/*!
* Basic JavaScript BN library - subset useful for RSA encryption. v1.3
*
* Copyright (c) 2005 Tom Wu
* All Rights Reserved.
* BSD License
* http://www-cs-students.stanford.edu/~tjw/jsbn/LICENSE
*
* Copyright Stephan Thomas
* Copyright bitaddress.org
*/
(function () {
// (public) Constructor function of Global BigInteger object
var BigInteger = window.BigInteger = 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);
};
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary & 0xffffff) == 0xefcafe);
// 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;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// 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;
}
// (protected) copy this to r
BigInteger.prototype.copyTo = function (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
BigInteger.prototype.fromInt = function (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;
};
// (protected) set from string and radix
BigInteger.prototype.fromString = function (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
BigInteger.prototype.clamp = function () {
var c = this.s & this.DM;
while (this.t > 0 && this[this.t - 1] == c) --this.t;
};
// (protected) r = this << n*DB
BigInteger.prototype.dlShiftTo = function (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
BigInteger.prototype.drShiftTo = function (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
BigInteger.prototype.lShiftTo = function (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
BigInteger.prototype.rShiftTo = function (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
BigInteger.prototype.subTo = function (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.
BigInteger.prototype.multiplyTo = function (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)
BigInteger.prototype.squareTo = function (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.
BigInteger.prototype.divRemTo = function (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);
};
// (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.
BigInteger.prototype.invDigit = function () {
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;
};
// (protected) true iff this is even
BigInteger.prototype.isEven = function () { 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)
BigInteger.prototype.exp = function (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) return string representation in given radix
BigInteger.prototype.toString = function (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
BigInteger.prototype.negate = function () { var r = nbi(); BigInteger.ZERO.subTo(this, r); return r; };
// (public) |this|
BigInteger.prototype.abs = function () { return (this.s < 0) ? this.negate() : this; };
// (public) return + if this > a, - if this < a, 0 if equal
BigInteger.prototype.compareTo = function (a) {
var r = this.s - a.s;
if (r != 0) return r;
var i = this.t;
r = i - a.t;
if (r != 0) return (this.s < 0) ? -r : r;
while (--i >= 0) if ((r = this[i] - a[i]) != 0) return r;
return 0;
}
// (public) return the number of bits in "this"
BigInteger.prototype.bitLength = function () {
if (this.t <= 0) return 0;
return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM));
};
// (public) this mod a
BigInteger.prototype.mod = function (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;
}
// (public) this^e % m, 0 <= e < 2^32
BigInteger.prototype.modPowInt = function (e, m) {
var z;
if (e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
return this.exp(e, z);
};
// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);
// Copyright (c) 2005-2009 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Extended JavaScript BN functions, required for RSA private ops.
// Version 1.1: new BigInteger("0", 10) returns "proper" zero
// Version 1.2: square() API, isProbablePrime fix
// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
if (x == 0) return -1;
var r = 0;
if ((x & 0xffff) == 0) { x >>= 16; r += 16; }
if ((x & 0xff) == 0) { x >>= 8; r += 8; }
if ((x & 0xf) == 0) { x >>= 4; r += 4; }
if ((x & 3) == 0) { x >>= 2; r += 2; }
if ((x & 1) == 0) ++r;
return r;
}
// return number of 1 bits in x
function cbit(x) {
var r = 0;
while (x != 0) { x &= x - 1; ++r; }
return r;
}
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, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997];
var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];
// (protected) return x s.t. r^x < DV
BigInteger.prototype.chunkSize = function (r) { return Math.floor(Math.LN2 * this.DB / Math.log(r)); };
// (protected) convert to radix string
BigInteger.prototype.toRadix = function (b) {
if (b == null) b = 10;
if (this.signum() == 0 || b < 2 || b > 36) return "0";
var cs = this.chunkSize(b);
var a = Math.pow(b, cs);
var d = nbv(a), y = nbi(), z = nbi(), r = "";
this.divRemTo(d, y, z);
while (y.signum() > 0) {
r = (a + z.intValue()).toString(b).substr(1) + r;
y.divRemTo(d, y, z);
}
return z.intValue().toString(b) + r;
};
// (protected) convert from radix string
BigInteger.prototype.fromRadix = function (s, b) {
this.fromInt(0);
if (b == null) b = 10;
var cs = this.chunkSize(b);
var d = Math.pow(b, cs), mi = false, j = 0, w = 0;
for (var i = 0; i < s.length; ++i) {
var x = intAt(s, i);
if (x < 0) {
if (s.charAt(i) == "-" && this.signum() == 0) mi = true;
continue;
}
w = b * w + x;
if (++j >= cs) {
this.dMultiply(d);
this.dAddOffset(w, 0);
j = 0;
w = 0;
}
}
if (j > 0) {
this.dMultiply(Math.pow(b, j));
this.dAddOffset(w, 0);
}
if (mi) BigInteger.ZERO.subTo(this, this);
};
// (protected) alternate constructor
BigInteger.prototype.fromNumber = function (a, b, c) {
if ("number" == typeof b) {
// new BigInteger(int,int,RNG)
if (a < 2) this.fromInt(1);
else {
this.fromNumber(a, c);
if (!this.testBit(a - 1)) // force MSB set
this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this);
if (this.isEven()) this.dAddOffset(1, 0); // force odd
while (!this.isProbablePrime(b)) {
this.dAddOffset(2, 0);
if (this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a - 1), this);
}
}
}
else {
// new BigInteger(int,RNG)
var x = new Array(), t = a & 7;
x.length = (a >> 3) + 1;
b.nextBytes(x);
if (t > 0) x[0] &= ((1 << t) - 1); else x[0] = 0;
this.fromString(x, 256);
}
};
// (protected) r = this op a (bitwise)
BigInteger.prototype.bitwiseTo = function (a, op, r) {
var i, f, m = Math.min(a.t, this.t);
for (i = 0; i < m; ++i) r[i] = op(this[i], a[i]);
if (a.t < this.t) {
f = a.s & this.DM;
for (i = m; i < this.t; ++i) r[i] = op(this[i], f);
r.t = this.t;
}
else {
f = this.s & this.DM;
for (i = m; i < a.t; ++i) r[i] = op(f, a[i]);
r.t = a.t;
}
r.s = op(this.s, a.s);
r.clamp();
};
// (protected) this op (1<