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} 1699