
 316
 317 // (protected) r = this << n*DB
 318 function bnpDLShiftTo(n,r) {
 319   var this_array = this.array;
 320   var r_array = r.array;
 321   var i;
 322   for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i];
 323   for(i = n-1; i >= 0; --i) r_array[i] = 0;
 324   r.t = this.t+n;
 325   r.s = this.s;
 326 }
 327
 328 // (protected) r = this >> n*DB
 329 function bnpDRShiftTo(n,r) {
 330   var this_array = this.array;
 331   var r_array = r.array;
 332   for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i];
 333   r.t = Math.max(this.t-n,0);
 334   r.s = this.s;
 335 }
 336
 337 // (protected) r = this << n
 338 function bnpLShiftTo(n,r) {
 339   var this_array = this.array;
 340   var r_array = r.array;
 341   var bs = n%BI_DB;
 342   var cbs = BI_DB-bs;
 343   var bm = (1<<cbs)-1;
 344   var ds = Math.floor(n/BI_DB), c = (this.s<<bs)&BI_DM, i;
 345   for(i = this.t-1; i >= 0; --i) {
 346     r_array[i+ds+1] = (this_array[i]>>cbs)|c;
 347     c = (this_array[i]&bm)<<bs;
 348   }
 349   for(i = ds-1; i >= 0; --i) r_array[i] = 0;
 350   r_array[ds] = c;
 351   r.t = this.t+ds+1;
 352   r.s = this.s;
 353   r.clamp();
 354 }
 355
 356 // (protected) r = this >> n
 357 function bnpRShiftTo(n,r) {
 358   var this_array = this.array;
 359   var r_array = r.array;
 360   r.s = this.s;
 361   var ds = Math.floor(n/BI_DB);
 362   if(ds >= this.t) { r.t = 0; return; }
 363   var bs = n%BI_DB;
 364   var cbs = BI_DB-bs;
 365   var bm = (1<<bs)-1;
 366   r_array[0] = this_array[ds]>>bs;
 367   for(var i = ds+1; i < this.t; ++i) {
 368     r_array[i-ds-1] |= (this_array[i]&bm)<<cbs;
 369     r_array[i-ds] = this_array[i]>>bs;
 370   }
 371   if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs;
 372   r.t = this.t-ds;
 373   r.clamp();
 374 }
 375
 376 // (protected) r = this - a
 377 function bnpSubTo(a,r) {
 378   var this_array = this.array;
 379   var r_array = r.array;
 380   var a_array = a.array;
 381   var i = 0, c = 0, m = Math.min(a.t,this.t);
 382   while(i < m) {
 383     c += this_array[i]-a_array[i];
 384     r_array[i++] = c&BI_DM;
 385     c >>= BI_DB;
 386   }
 387   if(a.t < this.t) {
 388     c -= a.s;
 389     while(i < this.t) {
 390       c += this_array[i];
 391       r_array[i++] = c&BI_DM;
 392       c >>= BI_DB;
 393     }
 394     c += this.s;
 395   }
 396   else {
 397     c += this.s;
 398     while(i < a.t) {
 399       c -= a_array[i];
 400       r_array[i++] = c&BI_DM;
 401       c >>= BI_DB;
 402     }
 403     c -= a.s;
 404   }
 405   r.s = (c<0)?-1:0;
 406   if(c < -1) r_array[i++] = BI_DV+c;
 407   else if(c > 0) r_array[i++] = c;
 408   r.t = i;
 409   r.clamp();
 410 }
 411
 412 // (protected) r = this * a, r != this,a (HAC 14.12)
 413 // "this" should be the larger one if appropriate.
 414 function bnpMultiplyTo(a,r) {
 415   var this_array = this.array;
 416   var r_array = r.array;
 417   var x = this.abs(), y = a.abs();
 418   var y_array = y.array;
 419
 420   var i = x.t;
 421   r.t = i+y.t;
 422   while(--i >= 0) r_array[i] = 0;
 423   for(i = 0; i < y.t; ++i) r_array[i+x.t] = x.am(0,y_array[i],r,i,0,x.t);
 424   r.s = 0;
 425   r.clamp();
 426   if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
 427 }
 428
 429 // (protected) r = this^2, r != this (HAC 14.16)
 430 function bnpSquareTo(r) {
 431   var x = this.abs();
 432   var x_array = x.array;
 433   var r_array = r.array;
 434
 435   var i = r.t = 2*x.t;
 436   while(--i >= 0) r_array[i] = 0;
 437   for(i = 0; i < x.t-1; ++i) {
 438     var c = x.am(i,x_array[i],r,2*i,0,1);
 439     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) {
 440       r_array[i+x.t] -= BI_DV;
 441       r_array[i+x.t+1] = 1;
 442     }
 443   }
 444   if(r.t > 0) r_array[r.t-1] += x.am(i,x_array[i],r,2*i,0,1);
 445   r.s = 0;
 446   r.clamp();
 447 }
 448
 449 // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
 450 // r != q, this != m.  q or r may be null.
 451 function bnpDivRemTo(m,q,r) {
 452   var pm = m.abs();
 453   if(pm.t <= 0) return;
 454   var pt = this.abs();
 455   if(pt.t < pm.t) {
 456     if(q != null) q.fromInt(0);
 457     if(r != null) this.copyTo(r);
 458     return;
 459   }
 460   if(r == null) r = nbi();
 461   var y = nbi(), ts = this.s, ms = m.s;
 462   var pm_array = pm.array;
 463   var nsh = BI_DB-nbits(pm_array[pm.t-1]);      // normalize modulus
 464   if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
 465   else { pm.copyTo(y); pt.copyTo(r); }
 466   var ys = y.t;
 467
 468   var y_array = y.array;
 469   var y0 = y_array[ys-1];
 470   if(y0 == 0) return;
 471   var yt = y0*(1<<BI_F1)+((ys>1)?y_array[ys-2]>>BI_F2:0);
 472   var d1 = BI_FV/yt, d2 = (1<<BI_F1)/yt, e = 1<<BI_F2;
 473   var i = r.t, j = i-ys, t = (q==null)?nbi():q;
 474   y.dlShiftTo(j,t);
 475
 476   var r_array = r.array;
 477   if(r.compareTo(t) >= 0) {
 478     r_array[r.t++] = 1;
 479     r.subTo(t,r);
 480   }
 481   BigInteger.ONE.dlShiftTo(ys,t);
 482   t.subTo(y,y); // "negative" y so we can replace sub with am later
 483   while(y.t < ys) y_array[y.t++] = 0;
 484   while(--j >= 0) {
 485     // Estimate quotient digit
 486     var qd = (r_array[--i]==y0)?BI_DM:Math.floor(r_array[i]*d1+(r_array[i-1]+e)*d2);
 487     if((r_array[i]+=y.am(0,qd,r,j,0,ys)) < qd) {        // Try it out
 488       y.dlShiftTo(j,t);
 489       r.subTo(t,r);
 490       while(r_array[i] < --qd) r.subTo(t,r);
 491     }
 492   }
 493   if(q != null) {
 494     r.drShiftTo(ys,q);
 495     if(ts != ms) BigInteger.ZERO.subTo(q,q);
 496   }
 497   r.t = ys;
 498   r.clamp();
 499   if(nsh > 0) r.rShiftTo(nsh,r);        // Denormalize remainder
 500   if(ts < 0) BigInteger.ZERO.subTo(r,r);
 501 }
 502
 503 // (public) this mod a
 504 function bnMod(a) {
 505   var r = nbi();
 506   this.abs().divRemTo(a,null,r);
 507   if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
 508   return r;
 509 }
 510
 511 // Modular reduction using "classic" algorithm
 512 function Classic(m) { this.m = m; }
 513 function cConvert(x) {
 514   if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
 515   else return x;
 516 }
 517 function cRevert(x) { return x; }
 518 function cReduce(x) { x.divRemTo(this.m,null,x); }
 519 function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
 520 function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
 521
 522 Classic.prototype.convert = cConvert;
 523 Classic.prototype.revert = cRevert;
 524 Classic.prototype.reduce = cReduce;
 525 Classic.prototype.mulTo = cMulTo;
 526 Classic.prototype.sqrTo = cSqrTo;
 527
 528 // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
 529 // justification:
 530 //         xy == 1 (mod m)
 531 //         xy =  1+km
 532 //   xy(2-xy) = (1+km)(1-km)
 533 // x[y(2-xy)] = 1-k^2m^2
 534 // x[y(2-xy)] == 1 (mod m^2)
 535 // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
 536 // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
 537 // JS multiply "overflows" differently from C/C++, so care is needed here.
 538 function bnpInvDigit() {
 539   var this_array = this.array;
 540   if(this.t < 1) return 0;
 541   var x = this_array[0];
 542   if((x&1) == 0) return 0;
 543   var y = x&3;          // y == 1/x mod 2^2
 544   y = (y*(2-(x&0xf)*y))&0xf;    // y == 1/x mod 2^4
 545   y = (y*(2-(x&0xff)*y))&0xff;  // y == 1/x mod 2^8
 546   y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;   // y == 1/x mod 2^16
 547   // last step - calculate inverse mod DV directly;
 548   // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
 549   y = (y*(2-x*y%BI_DV))%BI_DV;          // y == 1/x mod 2^dbits
 550   // we really want the negative inverse, and -DV < y < DV
 551   return (y>0)?BI_DV-y:-y;
 552 }
 553
 554 // Montgomery reduction
 555 function Montgomery(m) {
 556   this.m = m;
 557   this.mp = m.invDigit();
 558   this.mpl = this.mp&0x7fff;
 559   this.mph = this.mp>>15;
 560   this.um = (1<<(BI_DB-15))-1;
 561   this.mt2 = 2*m.t;
 562 }
 563
 564 // xR mod m
 565 function montConvert(x) {
 566   var r = nbi();
 567   x.abs().dlShiftTo(this.m.t,r);
 568   r.divRemTo(this.m,null,r);
 569   if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
 570   return r;
 571 }
 572
 573 // x/R mod m
 574 function montRevert(x) {
 575   var r = nbi();
 576   x.copyTo(r);
 577   this.reduce(r);
 578   return r;
 579 }
 580
 581 // x = x/R mod m (HAC 14.32)
 582 function montReduce(x) {
 583   var x_array = x.array;
 584   while(x.t <= this.mt2)        // pad x so am has enough room later
 585     x_array[x.t++] = 0;
 586   for(var i = 0; i < this.m.t; ++i) {
 587     // faster way of calculating u0 = x[i]*mp mod DV
 588     var j = x_array[i]&0x7fff;
 589     var u0 = (j*this.mpl+(((j*this.mph+(x_array[i]>>15)*this.mpl)&this.um)<<15))&BI_DM;
 590     // use am to combine the multiply-shift-add into one call
 591     j = i+this.m.t;
 592     x_array[j] += this.m.am(0,u0,x,i,0,this.m.t);
 593     // propagate carry
 594     while(x_array[j] >= BI_DV) { x_array[j] -= BI_DV; x_array[++j]++; }
 595   }
 596   x.clamp();
 597   x.drShiftTo(this.m.t,x);
 598   if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
 599 }
 600
 601 // r = "x^2/R mod m"; x != r
 602 function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
 603
 604 // r = "xy/R mod m"; x,y != r
 605 function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
 606
 607 Montgomery.prototype.convert = montConvert;
 608 Montgomery.prototype.revert = montRevert;
 609 Montgomery.prototype.reduce = montReduce;
 610 Montgomery.prototype.mulTo = montMulTo;
 611 Montgomery.prototype.sqrTo = montSqrTo;
 612
 613 // (protected) true iff this is even
 614 function bnpIsEven() {
 615   var this_array = this.array;
 616   return ((this.t>0)?(this_array[0]&1):this.s) == 0;
 617 }
 618
 619 // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
 620 function bnpExp(e,z) {
 621   if(e > 0xffffffff || e < 1) return BigInteger.ONE;
 622   var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
 623   g.copyTo(r);
 624   while(--i >= 0) {
 625     z.sqrTo(r,r2);
 626     if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
 627     else { var t = r; r = r2; r2 = t; }
 628   }
 629   return z.revert(r);
 630 }
 631
 632 // (public) this^e % m, 0 <= e < 2^32
 633 function bnModPowInt(e,m) {
 634   var z;
 635   if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
 636   return this.exp(e,z);
 637 }
 638
 639 // protected
 640 BigInteger.prototype.copyTo = bnpCopyTo;
 641 BigInteger.prototype.fromInt = bnpFromInt;
 642 BigInteger.prototype.fromString = bnpFromString;
 643 BigInteger.prototype.clamp = bnpClamp;
 644 BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
 645 BigInteger.prototype.drShiftTo = bnpDRShiftTo;
 646 BigInteger.prototype.lShiftTo = bnpLShiftTo;
 647 BigInteger.prototype.rShiftTo = bnpRShiftTo;
 648 BigInteger.prototype.subTo = bnpSubTo;
 649 BigInteger.prototype.multiplyTo = bnpMultiplyTo;
 650 BigInteger.prototype.squareTo = bnpSquareTo;
 651 BigInteger.prototype.divRemTo = bnpDivRemTo;
 652 BigInteger.prototype.invDigit = bnpInvDigit;
 653 BigInteger.prototype.isEven = bnpIsEven;
 654 BigInteger.prototype.exp = bnpExp;
 655
 656 // public
 657 BigInteger.prototype.toString = bnToString;
 658 BigInteger.prototype.negate = bnNegate;
 659 BigInteger.prototype.abs = bnAbs;
 660 BigInteger.prototype.compareTo = bnCompareTo;
 661 BigInteger.prototype.bitLength = bnBitLength;
 662 BigInteger.prototype.mod = bnMod;
 663 BigInteger.prototype.modPowInt = bnModPowInt;
 664
 665 // "constants"
 666 BigInteger.ZERO = nbv(0);
 667 BigInteger.ONE = nbv(1);
 668 // Copyright (c) 2005  Tom Wu
 669 // All Rights Reserved.
 670 // See "LICENSE" for details.
 671
 672 // Extended JavaScript BN functions, required for RSA private ops.
 673
 674 // (public)
 675 function bnClone() { var r = nbi(); this.copyTo(r); return r; }
 676
 677 // (public) return value as integer
 678 function bnIntValue() {
 679   var this_array = this.array;
 680   if(this.s < 0) {
 681     if(this.t == 1) return this_array[0]-BI_DV;
 682     else if(this.t == 0) return -1;
 683   }
 684   else if(this.t == 1) return this_array[0];
 685   else if(this.t == 0) return 0;
 686   // assumes 16 < DB < 32
 687   return ((this_array[1]&((1<<(32-BI_DB))-1))<<BI_DB)|this_array[0];
 688 }
 689
 690 // (public) return value as byte
 691 function bnByteValue() {
 692   var this_array = this.array;
 693   return (this.t==0)?this.s:(this_array[0]<<24)>>24;
 694 }
 695
 696 // (public) return value as short (assumes DB>=16)
 697 function bnShortValue() {
 698   var this_array = this.array;
 699   return (this.t==0)?this.s:(this_array[0]<<16)>>16;
 700 }
 701
 702 // (protected) return x s.t. r^x < DV
 703 function bnpChunkSize(r) { return Math.floor(Math.LN2*BI_DB/Math.log(r)); }
 704
 705 // (public) 0 if this == 0, 1 if this > 0
 706 function bnSigNum() {
 707   var this_array = this.array;
 708   if(this.s < 0) return -1;
 709   else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) return 0;
 710   else return 1;
 711 }
 712
 713 // (protected) convert to radix string
 714 function bnpToRadix(b) {
 715   if(b == null) b = 10;
 716   if(this.signum() == 0 || b < 2 || b > 36) return "0";
 717   var cs = this.chunkSize(b);
 718   var a = Math.pow(b,cs);
 719   var d = nbv(a), y = nbi(), z = nbi(), r = "";
 720   this.divRemTo(d,y,z);
 721   while(y.signum() > 0) {
 722     r = (a+z.intValue()).toString(b).substr(1) + r;
 723     y.divRemTo(d,y,z);
 724   }
 725   return z.intValue().toString(b) + r;
 726 }
 727
 728 // (protected) convert from radix string
 729 function bnpFromRadix(s,b) {
 730   this.fromInt(0);
 731   if(b == null) b = 10;
 732   var cs = this.chunkSize(b);
 733   var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
 734   for(var i = 0; i < s.length; ++i) {
 735     var x = intAt(s,i);
 736     if(x < 0) {
 737       if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
 738       continue;
 739     }
 740     w = b*w+x;
 741     if(++j >= cs) {
 742       this.dMultiply(d);
 743       this.dAddOffset(w,0);
 744       j = 0;
 745       w = 0;
 746     }
 747   }
 748   if(j > 0) {
 749     this.dMultiply(Math.pow(b,j));
 750     this.dAddOffset(w,0);
 751   }
 752   if(mi) BigInteger.ZERO.subTo(this,this);
 753 }
 754
 755 // (protected) alternate constructor
 756 function bnpFromNumber(a,b,c) {
 757   if("number" == typeof b) {
 758     // new BigInteger(int,int,RNG)
 759     if(a < 2) this.fromInt(1);
 760     else {
 761       this.fromNumber(a,c);
 762       if(!this.testBit(a-1))    // force MSB set
 763         this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
 764       if(this.isEven()) this.dAddOffset(1,0); // force odd
 765       while(!this.isProbablePrime(b)) {
 766         this.dAddOffset(2,0);
 767         if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
 768       }
 769     }
 770   }
 771   else {
 772     // new BigInteger(int,RNG)
 773     var x = new Array(), t = a&7;
 774     x.length = (a>>3)+1;
 775     b.nextBytes(x);
 776     if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
 777     this.fromString(x,256);
 778   }
 779 }
 780
 781 // (public) convert to bigendian byte array
 782 function bnToByteArray() {
 783   var this_array = this.array;
 784   var i = this.t, r = new Array();
 785   r[0] = this.s;
 786   var p = BI_DB-(i*BI_DB)%8, d, k = 0;
 787   if(i-- > 0) {
 788     if(p < BI_DB && (d = this_array[i]>>p) != (this.s&BI_DM)>>p)
 789       r[k++] = d|(this.s<<(BI_DB-p));
 790     while(i >= 0) {
 791       if(p < 8) {
 792         d = (this_array[i]&((1<<p)-1))<<(8-p);
 793         d |= this_array[--i]>>(p+=BI_DB-8);
 794       }
 795       else {
 796         d = (this_array[i]>>(p-=8))&0xff;
 797         if(p <= 0) { p += BI_DB; --i; }
 798       }
 799       if((d&0x80) != 0) d |= -256;
 800       if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
 801       if(k > 0 || d != this.s) r[k++] = d;
 802     }
 803   }
 804   return r;
 805 }
 806
 807 function bnEquals(a) { return(this.compareTo(a)==0); }
 808 function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
 809 function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
 810
 811 // (protected) r = this op a (bitwise)
 812 function bnpBitwiseTo(a,op,r) {
 813   var this_array = this.array;
 814   var a_array    = a.array;
 815   var r_array    = r.array;
 816   var i, f, m = Math.min(a.t,this.t);
 817   for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]);
 818   if(a.t < this.t) {
 819     f = a.s&BI_DM;
 820     for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f);
 821     r.t = this.t;
 822   }
 823   else {
 824     f = this.s&BI_DM;
 825     for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]);
 826     r.t = a.t;
 827   }
 828   r.s = op(this.s,a.s);
 829   r.clamp();
 830 }
 831
 832 // (public) this & a
 833 function op_and(x,y) { return x&y; }
 834 function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
 835
 836 // (public) this | a
 837 function op_or(x,y) { return x|y; }
 838 function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
 839
 840 // (public) this ^ a
 841 function op_xor(x,y) { return x^y; }
 842 function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
 843
 844 // (public) this & ~a
 845 function op_andnot(x,y) { return x&~y; }
 846 function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
 847
 848 // (public) ~this
 849 function bnNot() {
 850   var this_array = this.array;
 851   var r = nbi();
 852   var r_array = r.array;
 853
 854   for(var i = 0; i < this.t; ++i) r_array[i] = BI_DM&~this_array[i];
 855   r.t = this.t;
 856   r.s = ~this.s;
 857   return r;
 858 }
 859
 860 // (public) this << n
 861 function bnShiftLeft(n) {
 862   var r = nbi();
 863   if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
 864   return r;
 865 }
 866
 867 // (public) this >> n
 868 function bnShiftRight(n) {
 869   var r = nbi();
 870   if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
 871   return r;
 872 }
 873
 874 // return index of lowest 1-bit in x, x < 2^31
 875 function lbit(x) {
 876   if(x == 0) return -1;
 877   var r = 0;
 878   if((x&0xffff) == 0) { x >>= 16; r += 16; }
 879   if((x&0xff) == 0) { x >>= 8; r += 8; }
 880   if((x&0xf) == 0) { x >>= 4; r += 4; }
 881   if((x&3) == 0) { x >>= 2; r += 2; }
 882   if((x&1) == 0) ++r;
 883   return r;
 884 }
 885
 886 // (public) returns index of lowest 1-bit (or -1 if none)
 887 function bnGetLowestSetBit() {
 888   var this_array = this.array;
 889   for(var i = 0; i < this.t; ++i)
 890     if(this_array[i] != 0) return i*BI_DB+lbit(this_array[i]);
 891   if(this.s < 0) return this.t*BI_DB;
 892   return -1;
 893 }
 894
 895 // return number of 1 bits in x
 896 function cbit(x) {
 897   var r = 0;
 898   while(x != 0) { x &= x-1; ++r; }
 899   return r;
 900 }
 901
 902 // (public) return number of set bits
 903 function bnBitCount() {
 904   var r = 0, x = this.s&BI_DM;
 905   for(var i = 0; i < this.t; ++i) r += cbit(this_array[i]^x);
 906   return r;
 907 }
 908
 909 // (public) true iff nth bit is set
 910 function bnTestBit(n) {
 911   var this_array = this.array;
 912   var j = Math.floor(n/BI_DB);
 913   if(j >= this.t) return(this.s!=0);
 914   return((this_array[j]&(1<<(n%BI_DB)))!=0);
 915 }
 916
 917 // (protected) this op (1<<n)
 918 function bnpChangeBit(n,op) {
 919   var r = BigInteger.ONE.shiftLeft(n);
 920   this.bitwiseTo(r,op,r);
 921   return r;
 922 }
 923
 924 // (public) this | (1<<n)
 925 function bnSetBit(n) { return this.changeBit(n,op_or); }
 926
 927 // (public) this & ~(1<<n)
 928 function bnClearBit(n) { return this.changeBit(n,op_andnot); }
 929
 930 // (public) this ^ (1<<n)
 931 function bnFlipBit(n) { return this.changeBit(n,op_xor); }
 932
 933 // (protected) r = this + a
 934 function bnpAddTo(a,r) {
 935   var this_array = this.array;
 936   var a_array = a.array;
 937   var r_array = r.array;
 938   var i = 0, c = 0, m = Math.min(a.t,this.t);
 939   while(i < m) {
 940     c += this_array[i]+a_array[i];
 941     r_array[i++] = c&BI_DM;
 942     c >>= BI_DB;
 943   }
 944   if(a.t < this.t) {
 945     c += a.s;
 946     while(i < this.t) {
 947       c += this_array[i];
 948       r_array[i++] = c&BI_DM;
 949       c >>= BI_DB;
 950     }
 951     c += this.s;
 952   }
 953   else {
 954     c += this.s;
 955     while(i < a.t) {
 956       c += a_array[i];
 957       r_array[i++] = c&BI_DM;
 958       c >>= BI_DB;
 959     }
 960     c += a.s;
 961   }
 962   r.s = (c<0)?-1:0;
 963   if(c > 0) r_array[i++] = c;
 964   else if(c < -1) r_array[i++] = BI_DV+c;
 965   r.t = i;
 966   r.clamp();
 967 }
 968
 969 // (public) this + a
 970 function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
 971
 972 // (public) this - a
 973 function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
 974
 975 // (public) this * a
 976 function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
 977
 978 // (public) this / a
 979 function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
 980
 981 // (public) this % a
 982 function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
 983
 984 // (public) [this/a,this%a]
 985 function bnDivideAndRemainder(a) {
 986   var q = nbi(), r = nbi();
 987   this.divRemTo(a,q,r);
 988   return new Array(q,r);
 989 }
 990
 991 // (protected) this *= n, this >= 0, 1 < n < DV
 992 function bnpDMultiply(n) {
 993   var this_array = this.array;
 994   this_array[this.t] = this.am(0,n-1,this,0,0,this.t);
 995   ++this.t;
 996   this.clamp();
 997 }
 998
 999 // (protected) this += n << w words, this >= 0
1000 function bnpDAddOffset(n,w) {
1001   var this_array = this.array;
1002   while(this.t <= w) this_array[this.t++] = 0;
1003   this_array[w] += n;
1004   while(this_array[w] >= BI_DV) {
1005     this_array[w] -= BI_DV;
1006     if(++w >= this.t) this_array[this.t++] = 0;
1007     ++this_array[w];
1008   }
1009 }
1010
1011 // A "null" reducer
1012 function NullExp() {}
1013 function nNop(x) { return x; }
1014 function nMulTo(x,y,r) { x.multiplyTo(y,r); }
1015 function nSqrTo(x,r) { x.squareTo(r); }
1016
1017 NullExp.prototype.convert = nNop;
1018 NullExp.prototype.revert = nNop;
1019 NullExp.prototype.mulTo = nMulTo;
1020 NullExp.prototype.sqrTo = nSqrTo;
1021
1022 // (public) this^e
1023 function bnPow(e) { return this.exp(e,new NullExp()); }
1024
1025 // (protected) r = lower n words of "this * a", a.t <= n
1026 // "this" should be the larger one if appropriate.
1027 function bnpMultiplyLowerTo(a,n,r) {
1028   var r_array = r.array;
1029   var a_array = a.array;
1030   var i = Math.min(this.t+a.t,n);
1031   r.s = 0; // assumes a,this >= 0
1032   r.t = i;
1033   while(i > 0) r_array[--i] = 0;
1034   var j;
1035   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);
1036   for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a_array[i],r,i,0,n-i);
1037   r.clamp();
1038 }
1039
1040 // (protected) r = "this * a" without lower n words, n > 0
1041 // "this" should be the larger one if appropriate.
1042 function bnpMultiplyUpperTo(a,n,r) {
1043   var r_array = r.array;
1044   var a_array = a.array;
1045   --n;
1046   var i = r.t = this.t+a.t-n;
1047   r.s = 0; // assumes a,this >= 0
1048   while(--i >= 0) r_array[i] = 0;
1049   for(i = Math.max(n-this.t,0); i < a.t; ++i)
1050     r_array[this.t+i-n] = this.am(n-i,a_array[i],r,0,0,this.t+i-n);
1051   r.clamp();
1052   r.drShiftTo(1,r);
1053 }
1054
1055 // Barrett modular reduction
1056 function Barrett(m) {
1057   // setup Barrett
1058   this.r2 = nbi();
1059   this.q3 = nbi();
1060   BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
1061   this.mu = this.r2.divide(m);
1062   this.m = m;
1063 }
1064
1065 function barrettConvert(x) {
1066   if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
1067   else if(x.compareTo(this.m) < 0) return x;
1068   else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
1069 }
1070
1071 function barrettRevert(x) { return x; }
1072
1073 // x = x mod m (HAC 14.42)
1074 function barrettReduce(x) {
1075   x.drShiftTo(this.m.t-1,this.r2);
1076   if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
1077   this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
1078   this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
1079   while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
1080   x.subTo(this.r2,x);
1081   while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
1082 }
1083
1084 // r = x^2 mod m; x != r
1085 function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
1086
1087 // r = x*y mod m; x,y != r
1088 function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
1089
1090 Barrett.prototype.convert = barrettConvert;
1091 Barrett.prototype.revert = barrettRevert;
1092 Barrett.prototype.reduce = barrettReduce;
1093 Barrett.prototype.mulTo = barrettMulTo;
1094 Barrett.prototype.sqrTo = barrettSqrTo;
1095
1096 // (public) this^e % m (HAC 14.85)
1097 function bnModPow(e,m) {
1098   var e_array = e.array;
1099   var i = e.bitLength(), k, r = nbv(1), z;
1100   if(i <= 0) return r;
1101   else if(i < 18) k = 1;
1102   else if(i < 48) k = 3;
1103   else if(i < 144) k = 4;
1104   else if(i < 768) k = 5;
1105   else k = 6;
1106   if(i < 8)
1107     z = new Classic(m);
1108   else if(m.isEven())
1109     z = new Barrett(m);
1110   else
1111     z = new Montgomery(m);
1112
1113   // precomputation
1114   var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
1115   g[1] = z.convert(this);
1116   if(k > 1) {
1117     var g2 = nbi();
1118     z.sqrTo(g[1],g2);
1119     while(n <= km) {
1120       g[n] = nbi();
1121       z.mulTo(g2,g[n-2],g[n]);
1122       n += 2;
1123     }
1124   }
1125
1126   var j = e.t-1, w, is1 = true, r2 = nbi(), t;
1127   i = nbits(e_array[j])-1;
1128   while(j >= 0) {
1129     if(i >= k1) w = (e_array[j]>>(i-k1))&km;
1130     else {
1131       w = (e_array[j]&((1<<(i+1))-1))<<(k1-i);
1132       if(j > 0) w |= e_array[j-1]>>(BI_DB+i-k1);
1133     }
1134
1135     n = k;
1136     while((w&1) == 0) { w >>= 1; --n; }
1137     if((i -= n) < 0) { i += BI_DB; --j; }
1138     if(is1) {   // ret == 1, don't bother squaring or multiplying it
1139       g[w].copyTo(r);
1140       is1 = false;
1141     }
1142     else {
1143       while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
1144       if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
1145       z.mulTo(r2,g[w],r);
1146     }
1147
1148     while(j >= 0 && (e_array[j]&(1<<i)) == 0) {
1149       z.sqrTo(r,r2); t = r; r = r2; r2 = t;
1150       if(--i < 0) { i = BI_DB-1; --j; }
1151     }
1152   }
1153   return z.revert(r);
1154 }
1155
1156 // (public) gcd(this,a) (HAC 14.54)
1157 function bnGCD(a) {
1158   var x = (this.s<0)?this.negate():this.clone();
1159   var y = (a.s<0)?a.negate():a.clone();
1160   if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
1161   var i = x.getLowestSetBit(), g = y.getLowestSetBit();
1162   if(g < 0) return x;
1163   if(i < g) g = i;
1164   if(g > 0) {
1165     x.rShiftTo(g,x);
1166     y.rShiftTo(g,y);
1167   }
1168   while(x.signum() > 0) {
1169     if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
1170     if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
1171     if(x.compareTo(y) >= 0) {
1172       x.subTo(y,x);
1173       x.rShiftTo(1,x);
1174     }
1175     else {
1176       y.subTo(x,y);
1177       y.rShiftTo(1,y);
1178     }
1179   }
1180   if(g > 0) y.lShiftTo(g,y);
1181   return y;
1182 }
1183
1184 // (protected) this % n, n < 2^26
1185 function bnpModInt(n) {
1186   var this_array = this.array;
1187   if(n <= 0) return 0;
1188   var d = BI_DV%n, r = (this.s<0)?n-1:0;
1189   if(this.t > 0)
1190     if(d == 0) r = this_array[0]%n;
1191     else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n;
1192   return r;
1193 }
1194
1195 // (public) 1/this % m (HAC 14.61)
1196 function bnModInverse(m) {
1197   var ac = m.isEven();
1198   if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
1199   var u = m.clone(), v = this.clone();
1200   var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
1201   while(u.signum() != 0) {
1202     while(u.isEven()) {
1203       u.rShiftTo(1,u);
1204       if(ac) {
1205         if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
1206         a.rShiftTo(1,a);
1207       }
1208       else if(!b.isEven()) b.subTo(m,b);
1209       b.rShiftTo(1,b);
1210     }
1211     while(v.isEven()) {
1212       v.rShiftTo(1,v);
1213       if(ac) {
1214         if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
1215         c.rShiftTo(1,c);
1216       }
1217       else if(!d.isEven()) d.subTo(m,d);
1218       d.rShiftTo(1,d);
1219     }
1220     if(u.compareTo(v) >= 0) {
1221       u.subTo(v,u);
1222       if(ac) a.subTo(c,a);
1223       b.subTo(d,b);
1224     }
1225     else {
1226       v.subTo(u,v);
1227       if(ac) c.subTo(a,c);
1228       d.subTo(b,d);
1229     }
1230   }
1231   if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
1232   if(d.compareTo(m) >= 0) return d.subtract(m);
1233   if(d.signum() < 0) d.addTo(m,d); else return d;
1234   if(d.signum() < 0) return d.add(m); else return d;
1235 }
1236
1237 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];
1238 var lplim = (1<<26)/lowprimes[lowprimes.length-1];
1239
1240 // (public) test primality with certainty >= 1-.5^t
1241 function bnIsProbablePrime(t) {
1242   var i, x = this.abs();
1243   var x_array = x.array;
1244   if(x.t == 1 && x_array[0] <= lowprimes[lowprimes.length-1]) {
1245     for(i = 0; i < lowprimes.length; ++i)
1246       if(x_array[0] == lowprimes[i]) return true;
1247     return false;
1248   }
1249   if(x.isEven()) return false;
1250   i = 1;
1251   while(i < lowprimes.length) {
1252     var m = lowprimes[i], j = i+1;
1253     while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
1254     m = x.modInt(m);
1255     while(i < j) if(m%lowprimes[i++] == 0) return false;
1256   }
1257   return x.millerRabin(t);
1258 }
1259
1260 // (protected) true if probably prime (HAC 4.24, Miller-Rabin)
1261 function bnpMillerRabin(t) {
1262   var n1 = this.subtract(BigInteger.ONE);
1263   var k = n1.getLowestSetBit();
1264   if(k <= 0) return false;
1265   var r = n1.shiftRight(k);
1266   t = (t+1)>>1;
1267   if(t > lowprimes.length) t = lowprimes.length;
1268   var a = nbi();
1269   for(var i = 0; i < t; ++i) {
1270     a.fromInt(lowprimes[i]);
1271     var y = a.modPow(r,this);
1272     if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
1273       var j = 1;
1274       while(j++ < k && y.compareTo(n1) != 0) {
1275         y = y.modPowInt(2,this);
1276         if(y.compareTo(BigInteger.ONE) == 0) return false;
1277       }
1278       if(y.compareTo(n1) != 0) return false;
1279     }
1280   }
1281   return true;
1282 }
1283
1284 // protected
1285 BigInteger.prototype.chunkSize = bnpChunkSize;
1286 BigInteger.prototype.toRadix = bnpToRadix;
1287 BigInteger.prototype.fromRadix = bnpFromRadix;
1288 BigInteger.prototype.fromNumber = bnpFromNumber;
1289 BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
1290 BigInteger.prototype.changeBit = bnpChangeBit;
1291 BigInteger.prototype.addTo = bnpAddTo;
1292 BigInteger.prototype.dMultiply = bnpDMultiply;
1293 BigInteger.prototype.dAddOffset = bnpDAddOffset;
1294 BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
1295 BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
1296 BigInteger.prototype.modInt = bnpModInt;
1297 BigInteger.prototype.millerRabin = bnpMillerRabin;
1298
1299 // public
1300 BigInteger.prototype.clone = bnClone;
1301 BigInteger.prototype.intValue = bnIntValue;
1302 BigInteger.prototype.byteValue = bnByteValue;
1303 BigInteger.prototype.shortValue = bnShortValue;
1304 BigInteger.prototype.signum = bnSigNum;
1305 BigInteger.prototype.toByteArray = bnToByteArray;
1306 BigInteger.prototype.equals = bnEquals;
1307 BigInteger.prototype.min = bnMin;
1308 BigInteger.prototype.max = bnMax;
1309 BigInteger.prototype.and = bnAnd;
1310 BigInteger.prototype.or = bnOr;
1311 BigInteger.prototype.xor = bnXor;
1312 BigInteger.prototype.andNot = bnAndNot;
1313 BigInteger.prototype.not = bnNot;
1314 BigInteger.prototype.shiftLeft = bnShiftLeft;
1315 BigInteger.prototype.shiftRight = bnShiftRight;
1316 BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
1317 BigInteger.prototype.bitCount = bnBitCount;
1318 BigInteger.prototype.testBit = bnTestBit;
1319 BigInteger.prototype.setBit = bnSetBit;
1320 BigInteger.prototype.clearBit = bnClearBit;
1321 BigInteger.prototype.flipBit = bnFlipBit;
1322 BigInteger.prototype.add = bnAdd;
1323 BigInteger.prototype.subtract = bnSubtract;
1324 BigInteger.prototype.multiply = bnMultiply;
1325 BigInteger.prototype.divide = bnDivide;
1326 BigInteger.prototype.remainder = bnRemainder;
1327 BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
1328 BigInteger.prototype.modPow = bnModPow;
1329 BigInteger.prototype.modInverse = bnModInverse;
1330 BigInteger.prototype.pow = bnPow;
1331 BigInteger.prototype.gcd = bnGCD;
1332 BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
1333
1334 // BigInteger interfaces not implemented in jsbn:
1335
1336 // BigInteger(int signum, byte[] magnitude)
1337 // double doubleValue()
1338 // float floatValue()
1339 // int hashCode()
1340 // long longValue()
1341 // static BigInteger valueOf(long val)
1342 // prng4.js - uses Arcfour as a PRNG
1343
1344 function Arcfour() {
1345   this.i = 0;
1346   this.j = 0;
1347   this.S = new Array();
1348 }
1349
1350 // Initialize arcfour context from key, an array of ints, each from [0..255]
1351 function ARC4init(key) {
1352   var i, j, t;
1353   for(i = 0; i < 256; ++i)
1354     this.S[i] = i;
1355   j = 0;
1356   for(i = 0; i < 256; ++i) {
1357     j = (j + this.S[i] + key[i % key.length]) & 255;
1358     t = this.S[i];
1359     this.S[i] = this.S[j];
1360     this.S[j] = t;
1361   }
1362   this.i = 0;
1363   this.j = 0;
1364 }
1365
1366 function ARC4next() {
1367   var t;
1368   this.i = (this.i + 1) & 255;
1369   this.j = (this.j + this.S[this.i]) & 255;
1370   t = this.S[this.i];
1371   this.S[this.i] = this.S[this.j];
1372   this.S[this.j] = t;
1373   return this.S[(t + this.S[this.i]) & 255];
1374 }
1375
1376 Arcfour.prototype.init = ARC4init;
1377 Arcfour.prototype.next = ARC4next;
1378
1379 // Plug in your RNG constructor here
1380 function prng_newstate() {
1381   return new Arcfour();
1382 }
1383
1384 // Pool size must be a multiple of 4 and greater than 32.
1385 // An array of bytes the size of the pool will be passed to init()
1386 var rng_psize = 256;
1387 // Random number generator - requires a PRNG backend, e.g. prng4.js
1388
1389 // For best results, put code like
1390 // <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
1391 // in your main HTML document.
1392
1393 var rng_state;
1394 var rng_pool;
1395 var rng_pptr;
1396
1397 // Mix in a 32-bit integer into the pool
1398 function rng_seed_int(x) {
1399   rng_pool[rng_pptr++] ^= x & 255;
1400   rng_pool[rng_pptr++] ^= (x >> 8) & 255;
1401   rng_pool[rng_pptr++] ^= (x >> 16) & 255;
1402   rng_pool[rng_pptr++] ^= (x >> 24) & 255;
1403   if(rng_pptr >= rng_psize) rng_pptr -= rng_psize;
1404 }
1405
1406 // Mix in the current time (w/milliseconds) into the pool
1407 function rng_seed_time() {
1408   // Use pre-computed date to avoid making the benchmark
1409   // results dependent on the current date.
1410   rng_seed_int(1122926989487);
1411 }
1412
1413 // Initialize the pool with junk if needed.
1414 if(rng_pool == null) {
1415   rng_pool = new Array();
1416   rng_pptr = 0;
1417   var t;
1418   while(rng_pptr < rng_psize) {  // extract some randomness from Math.random()
1419     t = Math.floor(65536 * Math.random());
1420     rng_pool[rng_pptr++] = t >>> 8;
1421     rng_pool[rng_pptr++] = t & 255;
1422   }
1423   rng_pptr = 0;
1424   rng_seed_time();
1425   //rng_seed_int(window.screenX);
1426   //rng_seed_int(window.screenY);
1427 }
1428
1429 function rng_get_byte() {
1430   if(rng_state == null) {
1431     rng_seed_time();
1432     rng_state = prng_newstate();
1433     rng_state.init(rng_pool);
1434     for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
1435       rng_pool[rng_pptr] = 0;
1436     rng_pptr = 0;
1437     //rng_pool = null;
1438   }
1439   // TODO: allow reseeding after first request
1440   return rng_state.next();
1441 }
1442
1443 function rng_get_bytes(ba) {
1444   var i;
1445   for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
1446 }
1447
1448 function SecureRandom() {}
1449
1450 SecureRandom.prototype.nextBytes = rng_get_bytes;
1451 // Depends on jsbn.js and rng.js
1452
1453 // convert a (hex) string to a bignum object
1454 function parseBigInt(str,r) {
1455   return new BigInteger(str,r);
1456 }
1457
1458 function linebrk(s,n) {
1459   var ret = "";
1460   var i = 0;
1461   while(i + n < s.length) {
1462     ret += s.substring(i,i+n) + "\n";
1463     i += n;
1464   }
1465   return ret + s.substring(i,s.length);
1466 }
1467
1468 function byte2Hex(b) {
1469   if(b < 0x10)
1470     return "0" + b.toString(16);
1471   else
1472     return b.toString(16);
1473 }
1474
1475 // PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
1476 function pkcs1pad2(s,n) {
1477   if(n < s.length + 11) {
1478     alert("Message too long for RSA");
1479     return null;
1480   }
1481   var ba = new Array();
1482   var i = s.length - 1;
1483   while(i >= 0 && n > 0) ba[--n] = s.charCodeAt(i--);
1484   ba[--n] = 0;
1485   var rng = new SecureRandom();
1486   var x = new Array();
1487   while(n > 2) { // random non-zero pad
1488     x[0] = 0;
1489     while(x[0] == 0) rng.nextBytes(x);
1490     ba[--n] = x[0];
1491   }
1492   ba[--n] = 2;
1493   ba[--n] = 0;
1494   return new BigInteger(ba);
1495 }
1496
1497 // "empty" RSA key constructor
1498 function RSAKey() {
1499   this.n = null;
1500   this.e = 0;
1501   this.d = null;
1502   this.p = null;
1503   this.q = null;
1504   this.dmp1 = null;
1505   this.dmq1 = null;
1506   this.coeff = null;
1507 }
1508
1509 // Set the public key fields N and e from hex strings
1510 function RSASetPublic(N,E) {
1511   if(N != null && E != null && N.length > 0 && E.length > 0) {
1512     this.n = parseBigInt(N,16);
1513     this.e = parseInt(E,16);
1514   }
1515   else
1516     alert("Invalid RSA public key");
1517 }
1518
1519 // Perform raw public operation on "x": return x^e (mod n)
1520 function RSADoPublic(x) {
1521   return x.modPowInt(this.e, this.n);
1522 }
1523
1524 // Return the PKCS#1 RSA encryption of "text" as an even-length hex string
1525 function RSAEncrypt(text) {
1526   var m = pkcs1pad2(text,(this.n.bitLength()+7)>>3);
1527   if(m == null) return null;
1528   var c = this.doPublic(m);
1529   if(c == null) return null;
1530   var h = c.toString(16);
1531   if((h.length & 1) == 0) return h; else return "0" + h;
1532 }
1533
1534 // Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
1535 //function RSAEncryptB64(text) {
1536 //  var h = this.encrypt(text);
1537 //  if(h) return hex2b64(h); else return null;
1538 //}
1539
1540 // protected
1541 RSAKey.prototype.doPublic = RSADoPublic;
1542
1543 // public
1544 RSAKey.prototype.setPublic = RSASetPublic;
1545 RSAKey.prototype.encrypt = RSAEncrypt;
1546 //RSAKey.prototype.encrypt_b64 = RSAEncryptB64;
1547 // Depends on rsa.js and jsbn2.js
1548
1549 // Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
1550 function pkcs1unpad2(d,n) {
1551   var b = d.toByteArray();
1552   var i = 0;
1553   while(i < b.length && b[i] == 0) ++i;
1554   if(b.length-i != n-1 || b[i] != 2)
1555     return null;
1556   ++i;
1557   while(b[i] != 0)
1558     if(++i >= b.length) return null;
1559   var ret = "";
1560   while(++i < b.length)
1561     ret += String.fromCharCode(b[i]);
1562   return ret;
1563 }
1564
1565 // Set the private key fields N, e, and d from hex strings
1566 function RSASetPrivate(N,E,D) {
1567   if(N != null && E != null && N.length > 0 && E.length > 0) {
1568     this.n = parseBigInt(N,16);
1569     this.e = parseInt(E,16);
1570     this.d = parseBigInt(D,16);
1571   }
1572   else
1573     alert("Invalid RSA private key");
1574 }
1575
1576 // Set the private key fields N, e, d and CRT params from hex strings
1577 function RSASetPrivateEx(N,E,D,P,Q,DP,DQ,C) {
1578   if(N != null && E != null && N.length > 0 && E.length > 0) {
1579     this.n = parseBigInt(N,16);
1580     this.e = parseInt(E,16);
1581     this.d = parseBigInt(D,16);
1582     this.p = parseBigInt(P,16);
1583     this.q = parseBigInt(Q,16);
1584     this.dmp1 = parseBigInt(DP,16);
1585     this.dmq1 = parseBigInt(DQ,16);
1586     this.coeff = parseBigInt(C,16);
1587   }
1588   else
1589     alert("Invalid RSA private key");
1590 }
1591
1592 // Generate a new random private key B bits long, using public expt E
1593 function RSAGenerate(B,E) {
1594   var rng = new SecureRandom();
1595   var qs = B>>1;
1596   this.e = parseInt(E,16);
1597   var ee = new BigInteger(E,16);
1598   for(;;) {
1599     for(;;) {
1600       this.p = new BigInteger(B-qs,1,rng);
1601       if(this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break;
1602     }
1603     for(;;) {
1604       this.q = new BigInteger(qs,1,rng);
1605       if(this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break;
1606     }
1607     if(this.p.compareTo(this.q) <= 0) {
1608       var t = this.p;
1609       this.p = this.q;
1610       this.q = t;
1611     }
1612     var p1 = this.p.subtract(BigInteger.ONE);
1613     var q1 = this.q.subtract(BigInteger.ONE);
1614     var phi = p1.multiply(q1);
1615     if(phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
1616       this.n = this.p.multiply(this.q);
1617       this.d = ee.modInverse(phi);
1618       this.dmp1 = this.d.mod(p1);
1619       this.dmq1 = this.d.mod(q1);
1620       this.coeff = this.q.modInverse(this.p);
1621       break;
1622     }
1623   }
1624 }
1625
1626 // Perform raw private operation on "x": return x^d (mod n)
1627 function RSADoPrivate(x) {
1628   if(this.p == null || this.q == null)
1629     return x.modPow(this.d, this.n);
1630
1631   // TODO: re-calculate any missing CRT params
1632   var xp = x.mod(this.p).modPow(this.dmp1, this.p);
1633   var xq = x.mod(this.q).modPow(this.dmq1, this.q);
1634
1635   while(xp.compareTo(xq) < 0)
1636     xp = xp.add(this.p);
1637   return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq);
1638 }
1639
1640 // Return the PKCS#1 RSA decryption of "ctext".
1641 // "ctext" is an even-length hex string and the output is a plain string.
1642 function RSADecrypt(ctext) {
1643   var c = parseBigInt(ctext, 16);
1644   var m = this.doPrivate(c);
1645   if(m == null) return null;
1646   return pkcs1unpad2(m, (this.n.bitLength()+7)>>3);
1647 }
1648
1649 // Return the PKCS#1 RSA decryption of "ctext".
1650 // "ctext" is a Base64-encoded string and the output is a plain string.
1651 //function RSAB64Decrypt(ctext) {
1652 //  var h = b64tohex(ctext);
1653 //  if(h) return this.decrypt(h); else return null;
1654 //}
1655
1656 // protected
1657 RSAKey.prototype.doPrivate = RSADoPrivate;
1658
1659 // public
1660 RSAKey.prototype.setPrivate = RSASetPrivate;
1661 RSAKey.prototype.setPrivateEx = RSASetPrivateEx;
1662 RSAKey.prototype.generate = RSAGenerate;
1663 RSAKey.prototype.decrypt = RSADecrypt;
1664 //RSAKey.prototype.b64_decrypt = RSAB64Decrypt;
1665
1666
1667 nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3";
1668 eValue="10001";
1669 dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161";
1670 pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d";
1671 qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f";
1672 dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25";
1673 dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd";
1674 coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250";
1675
1676 setupEngine(am3, 28);
1677
1678 var TEXT = "The quick brown fox jumped over the extremely lazy frog! " +
1679     "Now is the time for all good men to come to the party.";
1680 var encrypted;
1681
1682 window.onload = function(){ startTest("v8-crypto", 'f0250ffa');
1683
1684 test("RSA Encrypt", function encrypt() {
1685   var RSA = new RSAKey();
1686   RSA.setPublic(nValue, eValue);
1687   RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
1688   encrypted = RSA.encrypt(TEXT);
1689 });
1690
1691 test("RSA Decrypt", function decrypt() {
1692   var RSA = new RSAKey();
1693   RSA.setPublic(nValue, eValue);
1694   RSA.setPrivateEx(nValue, eValue, dValue, pValue, qValue, dmp1Value, dmq1Value, coeffValue);
1695   var decrypted = RSA.decrypt(encrypted);
1696   if (decrypted != TEXT) {
1697     throw new Error("Crypto operation failed");
1698   }
1699 });
1700
1701 endTest(); };
1702 </script>
1703 </head>
1704 <body></body>
1705 </html>