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| 1 <html> |
| 2 <head> |
| 3 <script src="../htmlrunner.js"></script> |
| 4 <script> |
| 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 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,8
3,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,
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(x
q); |
| 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="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd9
4057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49
175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074
eafd036a5eb83359d2a698d3"; |
| 1668 eValue="10001"; |
| 1669 dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293f
c97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d
31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891
464fba23d0d965086277a161"; |
| 1670 pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bd
e14b2417951178ac152ceab6da7090905b478195498b352048f15e7d"; |
| 1671 qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d
54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f"; |
| 1672 dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500
038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25"; |
| 1673 dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d91433
7eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd"; |
| 1674 coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db17
34c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250"; |
| 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", ''); |
| 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> |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 269054:
Importing dromaeo performance tests to src/chrome/test/data.... (Closed)
Base URL: svn://chrome-svn/chrome/trunk/src/