https://kbig.kr/kbig/js/rsa/jsbn.js

1// Copyright (c) 2005  Tom Wu
2// All Rights Reserved.
3// See "LICENSE" for details.
4
5// Basic JavaScript BN library - subset useful for RSA encryption.
6
7// Bits per digit
8var dbits;
9
10// JavaScript engine analysis
11var canary = 0xdeadbeefcafe;
12var j_lm = ((canary&0xffffff)==0xefcafe);
13
14// (public) Constructor
15function BigInteger(a,b,c) {
16  if(a != null)
17    if("number" == typeof a) this.fromNumber(a,b,c);
18    else if(b == null && "string" != typeof a) this.fromString(a,256);
19    else this.fromString(a,b);
20}
21
22// return new, unset BigInteger
23function nbi() { return new BigInteger(null); }
24
25// am: Compute w_j += (x*this_i), propagate carries,
26// c is initial carry, returns final carry.
27// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
28// We need to select the fastest one that works in this environment.
29
30// am1: use a single mult and divide to get the high bits,
31// max digit bits should be 26 because
32// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
33function am1(i,x,w,j,c,n) {
34  while(--n >= 0) {
35    var v = x*this[i++]+w[j]+c;
36    c = Math.floor(v/0x4000000);
37    w[j++] = v&0x3ffffff;
38  }
39  return c;
40}
41// am2 avoids a big mult-and-extract completely.
42// Max digit bits should be <= 30 because we do bitwise ops
43// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
44function am2(i,x,w,j,c,n) {
45  var xl = x&0x7fff, xh = x>>15;
46  while(--n >= 0) {
47    var l = this[i]&0x7fff;
48    var h = this[i++]>>15;
49    var m = xh*l+h*xl;
50    l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
51    c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
52    w[j++] = l&0x3fffffff;
53  }
54  return c;
55}
56// Alternately, set max digit bits to 28 since some
57// browsers slow down when dealing with 32-bit numbers.
58function am3(i,x,w,j,c,n) {
59  var xl = x&0x3fff, xh = x>>14;
60  while(--n >= 0) {
61    var l = this[i]&0x3fff;
62    var h = this[i++]>>14;
63    var m = xh*l+h*xl;
64    l = xl*l+((m&0x3fff)<<14)+w[j]+c;
65    c = (l>>28)+(m>>14)+xh*h;
66    w[j++] = l&0xfffffff;
67  }
68  return c;
69}
70if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
71  BigInteger.prototype.am = am2;
72  dbits = 30;
73}
74else if(j_lm && (navigator.appName != "Netscape")) {
75  BigInteger.prototype.am = am1;
76  dbits = 26;
77}
78else { // Mozilla/Netscape seems to prefer am3
79  BigInteger.prototype.am = am3;
80  dbits = 28;
81}
82
83BigInteger.prototype.DB = dbits;
84BigInteger.prototype.DM = ((1<<dbits)-1);
85BigInteger.prototype.DV = (1<<dbits);
86
87var BI_FP = 52;
88BigInteger.prototype.FV = Math.pow(2,BI_FP);
89BigInteger.prototype.F1 = BI_FP-dbits;
90BigInteger.prototype.F2 = 2*dbits-BI_FP;
91
92// Digit conversions
93var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
94var BI_RC = new Array();
95var rr,vv;
96rr = "0".charCodeAt(0);
97for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
98rr = "a".charCodeAt(0);
99for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
100rr = "A".charCodeAt(0);
101for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
102
103function int2char(n) { return BI_RM.charAt(n); }
104function intAt(s,i) {
105  var c = BI_RC[s.charCodeAt(i)];
106  return (c==null)?-1:c;
107}
108
109// (protected) copy this to r
110function bnpCopyTo(r) {
111  for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
112  r.t = this.t;
113  r.s = this.s;
114}
115
116// (protected) set from integer value x, -DV <= x < DV
117function bnpFromInt(x) {
118  this.t = 1;
119  this.s = (x<0)?-1:0;
120  if(x > 0) this[0] = x;
121  else if(x < -1) this[0] = x+this.DV;
122  else this.t = 0;
123}
124
125// return bigint initialized to value
126function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
127
128// (protected) set from string and radix
129function bnpFromString(s,b) {
130  var k;
131  if(b == 16) k = 4;
132  else if(b == 8) k = 3;
133  else if(b == 256) k = 8; // byte array
134  else if(b == 2) k = 1;
135  else if(b == 32) k = 5;
136  else if(b == 4) k = 2;
137  else { this.fromRadix(s,b); return; }
138  this.t = 0;
139  this.s = 0;
140  var i = s.length, mi = false, sh = 0;
141  while(--i >= 0) {
142    var x = (k==8)?s[i]&0xff:intAt(s,i);
143    if(x < 0) {
144      if(s.charAt(i) == "-") mi = true;
145      continue;
146    }
147    mi = false;
148    if(sh == 0)
149      this[this.t++] = x;
150    else if(sh+k > this.DB) {
151      this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
152      this[this.t++] = (x>>(this.DB-sh));
153    }
154    else
155      this[this.t-1] |= x<<sh;
156    sh += k;
157    if(sh >= this.DB) sh -= this.DB;
158  }
159  if(k == 8 && (s[0]&0x80) != 0) {
160    this.s = -1;
161    if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
162  }
163  this.clamp();
164  if(mi) BigInteger.ZERO.subTo(this,this);
165}
166
167// (protected) clamp off excess high words
168function bnpClamp() {
169  var c = this.s&this.DM;
170  while(this.t > 0 && this[this.t-1] == c) --this.t;
171}
172
173// (public) return string representation in given radix
174function bnToString(b) {
175  if(this.s < 0) return "-"+this.negate().toString(b);
176  var k;
177  if(b == 16) k = 4;
178  else if(b == 8) k = 3;
179  else if(b == 2) k = 1;
180  else if(b == 32) k = 5;
181  else if(b == 4) k = 2;
182  else return this.toRadix(b);
183  var km = (1<<k)-1, d, m = false, r = "", i = this.t;
184  var p = this.DB-(i*this.DB)%k;
185  if(i-- > 0) {
186    if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
187    while(i >= 0) {
188      if(p < k) {
189        d = (this[i]&((1<<p)-1))<<(k-p);
190        d |= this[--i]>>(p+=this.DB-k);
191      }
192      else {
193        d = (this[i]>>(p-=k))&km;
194        if(p <= 0) { p += this.DB; --i; }
195      }
196      if(d > 0) m = true;
197      if(m) r += int2char(d);
198    }
199  }
200  return m?r:"0";
201}
202
203// (public) -this
204function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
205
206// (public) |this|
207function bnAbs() { return (this.s<0)?this.negate():this; }
208
209// (public) return + if this > a, - if this < a, 0 if equal
210function bnCompareTo(a) {
211  var r = this.s-a.s;
212  if(r != 0) return r;
213  var i = this.t;
214  r = i-a.t;
215  if(r != 0) return (this.s<0)?-r:r;
216  while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
217  return 0;
218}
219
220// returns bit length of the integer x
221function nbits(x) {
222  var r = 1, t;
223  if((t=x>>>16) != 0) { x = t; r += 16; }
224  if((t=x>>8) != 0) { x = t; r += 8; }
225  if((t=x>>4) != 0) { x = t; r += 4; }
226  if((t=x>>2) != 0) { x = t; r += 2; }
227  if((t=x>>1) != 0) { x = t; r += 1; }
228  return r;
229}
230
231// (public) return the number of bits in "this"
232function bnBitLength() {
233  if(this.t <= 0) return 0;
234  return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
235}
236
237// (protected) r = this << n*DB
238function bnpDLShiftTo(n,r) {
239  var i;
240  for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
241  for(i = n-1; i >= 0; --i) r[i] = 0;
242  r.t = this.t+n;
243  r.s = this.s;
244}
245
246// (protected) r = this >> n*DB
247function bnpDRShiftTo(n,r) {
248  for(var i = n; i < this.t; ++i) r[i-n] = this[i];
249  r.t = Math.max(this.t-n,0);
250  r.s = this.s;
251}
252
253// (protected) r = this << n
254function bnpLShiftTo(n,r) {
255  var bs = n%this.DB;
256  var cbs = this.DB-bs;
257  var bm = (1<<cbs)-1;
258  var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
259  for(i = this.t-1; i >= 0; --i) {
260    r[i+ds+1] = (this[i]>>cbs)|c;
261    c = (this[i]&bm)<<bs;
262  }
263  for(i = ds-1; i >= 0; --i) r[i] = 0;
264  r[ds] = c;
265  r.t = this.t+ds+1;
266  r.s = this.s;
267  r.clamp();
268}
269
270// (protected) r = this >> n
271function bnpRShiftTo(n,r) {
272  r.s = this.s;
273  var ds = Math.floor(n/this.DB);
274  if(ds >= this.t) { r.t = 0; return; }
275  var bs = n%this.DB;
276  var cbs = this.DB-bs;
277  var bm = (1<<bs)-1;
278  r[0] = this[ds]>>bs;
279  for(var i = ds+1; i < this.t; ++i) {
280    r[i-ds-1] |= (this[i]&bm)<<cbs;
281    r[i-ds] = this[i]>>bs;
282  }
283  if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
284  r.t = this.t-ds;
285  r.clamp();
286}
287
288// (protected) r = this - a
289function bnpSubTo(a,r) {
290  var i = 0, c = 0, m = Math.min(a.t,this.t);
291  while(i < m) {
292    c += this[i]-a[i];
293    r[i++] = c&this.DM;
294    c >>= this.DB;
295  }
296  if(a.t < this.t) {
297    c -= a.s;
298    while(i < this.t) {
299      c += this[i];
300      r[i++] = c&this.DM;
301      c >>= this.DB;
302    }
303    c += this.s;
304  }
305  else {
306    c += this.s;
307    while(i < a.t) {
308      c -= a[i];
309      r[i++] = c&this.DM;
310      c >>= this.DB;
311    }
312    c -= a.s;
313  }
314  r.s = (c<0)?-1:0;
315  if(c < -1) r[i++] = this.DV+c;
316  else if(c > 0) r[i++] = c;
317  r.t = i;
318  r.clamp();
319}
320
321// (protected) r = this * a, r != this,a (HAC 14.12)
322// "this" should be the larger one if appropriate.
323function bnpMultiplyTo(a,r) {
324  var x = this.abs(), y = a.abs();
325  var i = x.t;
326  r.t = i+y.t;
327  while(--i >= 0) r[i] = 0;
328  for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
329  r.s = 0;
330  r.clamp();
331  if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
332}
333
334// (protected) r = this^2, r != this (HAC 14.16)
335function bnpSquareTo(r) {
336  var x = this.abs();
337  var i = r.t = 2*x.t;
338  while(--i >= 0) r[i] = 0;
339  for(i = 0; i < x.t-1; ++i) {
340    var c = x.am(i,x[i],r,2*i,0,1);
341    if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
342      r[i+x.t] -= x.DV;
343      r[i+x.t+1] = 1;
344    }
345  }
346  if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
347  r.s = 0;
348  r.clamp();
349}
350
351// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
352// r != q, this != m.  q or r may be null.
353function bnpDivRemTo(m,q,r) {
354  var pm = m.abs();
355  if(pm.t <= 0) return;
356  var pt = this.abs();
357  if(pt.t < pm.t) {
358    if(q != null) q.fromInt(0);
359    if(r != null) this.copyTo(r);
360    return;
361  }
362  if(r == null) r = nbi();
363  var y = nbi(), ts = this.s, ms = m.s;
364  var nsh = this.DB-nbits(pm[pm.t-1]);	// normalize modulus
365  if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
366  else { pm.copyTo(y); pt.copyTo(r); }
367  var ys = y.t;
368  var y0 = y[ys-1];
369  if(y0 == 0) return;
370  var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
371  var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
372  var i = r.t, j = i-ys, t = (q==null)?nbi():q;
373  y.dlShiftTo(j,t);
374  if(r.compareTo(t) >= 0) {
375    r[r.t++] = 1;
376    r.subTo(t,r);
377  }
378  BigInteger.ONE.dlShiftTo(ys,t);
379  t.subTo(y,y);	// "negative" y so we can replace sub with am later
380  while(y.t < ys) y[y.t++] = 0;
381  while(--j >= 0) {
382    // Estimate quotient digit
383    var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
384    if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) {	// Try it out
385      y.dlShiftTo(j,t);
386      r.subTo(t,r);
387      while(r[i] < --qd) r.subTo(t,r);
388    }
389  }
390  if(q != null) {
391    r.drShiftTo(ys,q);
392    if(ts != ms) BigInteger.ZERO.subTo(q,q);
393  }
394  r.t = ys;
395  r.clamp();
396  if(nsh > 0) r.rShiftTo(nsh,r);	// Denormalize remainder
397  if(ts < 0) BigInteger.ZERO.subTo(r,r);
398}
399
400// (public) this mod a
401function bnMod(a) {
402  var r = nbi();
403  this.abs().divRemTo(a,null,r);
404  if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
405  return r;
406}
407
408// Modular reduction using "classic" algorithm
409function Classic(m) { this.m = m; }
410function cConvert(x) {
411  if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
412  else return x;
413}
414function cRevert(x) { return x; }
415function cReduce(x) { x.divRemTo(this.m,null,x); }
416function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
417function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
418
419Classic.prototype.convert = cConvert;
420Classic.prototype.revert = cRevert;
421Classic.prototype.reduce = cReduce;
422Classic.prototype.mulTo = cMulTo;
423Classic.prototype.sqrTo = cSqrTo;
424
425// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
426// justification:
427//         xy == 1 (mod m)
428//         xy =  1+km
429//   xy(2-xy) = (1+km)(1-km)
430// x[y(2-xy)] = 1-k^2m^2
431// x[y(2-xy)] == 1 (mod m^2)
432// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
433// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
434// JS multiply "overflows" differently from C/C++, so care is needed here.
435function bnpInvDigit() {
436  if(this.t < 1) return 0;
437  var x = this[0];
438  if((x&1) == 0) return 0;
439  var y = x&3;		// y == 1/x mod 2^2
440  y = (y*(2-(x&0xf)*y))&0xf;	// y == 1/x mod 2^4
441  y = (y*(2-(x&0xff)*y))&0xff;	// y == 1/x mod 2^8
442  y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;	// y == 1/x mod 2^16
443  // last step - calculate inverse mod DV directly;
444  // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
445  y = (y*(2-x*y%this.DV))%this.DV;		// y == 1/x mod 2^dbits
446  // we really want the negative inverse, and -DV < y < DV
447  return (y>0)?this.DV-y:-y;
448}
449
450// Montgomery reduction
451function Montgomery(m) {
452  this.m = m;
453  this.mp = m.invDigit();
454  this.mpl = this.mp&0x7fff;
455  this.mph = this.mp>>15;
456  this.um = (1<<(m.DB-15))-1;
457  this.mt2 = 2*m.t;
458}
459
460// xR mod m
461function montConvert(x) {
462  var r = nbi();
463  x.abs().dlShiftTo(this.m.t,r);
464  r.divRemTo(this.m,null,r);
465  if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
466  return r;
467}
468
469// x/R mod m
470function montRevert(x) {
471  var r = nbi();
472  x.copyTo(r);
473  this.reduce(r);
474  return r;
475}
476
477// x = x/R mod m (HAC 14.32)
478function montReduce(x) {
479  while(x.t <= this.mt2)	// pad x so am has enough room later
480    x[x.t++] = 0;
481  for(var i = 0; i < this.m.t; ++i) {
482    // faster way of calculating u0 = x[i]*mp mod DV
483    var j = x[i]&0x7fff;
484    var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
485    // use am to combine the multiply-shift-add into one call
486    j = i+this.m.t;
487    x[j] += this.m.am(0,u0,x,i,0,this.m.t);
488    // propagate carry
489    while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
490  }
491  x.clamp();
492  x.drShiftTo(this.m.t,x);
493  if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
494}
495
496// r = "x^2/R mod m"; x != r
497function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
498
499// r = "xy/R mod m"; x,y != r
500function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
501
502Montgomery.prototype.convert = montConvert;
503Montgomery.prototype.revert = montRevert;
504Montgomery.prototype.reduce = montReduce;
505Montgomery.prototype.mulTo = montMulTo;
506Montgomery.prototype.sqrTo = montSqrTo;
507
508// (protected) true iff this is even
509function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
510
511// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
512function bnpExp(e,z) {
513  if(e > 0xffffffff || e < 1) return BigInteger.ONE;
514  var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
515  g.copyTo(r);
516  while(--i >= 0) {
517    z.sqrTo(r,r2);
518    if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
519    else { var t = r; r = r2; r2 = t; }
520  }
521  return z.revert(r);
522}
523
524// (public) this^e % m, 0 <= e < 2^32
525function bnModPowInt(e,m) {
526  var z;
527  if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
528  return this.exp(e,z);
529}
530
531// protected
532BigInteger.prototype.copyTo = bnpCopyTo;
533BigInteger.prototype.fromInt = bnpFromInt;
534BigInteger.prototype.fromString = bnpFromString;
535BigInteger.prototype.clamp = bnpClamp;
536BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
537BigInteger.prototype.drShiftTo = bnpDRShiftTo;
538BigInteger.prototype.lShiftTo = bnpLShiftTo;
539BigInteger.prototype.rShiftTo = bnpRShiftTo;
540BigInteger.prototype.subTo = bnpSubTo;
541BigInteger.prototype.multiplyTo = bnpMultiplyTo;
542BigInteger.prototype.squareTo = bnpSquareTo;
543BigInteger.prototype.divRemTo = bnpDivRemTo;
544BigInteger.prototype.invDigit = bnpInvDigit;
545BigInteger.prototype.isEven = bnpIsEven;
546BigInteger.prototype.exp = bnpExp;
547
548// public
549BigInteger.prototype.toString = bnToString;
550BigInteger.prototype.negate = bnNegate;
551BigInteger.prototype.abs = bnAbs;
552BigInteger.prototype.compareTo = bnCompareTo;
553BigInteger.prototype.bitLength = bnBitLength;
554BigInteger.prototype.mod = bnMod;
555BigInteger.prototype.modPowInt = bnModPowInt;
556
557// "constants"
558BigInteger.ZERO = nbv(0);
559BigInteger.ONE = nbv(1);