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+/*
+ * Copyright (c) 2003-2005 Tom Wu
+ * All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
+ * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
+ *
+ * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
+ * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * In addition, the following condition applies:
+ *
+ * All redistributions must retain an intact copy of this copyright notice
+ * and disclaimer.
+ */
+
+// Basic JavaScript BN library - subset useful for RSA encryption.
+
+// Bits per digit
+var dbits;
+
+// JavaScript engine analysis
+var canary = 0xdeadbeefcafe;
+var j_lm = ((canary&0xffffff)==0xefcafe);
+
+// (public) Constructor
+function BigInteger(a,b,c) {
+ if(a != null)
+ if("number" == typeof a) this.fromNumber(a,b,c);
+ else if(b == null && "string" != typeof a) this.fromString(a,256);
+ else this.fromString(a,b);
+}
+
+// return new, unset BigInteger
+function nbi() { return new BigInteger(null); }
+
+// am: Compute w_j += (x*this_i), propagate carries,
+// c is initial carry, returns final carry.
+// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
+// We need to select the fastest one that works in this environment.
+
+// am1: use a single mult and divide to get the high bits,
+// max digit bits should be 26 because
+// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
+function am1(i,x,w,j,c,n) {
+ while(--n >= 0) {
+ var v = x*this[i++]+w[j]+c;
+ c = Math.floor(v/0x4000000);
+ w[j++] = v&0x3ffffff;
+ }
+ return c;
+}
+// am2 avoids a big mult-and-extract completely.
+// Max digit bits should be <= 30 because we do bitwise ops
+// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
+function am2(i,x,w,j,c,n) {
+ var xl = x&0x7fff, xh = x>>15;
+ while(--n >= 0) {
+ var l = this[i]&0x7fff;
+ var h = this[i++]>>15;
+ var m = xh*l+h*xl;
+ l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
+ c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
+ w[j++] = l&0x3fffffff;
+ }
+ return c;
+}
+// Alternately, set max digit bits to 28 since some
+// browsers slow down when dealing with 32-bit numbers.
+function am3(i,x,w,j,c,n) {
+ var xl = x&0x3fff, xh = x>>14;
+ while(--n >= 0) {
+ var l = this[i]&0x3fff;
+ var h = this[i++]>>14;
+ var m = xh*l+h*xl;
+ l = xl*l+((m&0x3fff)<<14)+w[j]+c;
+ c = (l>>28)+(m>>14)+xh*h;
+ w[j++] = l&0xfffffff;
+ }
+ return c;
+}
+if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
+ BigInteger.prototype.am = am2;
+ dbits = 30;
+}
+else if(j_lm && (navigator.appName != "Netscape")) {
+ BigInteger.prototype.am = am1;
+ dbits = 26;
+}
+else { // Mozilla/Netscape seems to prefer am3
+ BigInteger.prototype.am = am3;
+ dbits = 28;
+}
+
+BigInteger.prototype.DB = dbits;
+BigInteger.prototype.DM = ((1<<dbits)-1);
+BigInteger.prototype.DV = (1<<dbits);
+
+var BI_FP = 52;
+BigInteger.prototype.FV = Math.pow(2,BI_FP);
+BigInteger.prototype.F1 = BI_FP-dbits;
+BigInteger.prototype.F2 = 2*dbits-BI_FP;
+
+// Digit conversions
+var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
+var BI_RC = new Array();
+var rr,vv;
+rr = "0".charCodeAt(0);
+for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
+rr = "a".charCodeAt(0);
+for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
+rr = "A".charCodeAt(0);
+for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
+
+function int2char(n) { return BI_RM.charAt(n); }
+function intAt(s,i) {
+ var c = BI_RC[s.charCodeAt(i)];
+ return (c==null)?-1:c;
+}
+
+// (protected) copy this to r
+function bnpCopyTo(r) {
+ for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
+ r.t = this.t;
+ r.s = this.s;
+}
+
+// (protected) set from integer value x, -DV <= x < DV
+function bnpFromInt(x) {
+ this.t = 1;
+ this.s = (x<0)?-1:0;
+ if(x > 0) this[0] = x;
+ else if(x < -1) this[0] = x+DV;
+ else this.t = 0;
+}
+
+// return bigint initialized to value
+function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
+
+// (protected) set from string and radix
+function bnpFromString(s,b) {
+ var k;
+ if(b == 16) k = 4;
+ else if(b == 8) k = 3;
+ else if(b == 256) k = 8; // byte array
+ else if(b == 2) k = 1;
+ else if(b == 32) k = 5;
+ else if(b == 4) k = 2;
+ else { this.fromRadix(s,b); return; }
+ this.t = 0;
+ this.s = 0;
+ var i = s.length, mi = false, sh = 0;
+ while(--i >= 0) {
+ var x = (k==8)?s[i]&0xff:intAt(s,i);
+ if(x < 0) {
+ if(s.charAt(i) == "-") mi = true;
+ continue;
+ }
+ mi = false;
+ if(sh == 0)
+ this[this.t++] = x;
+ else if(sh+k > this.DB) {
+ this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
+ this[this.t++] = (x>>(this.DB-sh));
+ }
+ else
+ this[this.t-1] |= x<<sh;
+ sh += k;
+ if(sh >= this.DB) sh -= this.DB;
+ }
+ if(k == 8 && (s[0]&0x80) != 0) {
+ this.s = -1;
+ if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
+ }
+ this.clamp();
+ if(mi) BigInteger.ZERO.subTo(this,this);
+}
+
+// (protected) clamp off excess high words
+function bnpClamp() {
+ var c = this.s&this.DM;
+ while(this.t > 0 && this[this.t-1] == c) --this.t;
+}
+
+// (public) return string representation in given radix
+function bnToString(b) {
+ if(this.s < 0) return "-"+this.negate().toString(b);
+ var k;
+ if(b == 16) k = 4;
+ else if(b == 8) k = 3;
+ else if(b == 2) k = 1;
+ else if(b == 32) k = 5;
+ else if(b == 4) k = 2;
+ else return this.toRadix(b);
+ var km = (1<<k)-1, d, m = false, r = "", i = this.t;
+ var p = this.DB-(i*this.DB)%k;
+ if(i-- > 0) {
+ if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
+ while(i >= 0) {
+ if(p < k) {
+ d = (this[i]&((1<<p)-1))<<(k-p);
+ d |= this[--i]>>(p+=this.DB-k);
+ }
+ else {
+ d = (this[i]>>(p-=k))&km;
+ if(p <= 0) { p += this.DB; --i; }
+ }
+ if(d > 0) m = true;
+ if(m) r += int2char(d);
+ }
+ }
+ return m?r:"0";
+}
+
+// (public) -this
+function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
+
+// (public) |this|
+function bnAbs() { return (this.s<0)?this.negate():this; }
+
+// (public) return + if this > a, - if this < a, 0 if equal
+function bnCompareTo(a) {
+ var r = this.s-a.s;
+ if(r != 0) return r;
+ var i = this.t;
+ r = i-a.t;
+ if(r != 0) return r;
+ while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
+ return 0;
+}
+
+// returns bit length of the integer x
+function nbits(x) {
+ var r = 1, t;
+ if((t=x>>>16) != 0) { x = t; r += 16; }
+ if((t=x>>8) != 0) { x = t; r += 8; }
+ if((t=x>>4) != 0) { x = t; r += 4; }
+ if((t=x>>2) != 0) { x = t; r += 2; }
+ if((t=x>>1) != 0) { x = t; r += 1; }
+ return r;
+}
+
+// (public) return the number of bits in "this"
+function bnBitLength() {
+ if(this.t <= 0) return 0;
+ return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
+}
+
+// (protected) r = this << n*DB
+function bnpDLShiftTo(n,r) {
+ var i;
+ for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
+ for(i = n-1; i >= 0; --i) r[i] = 0;
+ r.t = this.t+n;
+ r.s = this.s;
+}
+
+// (protected) r = this >> n*DB
+function bnpDRShiftTo(n,r) {
+ for(var i = n; i < this.t; ++i) r[i-n] = this[i];
+ r.t = Math.max(this.t-n,0);
+ r.s = this.s;
+}
+
+// (protected) r = this << n
+function bnpLShiftTo(n,r) {
+ var bs = n%this.DB;
+ var cbs = this.DB-bs;
+ var bm = (1<<cbs)-1;
+ var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
+ for(i = this.t-1; i >= 0; --i) {
+ r[i+ds+1] = (this[i]>>cbs)|c;
+ c = (this[i]&bm)<<bs;
+ }
+ for(i = ds-1; i >= 0; --i) r[i] = 0;
+ r[ds] = c;
+ r.t = this.t+ds+1;
+ r.s = this.s;
+ r.clamp();
+}
+
+// (protected) r = this >> n
+function bnpRShiftTo(n,r) {
+ r.s = this.s;
+ var ds = Math.floor(n/this.DB);
+ if(ds >= this.t) { r.t = 0; return; }
+ var bs = n%this.DB;
+ var cbs = this.DB-bs;
+ var bm = (1<<bs)-1;
+ r[0] = this[ds]>>bs;
+ for(var i = ds+1; i < this.t; ++i) {
+ r[i-ds-1] |= (this[i]&bm)<<cbs;
+ r[i-ds] = this[i]>>bs;
+ }
+ if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
+ r.t = this.t-ds;
+ r.clamp();
+}
+
+// (protected) r = this - a
+function bnpSubTo(a,r) {
+ var i = 0, c = 0, m = Math.min(a.t,this.t);
+ while(i < m) {
+ c += this[i]-a[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ if(a.t < this.t) {
+ c -= a.s;
+ while(i < this.t) {
+ c += this[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ c += this.s;
+ }
+ else {
+ c += this.s;
+ while(i < a.t) {
+ c -= a[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ c -= a.s;
+ }
+ r.s = (c<0)?-1:0;
+ if(c < -1) r[i++] = this.DV+c;
+ else if(c > 0) r[i++] = c;
+ r.t = i;
+ r.clamp();
+}
+
+// (protected) r = this * a, r != this,a (HAC 14.12)
+// "this" should be the larger one if appropriate.
+function bnpMultiplyTo(a,r) {
+ var x = this.abs(), y = a.abs();
+ var i = x.t;
+ r.t = i+y.t;
+ while(--i >= 0) r[i] = 0;
+ for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
+ r.s = 0;
+ r.clamp();
+ if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
+}
+
+// (protected) r = this^2, r != this (HAC 14.16)
+function bnpSquareTo(r) {
+ var x = this.abs();
+ var i = r.t = 2*x.t;
+ while(--i >= 0) r[i] = 0;
+ for(i = 0; i < x.t-1; ++i) {
+ var c = x.am(i,x[i],r,2*i,0,1);
+ if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
+ r[i+x.t] -= x.DV;
+ r[i+x.t+1] = 1;
+ }
+ }
+ if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
+ r.s = 0;
+ r.clamp();
+}
+
+// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
+// r != q, this != m. q or r may be null.
+function bnpDivRemTo(m,q,r) {
+ var pm = m.abs();
+ if(pm.t <= 0) return;
+ var pt = this.abs();
+ if(pt.t < pm.t) {
+ if(q != null) q.fromInt(0);
+ if(r != null) this.copyTo(r);
+ return;
+ }
+ if(r == null) r = nbi();
+ var y = nbi(), ts = this.s, ms = m.s;
+ var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
+ if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
+ else { pm.copyTo(y); pt.copyTo(r); }
+ var ys = y.t;
+ var y0 = y[ys-1];
+ if(y0 == 0) return;
+ var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
+ var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
+ var i = r.t, j = i-ys, t = (q==null)?nbi():q;
+ y.dlShiftTo(j,t);
+ if(r.compareTo(t) >= 0) {
+ r[r.t++] = 1;
+ r.subTo(t,r);
+ }
+ BigInteger.ONE.dlShiftTo(ys,t);
+ t.subTo(y,y); // "negative" y so we can replace sub with am later
+ while(y.t < ys) y[y.t++] = 0;
+ while(--j >= 0) {
+ // Estimate quotient digit
+ var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
+ if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
+ y.dlShiftTo(j,t);
+ r.subTo(t,r);
+ while(r[i] < --qd) r.subTo(t,r);
+ }
+ }
+ if(q != null) {
+ r.drShiftTo(ys,q);
+ if(ts != ms) BigInteger.ZERO.subTo(q,q);
+ }
+ r.t = ys;
+ r.clamp();
+ if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
+ if(ts < 0) BigInteger.ZERO.subTo(r,r);
+}
+
+// (public) this mod a
+function bnMod(a) {
+ var r = nbi();
+ this.abs().divRemTo(a,null,r);
+ if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
+ return r;
+}
+
+// Modular reduction using "classic" algorithm
+function Classic(m) { this.m = m; }
+function cConvert(x) {
+ if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
+ else return x;
+}
+function cRevert(x) { return x; }
+function cReduce(x) { x.divRemTo(this.m,null,x); }
+function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+Classic.prototype.convert = cConvert;
+Classic.prototype.revert = cRevert;
+Classic.prototype.reduce = cReduce;
+Classic.prototype.mulTo = cMulTo;
+Classic.prototype.sqrTo = cSqrTo;
+
+// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
+// justification:
+// xy == 1 (mod m)
+// xy = 1+km
+// xy(2-xy) = (1+km)(1-km)
+// x[y(2-xy)] = 1-k^2m^2
+// x[y(2-xy)] == 1 (mod m^2)
+// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
+// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
+// JS multiply "overflows" differently from C/C++, so care is needed here.
+function bnpInvDigit() {
+ if(this.t < 1) return 0;
+ var x = this[0];
+ if((x&1) == 0) return 0;
+ var y = x&3; // y == 1/x mod 2^2
+ y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
+ y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
+ y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
+ // last step - calculate inverse mod DV directly;
+ // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
+ y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
+ // we really want the negative inverse, and -DV < y < DV
+ return (y>0)?this.DV-y:-y;
+}
+
+// Montgomery reduction
+function Montgomery(m) {
+ this.m = m;
+ this.mp = m.invDigit();
+ this.mpl = this.mp&0x7fff;
+ this.mph = this.mp>>15;
+ this.um = (1<<(m.DB-15))-1;
+ this.mt2 = 2*m.t;
+}
+
+// xR mod m
+function montConvert(x) {
+ var r = nbi();
+ x.abs().dlShiftTo(this.m.t,r);
+ r.divRemTo(this.m,null,r);
+ if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
+ return r;
+}
+
+// x/R mod m
+function montRevert(x) {
+ var r = nbi();
+ x.copyTo(r);
+ this.reduce(r);
+ return r;
+}
+
+// x = x/R mod m (HAC 14.32)
+function montReduce(x) {
+ while(x.t <= this.mt2) // pad x so am has enough room later
+ x[x.t++] = 0;
+ for(var i = 0; i < this.m.t; ++i) {
+ // faster way of calculating u0 = x[i]*mp mod DV
+ var j = x[i]&0x7fff;
+ var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
+ // use am to combine the multiply-shift-add into one call
+ j = i+this.m.t;
+ x[j] += this.m.am(0,u0,x,i,0,this.m.t);
+ // propagate carry
+ while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
+ }
+ x.clamp();
+ x.drShiftTo(this.m.t,x);
+ if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
+}
+
+// r = "x^2/R mod m"; x != r
+function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+// r = "xy/R mod m"; x,y != r
+function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+
+Montgomery.prototype.convert = montConvert;
+Montgomery.prototype.revert = montRevert;
+Montgomery.prototype.reduce = montReduce;
+Montgomery.prototype.mulTo = montMulTo;
+Montgomery.prototype.sqrTo = montSqrTo;
+
+// (protected) true iff this is even
+function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
+
+// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
+function bnpExp(e,z) {
+ if(e > 0xffffffff || e < 1) return BigInteger.ONE;
+ var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
+ g.copyTo(r);
+ while(--i >= 0) {
+ z.sqrTo(r,r2);
+ if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
+ else { var t = r; r = r2; r2 = t; }
+ }
+ return z.revert(r);
+}
+
+// (public) this^e % m, 0 <= e < 2^32
+function bnModPowInt(e,m) {
+ var z;
+ if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
+ return this.exp(e,z);
+}
+
+// protected
+BigInteger.prototype.copyTo = bnpCopyTo;
+BigInteger.prototype.fromInt = bnpFromInt;
+BigInteger.prototype.fromString = bnpFromString;
+BigInteger.prototype.clamp = bnpClamp;
+BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
+BigInteger.prototype.drShiftTo = bnpDRShiftTo;
+BigInteger.prototype.lShiftTo = bnpLShiftTo;
+BigInteger.prototype.rShiftTo = bnpRShiftTo;
+BigInteger.prototype.subTo = bnpSubTo;
+BigInteger.prototype.multiplyTo = bnpMultiplyTo;
+BigInteger.prototype.squareTo = bnpSquareTo;
+BigInteger.prototype.divRemTo = bnpDivRemTo;
+BigInteger.prototype.invDigit = bnpInvDigit;
+BigInteger.prototype.isEven = bnpIsEven;
+BigInteger.prototype.exp = bnpExp;
+
+// public
+BigInteger.prototype.toString = bnToString;
+BigInteger.prototype.negate = bnNegate;
+BigInteger.prototype.abs = bnAbs;
+BigInteger.prototype.compareTo = bnCompareTo;
+BigInteger.prototype.bitLength = bnBitLength;
+BigInteger.prototype.mod = bnMod;
+BigInteger.prototype.modPowInt = bnModPowInt;
+
+// "constants"
+BigInteger.ZERO = nbv(0);
+BigInteger.ONE = nbv(1);
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-20 04:24:00 +0000