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Issue 29354773: Issue 4465 - Move rsa module from adblockpluschrome (Closed)
Patch Set: Add unit tests Created Sept. 23, 2016, 1:45 p.m.
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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 // Basic JavaScript BN library - subset useful for RSA encryption.
33
34 // Bits per digit
35 var dbits;
36
37 // JavaScript engine analysis
38 var canary = 0xdeadbeefcafe;
39 var j_lm = ((canary&0xffffff)==0xefcafe);
40
41 // (public) Constructor
42 function BigInteger(a,b,c) {
43 if(a != null)
44 if("number" == typeof a) this.fromNumber(a,b,c);
45 else if(b == null && "string" != typeof a) this.fromString(a,256);
46 else this.fromString(a,b);
47 }
48 exports.BigInteger = BigInteger;
49
50 // return new, unset BigInteger
51 function nbi() { return new BigInteger(null); }
52
53 // am: Compute w_j += (x*this_i), propagate carries,
54 // c is initial carry, returns final carry.
55 // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
56 // We need to select the fastest one that works in this environment.
57
58 // am1: use a single mult and divide to get the high bits,
59 // max digit bits should be 26 because
60 // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
61 function am1(i,x,w,j,c,n) {
62 while(--n >= 0) {
63 var v = x*this[i++]+w[j]+c;
64 c = Math.floor(v/0x4000000);
65 w[j++] = v&0x3ffffff;
66 }
67 return c;
68 }
69 // am2 avoids a big mult-and-extract completely.
70 // Max digit bits should be <= 30 because we do bitwise ops
71 // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
72 function am2(i,x,w,j,c,n) {
73 var xl = x&0x7fff, xh = x>>15;
74 while(--n >= 0) {
75 var l = this[i]&0x7fff;
76 var h = this[i++]>>15;
77 var m = xh*l+h*xl;
78 l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
79 c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
80 w[j++] = l&0x3fffffff;
81 }
82 return c;
83 }
84 // Alternately, set max digit bits to 28 since some
85 // browsers slow down when dealing with 32-bit numbers.
86 function am3(i,x,w,j,c,n) {
87 var xl = x&0x3fff, xh = x>>14;
88 while(--n >= 0) {
89 var l = this[i]&0x3fff;
90 var h = this[i++]>>14;
91 var m = xh*l+h*xl;
92 l = xl*l+((m&0x3fff)<<14)+w[j]+c;
93 c = (l>>28)+(m>>14)+xh*h;
94 w[j++] = l&0xfffffff;
95 }
96 return c;
97 }
98 if(j_lm && (typeof navigator != "undefined" && navigator.appName == "Microsoft I nternet Explorer")) {
99 BigInteger.prototype.am = am2;
100 dbits = 30;
101 }
102 else if(j_lm && (typeof navigator != "undefined" && navigator.appName != "Netsca pe")) {
103 BigInteger.prototype.am = am1;
104 dbits = 26;
105 }
106 else { // Mozilla/Netscape seems to prefer am3
107 BigInteger.prototype.am = am3;
108 dbits = 28;
109 }
110
111 BigInteger.prototype.DB = dbits;
112 BigInteger.prototype.DM = ((1<<dbits)-1);
113 BigInteger.prototype.DV = (1<<dbits);
114
115 var BI_FP = 52;
116 BigInteger.prototype.FV = Math.pow(2,BI_FP);
117 BigInteger.prototype.F1 = BI_FP-dbits;
118 BigInteger.prototype.F2 = 2*dbits-BI_FP;
119
120 // Digit conversions
121 var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
122 var BI_RC = new Array();
123 var rr,vv;
124 rr = "0".charCodeAt(0);
125 for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
126 rr = "a".charCodeAt(0);
127 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
128 rr = "A".charCodeAt(0);
129 for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
130
131 function int2char(n) { return BI_RM.charAt(n); }
132 function intAt(s,i) {
133 var c = BI_RC[s.charCodeAt(i)];
134 return (c==null)?-1:c;
135 }
136
137 // (protected) copy this to r
138 function bnpCopyTo(r) {
139 for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
140 r.t = this.t;
141 r.s = this.s;
142 }
143
144 // (protected) set from integer value x, -DV <= x < DV
145 function bnpFromInt(x) {
146 this.t = 1;
147 this.s = (x<0)?-1:0;
148 if(x > 0) this[0] = x;
149 else if(x < -1) this[0] = x+DV;
150 else this.t = 0;
151 }
152
153 // return bigint initialized to value
154 function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
155
156 // (protected) set from string and radix
157 function bnpFromString(s,b) {
158 var k;
159 if(b == 16) k = 4;
160 else if(b == 8) k = 3;
161 else if(b == 256) k = 8; // byte array
162 else if(b == 2) k = 1;
163 else if(b == 32) k = 5;
164 else if(b == 4) k = 2;
165 else { this.fromRadix(s,b); return; }
166 this.t = 0;
167 this.s = 0;
168 var i = s.length, mi = false, sh = 0;
169 while(--i >= 0) {
170 var x = (k==8)?s.charCodeAt(i)&0xff:intAt(s,i); /** MODIFIED **/
171 if(x < 0) {
172 if(s.charAt(i) == "-") mi = true;
173 continue;
174 }
175 mi = false;
176 if(sh == 0)
177 this[this.t++] = x;
178 else if(sh+k > this.DB) {
179 this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
180 this[this.t++] = (x>>(this.DB-sh));
181 }
182 else
183 this[this.t-1] |= x<<sh;
184 sh += k;
185 if(sh >= this.DB) sh -= this.DB;
186 }
187 if(k == 8 && (s[0]&0x80) != 0) {
188 this.s = -1;
189 if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
190 }
191 this.clamp();
192 if(mi) BigInteger.ZERO.subTo(this,this);
193 }
194
195 // (protected) clamp off excess high words
196 function bnpClamp() {
197 var c = this.s&this.DM;
198 while(this.t > 0 && this[this.t-1] == c) --this.t;
199 }
200
201 // (public) return string representation in given radix
202 function bnToString(b) {
203 if(this.s < 0) return "-"+this.negate().toString(b);
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 /** MODIFIED **/
208 else if(b == 2) k = 1;
209 else if(b == 32) k = 5;
210 else if(b == 4) k = 2;
211 else return this.toRadix(b);
212 var km = (1<<k)-1, d, m = false, r = "", i = this.t;
213 var p = this.DB-(i*this.DB)%k;
214 if(i-- > 0) {
215 if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = (k==8)?String.fromCh arCode(d):int2char(d); } /** MODIFIED **/
216 while(i >= 0) {
217 if(p < k) {
218 d = (this[i]&((1<<p)-1))<<(k-p);
219 d |= this[--i]>>(p+=this.DB-k);
220 }
221 else {
222 d = (this[i]>>(p-=k))&km;
223 if(p <= 0) { p += this.DB; --i; }
224 }
225 if(d > 0) m = true;
226 if(m) r += (k==8)?String.fromCharCode(d):int2char(d); /** MODIFIED **/
227 }
228 }
229 return m?r:"0";
230 }
231
232 // (public) -this
233 function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
234
235 // (public) |this|
236 function bnAbs() { return (this.s<0)?this.negate():this; }
237
238 // (public) return + if this > a, - if this < a, 0 if equal
239 function bnCompareTo(a) {
240 var r = this.s-a.s;
241 if(r != 0) return r;
242 var i = this.t;
243 r = i-a.t;
244 if(r != 0) return r;
245 while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
246 return 0;
247 }
248
249 // returns bit length of the integer x
250 function nbits(x) {
251 var r = 1, t;
252 if((t=x>>>16) != 0) { x = t; r += 16; }
253 if((t=x>>8) != 0) { x = t; r += 8; }
254 if((t=x>>4) != 0) { x = t; r += 4; }
255 if((t=x>>2) != 0) { x = t; r += 2; }
256 if((t=x>>1) != 0) { x = t; r += 1; }
257 return r;
258 }
259
260 // (public) return the number of bits in "this"
261 function bnBitLength() {
262 if(this.t <= 0) return 0;
263 return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
264 }
265
266 // (protected) r = this << n*DB
267 function bnpDLShiftTo(n,r) {
268 var i;
269 for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
270 for(i = n-1; i >= 0; --i) r[i] = 0;
271 r.t = this.t+n;
272 r.s = this.s;
273 }
274
275 // (protected) r = this >> n*DB
276 function bnpDRShiftTo(n,r) {
277 for(var i = n; i < this.t; ++i) r[i-n] = this[i];
278 r.t = Math.max(this.t-n,0);
279 r.s = this.s;
280 }
281
282 // (protected) r = this << n
283 function bnpLShiftTo(n,r) {
284 var bs = n%this.DB;
285 var cbs = this.DB-bs;
286 var bm = (1<<cbs)-1;
287 var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
288 for(i = this.t-1; i >= 0; --i) {
289 r[i+ds+1] = (this[i]>>cbs)|c;
290 c = (this[i]&bm)<<bs;
291 }
292 for(i = ds-1; i >= 0; --i) r[i] = 0;
293 r[ds] = c;
294 r.t = this.t+ds+1;
295 r.s = this.s;
296 r.clamp();
297 }
298
299 // (protected) r = this >> n
300 function bnpRShiftTo(n,r) {
301 r.s = this.s;
302 var ds = Math.floor(n/this.DB);
303 if(ds >= this.t) { r.t = 0; return; }
304 var bs = n%this.DB;
305 var cbs = this.DB-bs;
306 var bm = (1<<bs)-1;
307 r[0] = this[ds]>>bs;
308 for(var i = ds+1; i < this.t; ++i) {
309 r[i-ds-1] |= (this[i]&bm)<<cbs;
310 r[i-ds] = this[i]>>bs;
311 }
312 if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
313 r.t = this.t-ds;
314 r.clamp();
315 }
316
317 // (protected) r = this - a
318 function bnpSubTo(a,r) {
319 var i = 0, c = 0, m = Math.min(a.t,this.t);
320 while(i < m) {
321 c += this[i]-a[i];
322 r[i++] = c&this.DM;
323 c >>= this.DB;
324 }
325 if(a.t < this.t) {
326 c -= a.s;
327 while(i < this.t) {
328 c += this[i];
329 r[i++] = c&this.DM;
330 c >>= this.DB;
331 }
332 c += this.s;
333 }
334 else {
335 c += this.s;
336 while(i < a.t) {
337 c -= a[i];
338 r[i++] = c&this.DM;
339 c >>= this.DB;
340 }
341 c -= a.s;
342 }
343 r.s = (c<0)?-1:0;
344 if(c < -1) r[i++] = this.DV+c;
345 else if(c > 0) r[i++] = c;
346 r.t = i;
347 r.clamp();
348 }
349
350 // (protected) r = this * a, r != this,a (HAC 14.12)
351 // "this" should be the larger one if appropriate.
352 function bnpMultiplyTo(a,r) {
353 var x = this.abs(), y = a.abs();
354 var i = x.t;
355 r.t = i+y.t;
356 while(--i >= 0) r[i] = 0;
357 for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
358 r.s = 0;
359 r.clamp();
360 if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
361 }
362
363 // (protected) r = this^2, r != this (HAC 14.16)
364 function bnpSquareTo(r) {
365 var x = this.abs();
366 var i = r.t = 2*x.t;
367 while(--i >= 0) r[i] = 0;
368 for(i = 0; i < x.t-1; ++i) {
369 var c = x.am(i,x[i],r,2*i,0,1);
370 if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
371 r[i+x.t] -= x.DV;
372 r[i+x.t+1] = 1;
373 }
374 }
375 if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
376 r.s = 0;
377 r.clamp();
378 }
379
380 // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
381 // r != q, this != m. q or r may be null.
382 function bnpDivRemTo(m,q,r) {
383 var pm = m.abs();
384 if(pm.t <= 0) return;
385 var pt = this.abs();
386 if(pt.t < pm.t) {
387 if(q != null) q.fromInt(0);
388 if(r != null) this.copyTo(r);
389 return;
390 }
391 if(r == null) r = nbi();
392 var y = nbi(), ts = this.s, ms = m.s;
393 var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
394 if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
395 else { pm.copyTo(y); pt.copyTo(r); }
396 var ys = y.t;
397 var y0 = y[ys-1];
398 if(y0 == 0) return;
399 var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
400 var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
401 var i = r.t, j = i-ys, t = (q==null)?nbi():q;
402 y.dlShiftTo(j,t);
403 if(r.compareTo(t) >= 0) {
404 r[r.t++] = 1;
405 r.subTo(t,r);
406 }
407 BigInteger.ONE.dlShiftTo(ys,t);
408 t.subTo(y,y); // "negative" y so we can replace sub with am later
409 while(y.t < ys) y[y.t++] = 0;
410 while(--j >= 0) {
411 // Estimate quotient digit
412 var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
413 if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
414 y.dlShiftTo(j,t);
415 r.subTo(t,r);
416 while(r[i] < --qd) r.subTo(t,r);
417 }
418 }
419 if(q != null) {
420 r.drShiftTo(ys,q);
421 if(ts != ms) BigInteger.ZERO.subTo(q,q);
422 }
423 r.t = ys;
424 r.clamp();
425 if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
426 if(ts < 0) BigInteger.ZERO.subTo(r,r);
427 }
428
429 // (public) this mod a
430 function bnMod(a) {
431 var r = nbi();
432 this.abs().divRemTo(a,null,r);
433 if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
434 return r;
435 }
436
437 // Modular reduction using "classic" algorithm
438 function Classic(m) { this.m = m; }
439 function cConvert(x) {
440 if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
441 else return x;
442 }
443 function cRevert(x) { return x; }
444 function cReduce(x) { x.divRemTo(this.m,null,x); }
445 function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
446 function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
447
448 Classic.prototype.convert = cConvert;
449 Classic.prototype.revert = cRevert;
450 Classic.prototype.reduce = cReduce;
451 Classic.prototype.mulTo = cMulTo;
452 Classic.prototype.sqrTo = cSqrTo;
453
454 // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
455 // justification:
456 // xy == 1 (mod m)
457 // xy = 1+km
458 // xy(2-xy) = (1+km)(1-km)
459 // x[y(2-xy)] = 1-k^2m^2
460 // x[y(2-xy)] == 1 (mod m^2)
461 // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
462 // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
463 // JS multiply "overflows" differently from C/C++, so care is needed here.
464 function bnpInvDigit() {
465 if(this.t < 1) return 0;
466 var x = this[0];
467 if((x&1) == 0) return 0;
468 var y = x&3; // y == 1/x mod 2^2
469 y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
470 y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
471 y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
472 // last step - calculate inverse mod DV directly;
473 // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
474 y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
475 // we really want the negative inverse, and -DV < y < DV
476 return (y>0)?this.DV-y:-y;
477 }
478
479 // Montgomery reduction
480 function Montgomery(m) {
481 this.m = m;
482 this.mp = m.invDigit();
483 this.mpl = this.mp&0x7fff;
484 this.mph = this.mp>>15;
485 this.um = (1<<(m.DB-15))-1;
486 this.mt2 = 2*m.t;
487 }
488
489 // xR mod m
490 function montConvert(x) {
491 var r = nbi();
492 x.abs().dlShiftTo(this.m.t,r);
493 r.divRemTo(this.m,null,r);
494 if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
495 return r;
496 }
497
498 // x/R mod m
499 function montRevert(x) {
500 var r = nbi();
501 x.copyTo(r);
502 this.reduce(r);
503 return r;
504 }
505
506 // x = x/R mod m (HAC 14.32)
507 function montReduce(x) {
508 while(x.t <= this.mt2) // pad x so am has enough room later
509 x[x.t++] = 0;
510 for(var i = 0; i < this.m.t; ++i) {
511 // faster way of calculating u0 = x[i]*mp mod DV
512 var j = x[i]&0x7fff;
513 var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
514 // use am to combine the multiply-shift-add into one call
515 j = i+this.m.t;
516 x[j] += this.m.am(0,u0,x,i,0,this.m.t);
517 // propagate carry
518 while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
519 }
520 x.clamp();
521 x.drShiftTo(this.m.t,x);
522 if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
523 }
524
525 // r = "x^2/R mod m"; x != r
526 function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
527
528 // r = "xy/R mod m"; x,y != r
529 function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
530
531 Montgomery.prototype.convert = montConvert;
532 Montgomery.prototype.revert = montRevert;
533 Montgomery.prototype.reduce = montReduce;
534 Montgomery.prototype.mulTo = montMulTo;
535 Montgomery.prototype.sqrTo = montSqrTo;
536
537 // (protected) true iff this is even
538 function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
539
540 // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
541 function bnpExp(e,z) {
542 if(e > 0xffffffff || e < 1) return BigInteger.ONE;
543 var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
544 g.copyTo(r);
545 while(--i >= 0) {
546 z.sqrTo(r,r2);
547 if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
548 else { var t = r; r = r2; r2 = t; }
549 }
550 return z.revert(r);
551 }
552
553 // (public) this^e % m, 0 <= e < 2^32
554 function bnModPowInt(e,m) {
555 var z;
556 if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
557 return this.exp(e,z);
558 }
559
560 // protected
561 BigInteger.prototype.copyTo = bnpCopyTo;
562 BigInteger.prototype.fromInt = bnpFromInt;
563 BigInteger.prototype.fromString = bnpFromString;
564 BigInteger.prototype.clamp = bnpClamp;
565 BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
566 BigInteger.prototype.drShiftTo = bnpDRShiftTo;
567 BigInteger.prototype.lShiftTo = bnpLShiftTo;
568 BigInteger.prototype.rShiftTo = bnpRShiftTo;
569 BigInteger.prototype.subTo = bnpSubTo;
570 BigInteger.prototype.multiplyTo = bnpMultiplyTo;
571 BigInteger.prototype.squareTo = bnpSquareTo;
572 BigInteger.prototype.divRemTo = bnpDivRemTo;
573 BigInteger.prototype.invDigit = bnpInvDigit;
574 BigInteger.prototype.isEven = bnpIsEven;
575 BigInteger.prototype.exp = bnpExp;
576
577 // public
578 BigInteger.prototype.toString = bnToString;
579 BigInteger.prototype.negate = bnNegate;
580 BigInteger.prototype.abs = bnAbs;
581 BigInteger.prototype.compareTo = bnCompareTo;
582 BigInteger.prototype.bitLength = bnBitLength;
583 BigInteger.prototype.mod = bnMod;
584 BigInteger.prototype.modPowInt = bnModPowInt;
585
586 // "constants"
587 BigInteger.ZERO = nbv(0);
588 BigInteger.ONE = nbv(1);
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