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comparison: js/src/v8/crypto.js

js/src/v8/crypto.js

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1 /*
2 * Copyright (c) 2003-2005 Tom Wu
3 * All Rights Reserved.
4 *
5 * Permission is hereby granted, free of charge, to any person obtaining
6 * a copy of this software and associated documentation files (the
7 * "Software"), to deal in the Software without restriction, including
8 * without limitation the rights to use, copy, modify, merge, publish,
9 * distribute, sublicense, and/or sell copies of the Software, and to
10 * permit persons to whom the Software is furnished to do so, subject to
11 * the following conditions:
12 *
13 * The above copyright notice and this permission notice shall be
14 * included in all copies or substantial portions of the Software.
15 *
16 * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
17 * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
18 * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
19 *
20 * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
21 * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
22 * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
23 * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
24 * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
25 *
26 * In addition, the following condition applies:
27 *
28 * All redistributions must retain an intact copy of this copyright notice
29 * and disclaimer.
30 */
31
32
33 // The code has been adapted for use as a benchmark by Google.
34 var 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
43 var dbits;
44 var BI_DB;
45 var BI_DM;
46 var BI_DV;
47
48 var BI_FP;
49 var BI_FV;
50 var BI_F1;
51 var BI_F2;
52
53 // JavaScript engine analysis
54 var canary = 0xdeadbeefcafe;
55 var j_lm = ((canary&0xffffff)==0xefcafe);
56
57 // (public) Constructor
58 function 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
67 function 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)
77 function 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)
91 function 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.
108 function 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.
126 function 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
147 setupEngine = 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
163 var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
164 var BI_RC = new Array();
165 var rr,vv;
166 rr = "0".charCodeAt(0);
167 for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
168 rr = "a".charCodeAt(0);
169 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
170 rr = "A".charCodeAt(0);
171 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
172
173 function int2char(n) { return BI_RM.charAt(n); }
174 function 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
180 function 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
190 function 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
200 function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
201
202 // (protected) set from string and radix
203 function 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
243 function 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
250 function 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
281 function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
282
283 // (public) |this|
284 function bnAbs() { return (this.s<0)?this.negate():this; }
285
286 // (public) return + if this > a, - if this < a, 0 if equal
287 function 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
301 function 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"
312 function 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
319 function 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
330 function 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
339 function 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
358 function 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
378 function 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.
415 function 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)
431 function 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.
452 function 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
505 function 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
513 function Classic(m) { this.m = m; }
514 function cConvert(x) {
515 if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
516 else return x;
517 }
518 function cRevert(x) { return x; }
519 function cReduce(x) { x.divRemTo(this.m,null,x); }
520 function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
521 function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
522
523 Classic.prototype.convert = cConvert;
524 Classic.prototype.revert = cRevert;
525 Classic.prototype.reduce = cReduce;
526 Classic.prototype.mulTo = cMulTo;
527 Classic.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.
539 function 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
556 function 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
566 function 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
575 function 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)
583 function 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
603 function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
604
605 // r = "xy/R mod m"; x,y != r
606 function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
607
608 Montgomery.prototype.convert = montConvert;
609 Montgomery.prototype.revert = montRevert;
610 Montgomery.prototype.reduce = montReduce;
611 Montgomery.prototype.mulTo = montMulTo;
612 Montgomery.prototype.sqrTo = montSqrTo;
613
614 // (protected) true iff this is even
615 function 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)
621 function 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
634 function 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
641 BigInteger.prototype.copyTo = bnpCopyTo;
642 BigInteger.prototype.fromInt = bnpFromInt;
643 BigInteger.prototype.fromString = bnpFromString;
644 BigInteger.prototype.clamp = bnpClamp;
645 BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
646 BigInteger.prototype.drShiftTo = bnpDRShiftTo;
647 BigInteger.prototype.lShiftTo = bnpLShiftTo;
648 BigInteger.prototype.rShiftTo = bnpRShiftTo;
649 BigInteger.prototype.subTo = bnpSubTo;
650 BigInteger.prototype.multiplyTo = bnpMultiplyTo;
651 BigInteger.prototype.squareTo = bnpSquareTo;
652 BigInteger.prototype.divRemTo = bnpDivRemTo;
653 BigInteger.prototype.invDigit = bnpInvDigit;
654 BigInteger.prototype.isEven = bnpIsEven;
655 BigInteger.prototype.exp = bnpExp;
656
657 // public
658 BigInteger.prototype.toString = bnToString;
659 BigInteger.prototype.negate = bnNegate;
660 BigInteger.prototype.abs = bnAbs;
661 BigInteger.prototype.compareTo = bnCompareTo;
662 BigInteger.prototype.bitLength = bnBitLength;
663 BigInteger.prototype.mod = bnMod;
664 BigInteger.prototype.modPowInt = bnModPowInt;
665
666 // "constants"
667 BigInteger.ZERO = nbv(0);
668 BigInteger.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)
676 function bnClone() { var r = nbi(); this.copyTo(r); return r; }
677
678 // (public) return value as integer
679 function 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
692 function 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)
698 function 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
704 function bnpChunkSize(r) { return Math.floor(Math.LN2*BI_DB/Math.log(r)); }
705
706 // (public) 0 if this == 0, 1 if this > 0
707 function 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
715 function 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
730 function 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
757 function 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
783 function 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
808 function bnEquals(a) { return(this.compareTo(a)==0); }
809 function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
810 function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
811
812 // (protected) r = this op a (bitwise)
813 function 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
834 function op_and(x,y) { return x&y; }
835 function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
836
837 // (public) this | a
838 function op_or(x,y) { return x|y; }
839 function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
840
841 // (public) this ^ a
842 function op_xor(x,y) { return x^y; }
843 function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
844
845 // (public) this & ~a
846 function op_andnot(x,y) { return x&~y; }
847 function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
848
849 // (public) ~this
850 function 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
862 function 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
869 function 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
876 function 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)
888 function 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
897 function 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
904 function 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
911 function 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)
919 function 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)
926 function bnSetBit(n) { return this.changeBit(n,op_or); }
927
928 // (public) this & ~(1<<n)
929 function bnClearBit(n) { return this.changeBit(n,op_andnot); }
930
931 // (public) this ^ (1<<n)
932 function bnFlipBit(n) { return this.changeBit(n,op_xor); }
933
934 // (protected) r = this + a
935 function 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
971 function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
972
973 // (public) this - a
974 function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
975
976 // (public) this * a
977 function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
978
979 // (public) this / a
980 function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
981
982 // (public) this % a
983 function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
984
985 // (public) [this/a,this%a]
986 function 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
993 function 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
1001 function 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
1013 function NullExp() {}
1014 function nNop(x) { return x; }
1015 function nMulTo(x,y,r) { x.multiplyTo(y,r); }
1016 function nSqrTo(x,r) { x.squareTo(r); }
1017
1018 NullExp.prototype.convert = nNop;
1019 NullExp.prototype.revert = nNop;
1020 NullExp.prototype.mulTo = nMulTo;
1021 NullExp.prototype.sqrTo = nSqrTo;
1022
1023 // (public) this^e
1024 function 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.
1028 function 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.
1043 function 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
1057 function 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
1066 function 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
1072 function barrettRevert(x) { return x; }
1073
1074 // x = x mod m (HAC 14.42)
1075 function 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
1086 function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
1087
1088 // r = x*y mod m; x,y != r
1089 function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
1090
1091 Barrett.prototype.convert = barrettConvert;
1092 Barrett.prototype.revert = barrettRevert;
1093 Barrett.prototype.reduce = barrettReduce;
1094 Barrett.prototype.mulTo = barrettMulTo;
1095 Barrett.prototype.sqrTo = barrettSqrTo;
1096
1097 // (public) this^e % m (HAC 14.85)
1098 function 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)
1158 function 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
1186 function 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)
1197 function 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
1238 var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
1239 var lplim = (1<<26)/lowprimes[lowprimes.length-1];
1240
1241 // (public) test primality with certainty >= 1-.5^t
1242 function 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)
1262 function 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
1286 BigInteger.prototype.chunkSize = bnpChunkSize;
1287 BigInteger.prototype.toRadix = bnpToRadix;
1288 BigInteger.prototype.fromRadix = bnpFromRadix;
1289 BigInteger.prototype.fromNumber = bnpFromNumber;
1290 BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
1291 BigInteger.prototype.changeBit = bnpChangeBit;
1292 BigInteger.prototype.addTo = bnpAddTo;
1293 BigInteger.prototype.dMultiply = bnpDMultiply;
1294 BigInteger.prototype.dAddOffset = bnpDAddOffset;
1295 BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
1296 BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
1297 BigInteger.prototype.modInt = bnpModInt;
1298 BigInteger.prototype.millerRabin = bnpMillerRabin;
1299
1300 // public
1301 BigInteger.prototype.clone = bnClone;
1302 BigInteger.prototype.intValue = bnIntValue;
1303 BigInteger.prototype.byteValue = bnByteValue;
1304 BigInteger.prototype.shortValue = bnShortValue;
1305 BigInteger.prototype.signum = bnSigNum;
1306 BigInteger.prototype.toByteArray = bnToByteArray;
1307 BigInteger.prototype.equals = bnEquals;
1308 BigInteger.prototype.min = bnMin;
1309 BigInteger.prototype.max = bnMax;
1310 BigInteger.prototype.and = bnAnd;
1311 BigInteger.prototype.or = bnOr;
1312 BigInteger.prototype.xor = bnXor;
1313 BigInteger.prototype.andNot = bnAndNot;
1314 BigInteger.prototype.not = bnNot;
1315 BigInteger.prototype.shiftLeft = bnShiftLeft;
1316 BigInteger.prototype.shiftRight = bnShiftRight;
1317 BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
1318 BigInteger.prototype.bitCount = bnBitCount;
1319 BigInteger.prototype.testBit = bnTestBit;
1320 BigInteger.prototype.setBit = bnSetBit;
1321 BigInteger.prototype.clearBit = bnClearBit;
1322 BigInteger.prototype.flipBit = bnFlipBit;
1323 BigInteger.prototype.add = bnAdd;
1324 BigInteger.prototype.subtract = bnSubtract;
1325 BigInteger.prototype.multiply = bnMultiply;
1326 BigInteger.prototype.divide = bnDivide;
1327 BigInteger.prototype.remainder = bnRemainder;
1328 BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
1329 BigInteger.prototype.modPow = bnModPow;
1330 BigInteger.prototype.modInverse = bnModInverse;
1331 BigInteger.prototype.pow = bnPow;
1332 BigInteger.prototype.gcd = bnGCD;
1333 BigInteger.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
1345 function 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]
1352 function 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
1367 function 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
1377 Arcfour.prototype.init = ARC4init;
1378 Arcfour.prototype.next = ARC4next;
1379
1380 // Plug in your RNG constructor here
1381 function 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()
1387 var 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
1394 var rng_state;
1395 var rng_pool;
1396 var rng_pptr;
1397
1398 // Mix in a 32-bit integer into the pool
1399 function 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
1408 function 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.
1415 if(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
1430 function 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
1444 function rng_get_bytes(ba) {
1445 var i;
1446 for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
1447 }
1448
1449 function SecureRandom() {}
1450
1451 SecureRandom.prototype.nextBytes = rng_get_bytes;
1452 // Depends on jsbn.js and rng.js
1453
1454 // convert a (hex) string to a bignum object
1455 function parseBigInt(str,r) {
1456 return new BigInteger(str,r);
1457 }
1458
1459 function 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
1469 function 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
1477 function 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
1499 function 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
1511 function 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)
1521 function 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
1526 function 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
1542 RSAKey.prototype.doPublic = RSADoPublic;
1543
1544 // public
1545 RSAKey.prototype.setPublic = RSASetPublic;
1546 RSAKey.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
1551 function 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
1567 function 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
1578 function 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
1594 function 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)
1628 function 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.
1643 function 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
1658 RSAKey.prototype.doPrivate = RSADoPrivate;
1659
1660 // public
1661 RSAKey.prototype.setPrivate = RSASetPrivate;
1662 RSAKey.prototype.setPrivateEx = RSASetPrivateEx;
1663 RSAKey.prototype.generate = RSAGenerate;
1664 RSAKey.prototype.decrypt = RSADecrypt;
1665 //RSAKey.prototype.b64_decrypt = RSAB64Decrypt;
1666
1667
1668 nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3";
1669 eValue="10001";
1670 dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161";
1671 pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d";
1672 qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f";
1673 dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25";
1674 dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd";
1675 coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250";
1676
1677 setupEngine(am3, 28);
1678
1679 var 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.";
1681 var encrypted;
1682
1683 function 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
1690 function 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 }

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