/**!!!
* Elliptic Curve and BigInteger implementation
* 
* Copyright for each portion of code are included in their respective portions.
* Compiled and Put together by LOTW (^_^)
*/

(function () {
	// Copyright (c) 2005  Tom Wu
	// All Rights Reserved.
	// See "LICENSE" for details.

	// 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;
	}
	var inBrowser = typeof navigator !== 'undefined';
	if (inBrowser && j_lm && navigator.appName == 'Microsoft Internet Explorer') {
		BigInteger.prototype.am = am2;
		dbits = 30;
	} else if (inBrowser && 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 + this.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) {
		// Auto-detect string notations
		if (!b && s.length >= 2 && s[0] === '0') {
			var isDetected = true;
			switch (s[1]) {
				case 'x': // Hexadecimal notation
					b = 16;
					break;
				case 'b': // Binary notation
					b = 2;
					break;
				case 'o': // Octal notation
					b = 8;
					break;
				default:
					isDetected = false;
			}

			// Remove the notation string if any has been detected
			if (isDetected) {
				s = s.substr(2);
			}
		}

		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 this.s < 0 ? -r : 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);
	BigInteger.valueOf = nbv;

	// 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

	// (public)
	function bnClone() {
		var r = nbi();
		this.copyTo(r);
		return r;
	}

	// (public) return value as integer
	function bnIntValue() {
		if (this.s < 0) {
			if (this.t == 1) return this[0] - this.DV;
			else if (this.t == 0) return -1;
		} else if (this.t == 1) return this[0];
		else if (this.t == 0) return 0;
		// assumes 16 < DB < 32
		return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0];
	}

	// (public) return value as byte
	function bnByteValue() {
		return this.t == 0 ? this.s : (this[0] << 24) >> 24;
	}

	// (public) return value as short (assumes DB>=16)
	function bnShortValue() {
		return this.t == 0 ? this.s : (this[0] << 16) >> 16;
	}

	// (protected) return x s.t. r^x < DV
	function bnpChunkSize(r) {
		return Math.floor((Math.LN2 * this.DB) / Math.log(r));
	}

	// (public) 0 if this == 0, 1 if this > 0
	function bnSigNum() {
		if (this.s < 0) return -1;
		else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
		else return 1;
	}

	// (protected) convert to radix string
	function bnpToRadix(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
	function bnpFromRadix(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
	function bnpFromNumber(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);
		}
	}

	// (public) convert to bigendian byte array
	function bnToByteArray() {
		var i = this.t,
			r = new Array();
		r[0] = this.s;
		var p = this.DB - ((i * this.DB) % 8),
			d,
			k = 0;
		if (i-- > 0) {
			if (p < this.DB && (d = this[i] >> p) != (this.s & this.DM) >> p)
				r[k++] = d | (this.s << (this.DB - p));
			while (i >= 0) {
				if (p < 8) {
					d = (this[i] & ((1 << p) - 1)) << (8 - p);
					d |= this[--i] >> (p += this.DB - 8);
				} else {
					d = (this[i] >> (p -= 8)) & 0xff;
					if (p <= 0) {
						p += this.DB;
						--i;
					}
				}
				if ((d & 0x80) != 0) d |= -256;
				if (k == 0 && (this.s & 0x80) != (d & 0x80)) ++k;
				if (k > 0 || d != this.s) r[k++] = d;
			}
		}
		return r;
	}

	function bnEquals(a) {
		return this.compareTo(a) == 0;
	}
	function bnMin(a) {
		return this.compareTo(a) < 0 ? this : a;
	}
	function bnMax(a) {
		return this.compareTo(a) > 0 ? this : a;
	}

	// (protected) r = this op a (bitwise)
	function bnpBitwiseTo(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();
	}

	// (public) this & a
	function op_and(x, y) {
		return x & y;
	}
	function bnAnd(a) {
		var r = nbi();
		this.bitwiseTo(a, op_and, r);
		return r;
	}

	// (public) this | a
	function op_or(x, y) {
		return x | y;
	}
	function bnOr(a) {
		var r = nbi();
		this.bitwiseTo(a, op_or, r);
		return r;
	}

	// (public) this ^ a
	function op_xor(x, y) {
		return x ^ y;
	}
	function bnXor(a) {
		var r = nbi();
		this.bitwiseTo(a, op_xor, r);
		return r;
	}

	// (public) this & ~a
	function op_andnot(x, y) {
		return x & ~y;
	}
	function bnAndNot(a) {
		var r = nbi();
		this.bitwiseTo(a, op_andnot, r);
		return r;
	}

	// (public) ~this
	function bnNot() {
		var r = nbi();
		for (var i = 0; i < this.t; ++i) r[i] = this.DM & ~this[i];
		r.t = this.t;
		r.s = ~this.s;
		return r;
	}

	// (public) this << n
	function bnShiftLeft(n) {
		var r = nbi();
		if (n < 0) this.rShiftTo(-n, r);
		else this.lShiftTo(n, r);
		return r;
	}

	// (public) this >> n
	function bnShiftRight(n) {
		var r = nbi();
		if (n < 0) this.lShiftTo(-n, r);
		else this.rShiftTo(n, r);
		return r;
	}

	// 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;
	}

	// (public) returns index of lowest 1-bit (or -1 if none)
	function bnGetLowestSetBit() {
		for (var i = 0; i < this.t; ++i)
			if (this[i] != 0) return i * this.DB + lbit(this[i]);
		if (this.s < 0) return this.t * this.DB;
		return -1;
	}

	// return number of 1 bits in x
	function cbit(x) {
		var r = 0;
		while (x != 0) {
			x &= x - 1;
			++r;
		}
		return r;
	}

	// (public) return number of set bits
	function bnBitCount() {
		var r = 0,
			x = this.s & this.DM;
		for (var i = 0; i < this.t; ++i) r += cbit(this[i] ^ x);
		return r;
	}

	// (public) true iff nth bit is set
	function bnTestBit(n) {
		var j = Math.floor(n / this.DB);
		if (j >= this.t) return this.s != 0;
		return (this[j] & (1 << n % this.DB)) != 0;
	}

	// (protected) this op (1<<n)
	function bnpChangeBit(n, op) {
		var r = BigInteger.ONE.shiftLeft(n);
		this.bitwiseTo(r, op, r);
		return r;
	}

	// (public) this | (1<<n)
	function bnSetBit(n) {
		return this.changeBit(n, op_or);
	}

	// (public) this & ~(1<<n)
	function bnClearBit(n) {
		return this.changeBit(n, op_andnot);
	}

	// (public) this ^ (1<<n)
	function bnFlipBit(n) {
		return this.changeBit(n, op_xor);
	}

	// (protected) r = this + a
	function bnpAddTo(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 > 0) r[i++] = c;
		else if (c < -1) r[i++] = this.DV + c;
		r.t = i;
		r.clamp();
	}

	// (public) this + a
	function bnAdd(a) {
		var r = nbi();
		this.addTo(a, r);
		return r;
	}

	// (public) this - a
	function bnSubtract(a) {
		var r = nbi();
		this.subTo(a, r);
		return r;
	}

	// (public) this * a
	function bnMultiply(a) {
		var r = nbi();
		this.multiplyTo(a, r);
		return r;
	}

	// (public) this^2
	function bnSquare() {
		var r = nbi();
		this.squareTo(r);
		return r;
	}

	// (public) this / a
	function bnDivide(a) {
		var r = nbi();
		this.divRemTo(a, r, null);
		return r;
	}

	// (public) this % a
	function bnRemainder(a) {
		var r = nbi();
		this.divRemTo(a, null, r);
		return r;
	}

	// (public) [this/a,this%a]
	function bnDivideAndRemainder(a) {
		var q = nbi(),
			r = nbi();
		this.divRemTo(a, q, r);
		return new Array(q, r);
	}

	// (protected) this *= n, this >= 0, 1 < n < DV
	function bnpDMultiply(n) {
		this[this.t] = this.am(0, n - 1, this, 0, 0, this.t);
		++this.t;
		this.clamp();
	}

	// (protected) this += n << w words, this >= 0
	function bnpDAddOffset(n, w) {
		if (n == 0) return;
		while (this.t <= w) this[this.t++] = 0;
		this[w] += n;
		while (this[w] >= this.DV) {
			this[w] -= this.DV;
			if (++w >= this.t) this[this.t++] = 0;
			++this[w];
		}
	}

	// A "null" reducer
	function NullExp() { }
	function nNop(x) {
		return x;
	}
	function nMulTo(x, y, r) {
		x.multiplyTo(y, r);
	}
	function nSqrTo(x, r) {
		x.squareTo(r);
	}

	NullExp.prototype.convert = nNop;
	NullExp.prototype.revert = nNop;
	NullExp.prototype.mulTo = nMulTo;
	NullExp.prototype.sqrTo = nSqrTo;

	// (public) this^e
	function bnPow(e) {
		return this.exp(e, new NullExp());
	}

	// (protected) r = lower n words of "this * a", a.t <= n
	// "this" should be the larger one if appropriate.
	function bnpMultiplyLowerTo(a, n, r) {
		var i = Math.min(this.t + a.t, n);
		r.s = 0; // assumes a,this >= 0
		r.t = i;
		while (i > 0) r[--i] = 0;
		var j;
		for (j = r.t - this.t; i < j; ++i)
			r[i + this.t] = this.am(0, a[i], r, i, 0, this.t);
		for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a[i], r, i, 0, n - i);
		r.clamp();
	}

	// (protected) r = "this * a" without lower n words, n > 0
	// "this" should be the larger one if appropriate.
	function bnpMultiplyUpperTo(a, n, r) {
		--n;
		var i = (r.t = this.t + a.t - n);
		r.s = 0; // assumes a,this >= 0
		while (--i >= 0) r[i] = 0;
		for (i = Math.max(n - this.t, 0); i < a.t; ++i)
			r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n);
		r.clamp();
		r.drShiftTo(1, r);
	}

	// Barrett modular reduction
	function Barrett(m) {
		// setup Barrett
		this.r2 = nbi();
		this.q3 = nbi();
		BigInteger.ONE.dlShiftTo(2 * m.t, this.r2);
		this.mu = this.r2.divide(m);
		this.m = m;
	}

	function barrettConvert(x) {
		if (x.s < 0 || x.t > 2 * this.m.t) return x.mod(this.m);
		else if (x.compareTo(this.m) < 0) return x;
		else {
			var r = nbi();
			x.copyTo(r);
			this.reduce(r);
			return r;
		}
	}

	function barrettRevert(x) {
		return x;
	}

	// x = x mod m (HAC 14.42)
	function barrettReduce(x) {
		x.drShiftTo(this.m.t - 1, this.r2);
		if (x.t > this.m.t + 1) {
			x.t = this.m.t + 1;
			x.clamp();
		}
		this.mu.multiplyUpperTo(this.r2, this.m.t + 1, this.q3);
		this.m.multiplyLowerTo(this.q3, this.m.t + 1, this.r2);
		while (x.compareTo(this.r2) < 0) x.dAddOffset(1, this.m.t + 1);
		x.subTo(this.r2, x);
		while (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
	}

	// r = x^2 mod m; x != r
	function barrettSqrTo(x, r) {
		x.squareTo(r);
		this.reduce(r);
	}

	// r = x*y mod m; x,y != r
	function barrettMulTo(x, y, r) {
		x.multiplyTo(y, r);
		this.reduce(r);
	}

	Barrett.prototype.convert = barrettConvert;
	Barrett.prototype.revert = barrettRevert;
	Barrett.prototype.reduce = barrettReduce;
	Barrett.prototype.mulTo = barrettMulTo;
	Barrett.prototype.sqrTo = barrettSqrTo;

	// (public) this^e % m (HAC 14.85)
	function bnModPow(e, m) {
		var i = e.bitLength(),
			k,
			r = nbv(1),
			z;
		if (i <= 0) return r;
		else if (i < 18) k = 1;
		else if (i < 48) k = 3;
		else if (i < 144) k = 4;
		else if (i < 768) k = 5;
		else k = 6;
		if (i < 8) z = new Classic(m);
		else if (m.isEven()) z = new Barrett(m);
		else z = new Montgomery(m);

		// precomputation
		var g = new Array(),
			n = 3,
			k1 = k - 1,
			km = (1 << k) - 1;
		g[1] = z.convert(this);
		if (k > 1) {
			var g2 = nbi();
			z.sqrTo(g[1], g2);
			while (n <= km) {
				g[n] = nbi();
				z.mulTo(g2, g[n - 2], g[n]);
				n += 2;
			}
		}

		var j = e.t - 1,
			w,
			is1 = true,
			r2 = nbi(),
			t;
		i = nbits(e[j]) - 1;
		while (j >= 0) {
			if (i >= k1) w = (e[j] >> (i - k1)) & km;
			else {
				w = (e[j] & ((1 << (i + 1)) - 1)) << (k1 - i);
				if (j > 0) w |= e[j - 1] >> (this.DB + i - k1);
			}

			n = k;
			while ((w & 1) == 0) {
				w >>= 1;
				--n;
			}
			if ((i -= n) < 0) {
				i += this.DB;
				--j;
			}
			if (is1) {
				// ret == 1, don't bother squaring or multiplying it
				g[w].copyTo(r);
				is1 = false;
			} else {
				while (n > 1) {
					z.sqrTo(r, r2);
					z.sqrTo(r2, r);
					n -= 2;
				}
				if (n > 0) z.sqrTo(r, r2);
				else {
					t = r;
					r = r2;
					r2 = t;
				}
				z.mulTo(r2, g[w], r);
			}

			while (j >= 0 && (e[j] & (1 << i)) == 0) {
				z.sqrTo(r, r2);
				t = r;
				r = r2;
				r2 = t;
				if (--i < 0) {
					i = this.DB - 1;
					--j;
				}
			}
		}
		return z.revert(r);
	}

	// (public) gcd(this,a) (HAC 14.54)
	function bnGCD(a) {
		var x = this.s < 0 ? this.negate() : this.clone();
		var y = a.s < 0 ? a.negate() : a.clone();
		if (x.compareTo(y) < 0) {
			var t = x;
			x = y;
			y = t;
		}
		var i = x.getLowestSetBit(),
			g = y.getLowestSetBit();
		if (g < 0) return x;
		if (i < g) g = i;
		if (g > 0) {
			x.rShiftTo(g, x);
			y.rShiftTo(g, y);
		}
		while (x.signum() > 0) {
			if ((i = x.getLowestSetBit()) > 0) x.rShiftTo(i, x);
			if ((i = y.getLowestSetBit()) > 0) y.rShiftTo(i, y);
			if (x.compareTo(y) >= 0) {
				x.subTo(y, x);
				x.rShiftTo(1, x);
			} else {
				y.subTo(x, y);
				y.rShiftTo(1, y);
			}
		}
		if (g > 0) y.lShiftTo(g, y);
		return y;
	}

	// (protected) this % n, n < 2^26
	function bnpModInt(n) {
		if (n <= 0) return 0;
		var d = this.DV % n,
			r = this.s < 0 ? n - 1 : 0;
		if (this.t > 0)
			if (d == 0) r = this[0] % n;
			else for (var i = this.t - 1; i >= 0; --i) r = (d * r + this[i]) % n;
		return r;
	}

	// (public) 1/this % m (HAC 14.61)
	function bnModInverse(m) {
		var ac = m.isEven();
		if ((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
		var u = m.clone(),
			v = this.clone();
		var a = nbv(1),
			b = nbv(0),
			c = nbv(0),
			d = nbv(1);
		while (u.signum() != 0) {
			while (u.isEven()) {
				u.rShiftTo(1, u);
				if (ac) {
					if (!a.isEven() || !b.isEven()) {
						a.addTo(this, a);
						b.subTo(m, b);
					}
					a.rShiftTo(1, a);
				} else if (!b.isEven()) b.subTo(m, b);
				b.rShiftTo(1, b);
			}
			while (v.isEven()) {
				v.rShiftTo(1, v);
				if (ac) {
					if (!c.isEven() || !d.isEven()) {
						c.addTo(this, c);
						d.subTo(m, d);
					}
					c.rShiftTo(1, c);
				} else if (!d.isEven()) d.subTo(m, d);
				d.rShiftTo(1, d);
			}
			if (u.compareTo(v) >= 0) {
				u.subTo(v, u);
				if (ac) a.subTo(c, a);
				b.subTo(d, b);
			} else {
				v.subTo(u, v);
				if (ac) c.subTo(a, c);
				d.subTo(b, d);
			}
		}
		if (v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
		if (d.compareTo(m) >= 0) return d.subtract(m);
		if (d.signum() < 0) d.addTo(m, d);
		else return d;
		if (d.signum() < 0) return d.add(m);
		else return d;
	}

	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];

	// (public) test primality with certainty >= 1-.5^t
	function bnIsProbablePrime(t) {
		var i,
			x = this.abs();
		if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) {
			for (i = 0; i < lowprimes.length; ++i)
				if (x[0] == lowprimes[i]) return true;
			return false;
		}
		if (x.isEven()) return false;
		i = 1;
		while (i < lowprimes.length) {
			var m = lowprimes[i],
				j = i + 1;
			while (j < lowprimes.length && m < lplim) m *= lowprimes[j++];
			m = x.modInt(m);
			while (i < j) if (m % lowprimes[i++] == 0) return false;
		}
		return x.millerRabin(t);
	}

	// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
	function bnpMillerRabin(t) {
		var n1 = this.subtract(BigInteger.ONE);
		var k = n1.getLowestSetBit();
		if (k <= 0) return false;
		var r = n1.shiftRight(k);
		t = (t + 1) >> 1;
		if (t > lowprimes.length) t = lowprimes.length;
		var a = nbi();
		for (var i = 0; i < t; ++i) {
			//Pick bases at random, instead of starting at 2
			a.fromInt(lowprimes[Math.floor(Math.random() * lowprimes.length)]);
			var y = a.modPow(r, this);
			if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
				var j = 1;
				while (j++ < k && y.compareTo(n1) != 0) {
					y = y.modPowInt(2, this);
					if (y.compareTo(BigInteger.ONE) == 0) return false;
				}
				if (y.compareTo(n1) != 0) return false;
			}
		}
		return true;
	}

	// protected
	BigInteger.prototype.chunkSize = bnpChunkSize;
	BigInteger.prototype.toRadix = bnpToRadix;
	BigInteger.prototype.fromRadix = bnpFromRadix;
	BigInteger.prototype.fromNumber = bnpFromNumber;
	BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
	BigInteger.prototype.changeBit = bnpChangeBit;
	BigInteger.prototype.addTo = bnpAddTo;
	BigInteger.prototype.dMultiply = bnpDMultiply;
	BigInteger.prototype.dAddOffset = bnpDAddOffset;
	BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
	BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
	BigInteger.prototype.modInt = bnpModInt;
	BigInteger.prototype.millerRabin = bnpMillerRabin;

	// public
	BigInteger.prototype.clone = bnClone;
	BigInteger.prototype.intValue = bnIntValue;
	BigInteger.prototype.byteValue = bnByteValue;
	BigInteger.prototype.shortValue = bnShortValue;
	BigInteger.prototype.signum = bnSigNum;
	BigInteger.prototype.toByteArray = bnToByteArray;
	BigInteger.prototype.equals = bnEquals;
	BigInteger.prototype.min = bnMin;
	BigInteger.prototype.max = bnMax;
	BigInteger.prototype.and = bnAnd;
	BigInteger.prototype.or = bnOr;
	BigInteger.prototype.xor = bnXor;
	BigInteger.prototype.andNot = bnAndNot;
	BigInteger.prototype.not = bnNot;
	BigInteger.prototype.shiftLeft = bnShiftLeft;
	BigInteger.prototype.shiftRight = bnShiftRight;
	BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
	BigInteger.prototype.bitCount = bnBitCount;
	BigInteger.prototype.testBit = bnTestBit;
	BigInteger.prototype.setBit = bnSetBit;
	BigInteger.prototype.clearBit = bnClearBit;
	BigInteger.prototype.flipBit = bnFlipBit;
	BigInteger.prototype.add = bnAdd;
	BigInteger.prototype.subtract = bnSubtract;
	BigInteger.prototype.multiply = bnMultiply;
	BigInteger.prototype.divide = bnDivide;
	BigInteger.prototype.remainder = bnRemainder;
	BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
	BigInteger.prototype.modPow = bnModPow;
	BigInteger.prototype.modInverse = bnModInverse;
	BigInteger.prototype.pow = bnPow;
	BigInteger.prototype.gcd = bnGCD;
	BigInteger.prototype.isProbablePrime = bnIsProbablePrime;

	// JSBN-specific extension
	BigInteger.prototype.square = bnSquare;

	// Expose the Barrett function
	BigInteger.prototype.Barrett = Barrett;

	// BigInteger interfaces not implemented in jsbn:

	// BigInteger(int signum, byte[] magnitude)
	// double doubleValue()
	// float floatValue()
	// int hashCode()
	// long longValue()
	// static BigInteger valueOf(long val)

	// Imported from bitcoinjs-lib

	/**
	 * Turns a byte array into a big integer.
	 *
	 * This function will interpret a byte array as a big integer in big
	 * endian notation and ignore leading zeros.
	 */

	BigInteger.fromByteArrayUnsigned = function (ba) {

		if (!ba.length) {
			return new BigInteger.valueOf(0);
		} else if (ba[0] & 0x80) {
			// Prepend a zero so the BigInteger class doesn't mistake this
			// for a negative integer.
			return new BigInteger([0].concat(ba));
		} else {
			return new BigInteger(ba);
		}
	};

	/**
	 * Parse a signed big integer byte representation.
	 *
	 * For details on the format please see BigInteger.toByteArraySigned.
	 */

	BigInteger.fromByteArraySigned = function (ba) {
		// Check for negative value
		if (ba[0] & 0x80) {
			// Remove sign bit
			ba[0] &= 0x7f;

			return BigInteger.fromByteArrayUnsigned(ba).negate();
		} else {
			return BigInteger.fromByteArrayUnsigned(ba);
		}
	};

	/**
	 * Returns a byte array representation of the big integer.
	 *
	 * This returns the absolute of the contained value in big endian
	 * form. A value of zero results in an empty array.
	 */

	BigInteger.prototype.toByteArrayUnsigned = function () {
		var ba = this.abs().toByteArray();

		// Empty array, nothing to do
		if (!ba.length) {
			return ba;
		}

		// remove leading 0
		if (ba[0] === 0) {
			ba = ba.slice(1);
		}

		// all values must be positive
		for (var i = 0; i < ba.length; ++i) {
			ba[i] = (ba[i] < 0) ? ba[i] + 256 : ba[i];
		}

		return ba;
	};

	/*
	 * Converts big integer to signed byte representation.
	 *
	 * The format for this value uses the most significant bit as a sign
	 * bit. If the most significant bit is already occupied by the
	 * absolute value, an extra byte is prepended and the sign bit is set
	 * there.
	 *
	 * Examples:
	 *
	 *      0 =>     0x00
	 *      1 =>     0x01
	 *     -1 =>     0x81
	 *    127 =>     0x7f
	 *   -127 =>     0xff
	 *    128 =>   0x0080
	 *   -128 =>   0x8080
	 *    255 =>   0x00ff
	 *   -255 =>   0x80ff
	 *  16300 =>   0x3fac
	 * -16300 =>   0xbfac
	 *  62300 => 0x00f35c
	 * -62300 => 0x80f35c
	*/

	BigInteger.prototype.toByteArraySigned = function () {
		var val = this.toByteArrayUnsigned();
		var neg = this.s < 0;

		// if the first bit is set, we always unshift
		// either unshift 0x80 or 0x00
		if (val[0] & 0x80) {
			val.unshift((neg) ? 0x80 : 0x00);
		}
		// if the first bit isn't set, set it if negative
		else if (neg) {
			val[0] |= 0x80;
		}

		return val;
	};

	// Random number generator - requires a PRNG backend, e.g. prng4.js

	// For best results, put code like
	// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
	// in your main HTML document.

	var rng_state;
	var rng_pool;
	var rng_pptr;

	// Mix in a 32-bit integer into the pool
	function rng_seed_int(x) {
		rng_pool[rng_pptr++] ^= x & 255;
		rng_pool[rng_pptr++] ^= (x >> 8) & 255;
		rng_pool[rng_pptr++] ^= (x >> 16) & 255;
		rng_pool[rng_pptr++] ^= (x >> 24) & 255;
		if (rng_pptr >= rng_psize) rng_pptr -= rng_psize;
	}

	// Mix in the current time (w/milliseconds) into the pool
	function rng_seed_time() {
		rng_seed_int(new Date().getTime());
	}

	// Initialize the pool with junk if needed.
	if (rng_pool == null) {
		rng_pool = new Array();
		rng_pptr = 0;
		var t;
		if (typeof window !== 'undefined' && window.crypto) {
			if (window.crypto.getRandomValues) {
				// Use webcrypto if available
				var ua = new Uint8Array(32);
				window.crypto.getRandomValues(ua);
				for (t = 0; t < 32; ++t) rng_pool[rng_pptr++] = ua[t];
			} else if (
				navigator.appName == 'Netscape' &&
				navigator.appVersion < '5'
			) {
				// Extract entropy (256 bits) from NS4 RNG if available
				var z = window.crypto.random(32);
				for (t = 0; t < z.length; ++t)
					rng_pool[rng_pptr++] = z.charCodeAt(t) & 255;
			}
		}
		while (rng_pptr < rng_psize) {
			// extract some randomness from Math.random()
			t = Math.floor(65536 * Math.random());
			rng_pool[rng_pptr++] = t >>> 8;
			rng_pool[rng_pptr++] = t & 255;
		}
		rng_pptr = 0;
		rng_seed_time();
	}

	function rng_get_byte() {
		if (rng_state == null) {
			rng_seed_time();
			rng_state = prng_newstate();
			rng_state.init(rng_pool);
			for (rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
				rng_pool[rng_pptr] = 0;
			rng_pptr = 0;
		}
		// TODO: allow reseeding after first request
		return rng_state.next();
	}

	function rng_get_bytes(ba) {
		var i;
		for (i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
	}

	function SecureRandom() { }

	SecureRandom.prototype.nextBytes = rng_get_bytes;

	// prng4.js - uses Arcfour as a PRNG
	function Arcfour() {
		this.i = 0;
		this.j = 0;
		this.S = new Array();
	}

	// Initialize arcfour context from key, an array of ints, each from [0..255]
	function ARC4init(key) {
		var i, j, t;
		for (i = 0; i < 256; ++i) this.S[i] = i;
		j = 0;
		for (i = 0; i < 256; ++i) {
			j = (j + this.S[i] + key[i % key.length]) & 255;
			t = this.S[i];
			this.S[i] = this.S[j];
			this.S[j] = t;
		}
		this.i = 0;
		this.j = 0;
	}

	function ARC4next() {
		var t;
		this.i = (this.i + 1) & 255;
		this.j = (this.j + this.S[this.i]) & 255;
		t = this.S[this.i];
		this.S[this.i] = this.S[this.j];
		this.S[this.j] = t;
		return this.S[(t + this.S[this.i]) & 255];
	}

	Arcfour.prototype.init = ARC4init;
	Arcfour.prototype.next = ARC4next;

	// Plug in your RNG constructor here
	function prng_newstate() {
		return new Arcfour();
	}

	// Pool size must be a multiple of 4 and greater than 32.
	// An array of bytes the size of the pool will be passed to init()
	var rng_psize = 256;

	/*!
	* Basic Javascript Elliptic Curve implementation
	* Ported loosely from BouncyCastle's Java EC code
	* Only Fp curves implemented for now
	*
	* Copyright Tom Wu, bitaddress.org  BSD License.
	* http://www-cs-students.stanford.edu/~tjw/jsbn/LICENSE
	*/

	// Constructor function of Global EllipticCurve object
	var ec = function () { };

	// ----------------
	// ECFieldElementFp constructor
	// q instanceof BigInteger
	// x instanceof BigInteger
	ec.FieldElementFp = function (q, x) {
		this.x = x;
		// TODO if(x.compareTo(q) >= 0) error
		this.q = q;
	};

	ec.FieldElementFp.prototype.equals = function (other) {
		if (other == this) return true;
		return (this.q.equals(other.q) && this.x.equals(other.x));
	};

	ec.FieldElementFp.prototype.toBigInteger = function () {
		return this.x;
	};

	ec.FieldElementFp.prototype.negate = function () {
		return new ec.FieldElementFp(this.q, this.x.negate().mod(this.q));
	};

	ec.FieldElementFp.prototype.add = function (b) {
		return new ec.FieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q));
	};

	ec.FieldElementFp.prototype.subtract = function (b) {
		return new ec.FieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));
	};

	ec.FieldElementFp.prototype.multiply = function (b) {
		return new ec.FieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));
	};

	ec.FieldElementFp.prototype.square = function () {
		return new ec.FieldElementFp(this.q, this.x.square().mod(this.q));
	};

	ec.FieldElementFp.prototype.divide = function (b) {
		return new ec.FieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));
	};

	ec.FieldElementFp.prototype.getByteLength = function () {
		return Math.floor((this.toBigInteger().bitLength() + 7) / 8);
	};

	// D.1.4 91
	/**
	* return a sqrt root - the routine verifies that the calculation
	* returns the right value - if none exists it returns null.
	* 
	* Copyright (c) 2000 - 2011 The Legion Of The Bouncy Castle (http://www.bouncycastle.org)
	* Ported to JavaScript by bitaddress.org
	*/
	ec.FieldElementFp.prototype.sqrt = function () {
		if (!this.q.testBit(0)) throw new Error("even value of q");

		// p mod 4 == 3
		if (this.q.testBit(1)) {
			// z = g^(u+1) + p, p = 4u + 3
			var z = new ec.FieldElementFp(this.q, this.x.modPow(this.q.shiftRight(2).add(BigInteger.ONE), this.q));
			return z.square().equals(this) ? z : null;
		}

		// p mod 4 == 1
		var qMinusOne = this.q.subtract(BigInteger.ONE);
		var legendreExponent = qMinusOne.shiftRight(1);
		if (!(this.x.modPow(legendreExponent, this.q).equals(BigInteger.ONE))) return null;
		var u = qMinusOne.shiftRight(2);
		var k = u.shiftLeft(1).add(BigInteger.ONE);
		var Q = this.x;
		var fourQ = Q.shiftLeft(2).mod(this.q);
		var U, V;

		do {
			var rand = new SecureRandom();
			var P;
			do {
				P = new BigInteger(this.q.bitLength(), rand);
			}
			while (P.compareTo(this.q) >= 0 || !(P.multiply(P).subtract(fourQ).modPow(legendreExponent, this.q).equals(qMinusOne)));

			var result = ec.FieldElementFp.fastLucasSequence(this.q, P, Q, k);

			U = result[0];
			V = result[1];
			if (V.multiply(V).mod(this.q).equals(fourQ)) {
				// Integer division by 2, mod q
				if (V.testBit(0)) {
					V = V.add(this.q);
				}
				V = V.shiftRight(1);
				return new ec.FieldElementFp(this.q, V);
			}
		}
		while (U.equals(BigInteger.ONE) || U.equals(qMinusOne));

		return null;
	};

	/*
	* Copyright (c) 2000 - 2011 The Legion Of The Bouncy Castle (http://www.bouncycastle.org)
	* Ported to JavaScript by bitaddress.org
	*/
	ec.FieldElementFp.fastLucasSequence = function (p, P, Q, k) {
		// TODO Research and apply "common-multiplicand multiplication here"

		var n = k.bitLength();
		var s = k.getLowestSetBit();
		var Uh = BigInteger.ONE;
		var Vl = BigInteger.TWO;
		var Vh = P;
		var Ql = BigInteger.ONE;
		var Qh = BigInteger.ONE;

		for (var j = n - 1; j >= s + 1; --j) {
			Ql = Ql.multiply(Qh).mod(p);
			if (k.testBit(j)) {
				Qh = Ql.multiply(Q).mod(p);
				Uh = Uh.multiply(Vh).mod(p);
				Vl = Vh.multiply(Vl).subtract(P.multiply(Ql)).mod(p);
				Vh = Vh.multiply(Vh).subtract(Qh.shiftLeft(1)).mod(p);
			}
			else {
				Qh = Ql;
				Uh = Uh.multiply(Vl).subtract(Ql).mod(p);
				Vh = Vh.multiply(Vl).subtract(P.multiply(Ql)).mod(p);
				Vl = Vl.multiply(Vl).subtract(Ql.shiftLeft(1)).mod(p);
			}
		}

		Ql = Ql.multiply(Qh).mod(p);
		Qh = Ql.multiply(Q).mod(p);
		Uh = Uh.multiply(Vl).subtract(Ql).mod(p);
		Vl = Vh.multiply(Vl).subtract(P.multiply(Ql)).mod(p);
		Ql = Ql.multiply(Qh).mod(p);

		for (var j = 1; j <= s; ++j) {
			Uh = Uh.multiply(Vl).mod(p);
			Vl = Vl.multiply(Vl).subtract(Ql.shiftLeft(1)).mod(p);
			Ql = Ql.multiply(Ql).mod(p);
		}

		return [Uh, Vl];
	};

	// ----------------
	// ECPointFp constructor
	ec.PointFp = function (curve, x, y, z, compressed) {
		this.curve = curve;
		this.x = x;
		this.y = y;
		// Projective coordinates: either zinv == null or z * zinv == 1
		// z and zinv are just BigIntegers, not fieldElements
		if (z == null) {
			this.z = BigInteger.ONE;
		}
		else {
			this.z = z;
		}
		this.zinv = null;
		// compression flag
		this.compressed = !!compressed;
	};

	ec.PointFp.prototype.getX = function () {
		if (this.zinv == null) {
			this.zinv = this.z.modInverse(this.curve.q);
		}
		var r = this.x.toBigInteger().multiply(this.zinv);
		this.curve.reduce(r);
		return this.curve.fromBigInteger(r);
	};

	ec.PointFp.prototype.getY = function () {
		if (this.zinv == null) {
			this.zinv = this.z.modInverse(this.curve.q);
		}
		var r = this.y.toBigInteger().multiply(this.zinv);
		this.curve.reduce(r);
		return this.curve.fromBigInteger(r);
	};

	ec.PointFp.prototype.equals = function (other) {
		if (other == this) return true;
		if (this.isInfinity()) return other.isInfinity();
		if (other.isInfinity()) return this.isInfinity();
		var u, v;
		// u = Y2 * Z1 - Y1 * Z2
		u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);
		if (!u.equals(BigInteger.ZERO)) return false;
		// v = X2 * Z1 - X1 * Z2
		v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);
		return v.equals(BigInteger.ZERO);
	};

	ec.PointFp.prototype.isInfinity = function () {
		if ((this.x == null) && (this.y == null)) return true;
		return this.z.equals(BigInteger.ZERO) && !this.y.toBigInteger().equals(BigInteger.ZERO);
	};

	ec.PointFp.prototype.negate = function () {
		return new ec.PointFp(this.curve, this.x, this.y.negate(), this.z);
	};

	ec.PointFp.prototype.add = function (b) {
		if (this.isInfinity()) return b;
		if (b.isInfinity()) return this;

		// u = Y2 * Z1 - Y1 * Z2
		var u = b.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(b.z)).mod(this.curve.q);
		// v = X2 * Z1 - X1 * Z2
		var v = b.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(b.z)).mod(this.curve.q);


		if (BigInteger.ZERO.equals(v)) {
			if (BigInteger.ZERO.equals(u)) {
				return this.twice(); // this == b, so double
			}
			return this.curve.getInfinity(); // this = -b, so infinity
		}

		var THREE = new BigInteger("3");
		var x1 = this.x.toBigInteger();
		var y1 = this.y.toBigInteger();
		var x2 = b.x.toBigInteger();
		var y2 = b.y.toBigInteger();

		var v2 = v.square();
		var v3 = v2.multiply(v);
		var x1v2 = x1.multiply(v2);
		var zu2 = u.square().multiply(this.z);

		// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
		var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.q);
		// y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
		var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.q);
		// z3 = v^3 * z1 * z2
		var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q);

		return new ec.PointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
	};

	ec.PointFp.prototype.twice = function () {
		if (this.isInfinity()) return this;
		if (this.y.toBigInteger().signum() == 0) return this.curve.getInfinity();

		// TODO: optimized handling of constants
		var THREE = new BigInteger("3");
		var x1 = this.x.toBigInteger();
		var y1 = this.y.toBigInteger();

		var y1z1 = y1.multiply(this.z);
		var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q);
		var a = this.curve.a.toBigInteger();

		// w = 3 * x1^2 + a * z1^2
		var w = x1.square().multiply(THREE);
		if (!BigInteger.ZERO.equals(a)) {
			w = w.add(this.z.square().multiply(a));
		}
		w = w.mod(this.curve.q);
		//this.curve.reduce(w);
		// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
		var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q);
		// y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
		var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.square().multiply(w)).mod(this.curve.q);
		// z3 = 8 * (y1 * z1)^3
		var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q);

		return new ec.PointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
	};

	// Simple NAF (Non-Adjacent Form) multiplication algorithm
	// TODO: modularize the multiplication algorithm
	ec.PointFp.prototype.multiply = function (k) {
		if (this.isInfinity()) return this;
		if (k.signum() == 0) return this.curve.getInfinity();

		var e = k;
		var h = e.multiply(new BigInteger("3"));

		var neg = this.negate();
		var R = this;

		var i;
		for (i = h.bitLength() - 2; i > 0; --i) {
			R = R.twice();

			var hBit = h.testBit(i);
			var eBit = e.testBit(i);

			if (hBit != eBit) {
				R = R.add(hBit ? this : neg);
			}
		}

		return R;
	};

	// Compute this*j + x*k (simultaneous multiplication)
	ec.PointFp.prototype.multiplyTwo = function (j, x, k) {
		var i;
		if (j.bitLength() > k.bitLength())
			i = j.bitLength() - 1;
		else
			i = k.bitLength() - 1;

		var R = this.curve.getInfinity();
		var both = this.add(x);
		while (i >= 0) {
			R = R.twice();
			if (j.testBit(i)) {
				if (k.testBit(i)) {
					R = R.add(both);
				}
				else {
					R = R.add(this);
				}
			}
			else {
				if (k.testBit(i)) {
					R = R.add(x);
				}
			}
			--i;
		}

		return R;
	};

	// patched by bitaddress.org and Casascius for use with Bitcoin.ECKey
	// patched by coretechs to support compressed public keys
	ec.PointFp.prototype.getEncoded = function (compressed) {
		var x = this.getX().toBigInteger();
		var y = this.getY().toBigInteger();
		var len = 32; // integerToBytes will zero pad if integer is less than 32 bytes. 32 bytes length is required by the Bitcoin protocol.
		var enc = ec.integerToBytes(x, len);

		// when compressed prepend byte depending if y point is even or odd 
		if (compressed) {
			if (y.isEven()) {
				enc.unshift(0x02);
			}
			else {
				enc.unshift(0x03);
			}
		}
		else {
			enc.unshift(0x04);
			enc = enc.concat(ec.integerToBytes(y, len)); // uncompressed public key appends the bytes of the y point
		}
		return enc;
	};

	ec.PointFp.decodeFrom = function (curve, enc) {
		var type = enc[0];
		var dataLen = enc.length - 1;

		// Extract x and y as byte arrays
		var xBa = enc.slice(1, 1 + dataLen / 2);
		var yBa = enc.slice(1 + dataLen / 2, 1 + dataLen);

		// Prepend zero byte to prevent interpretation as negative integer
		xBa.unshift(0);
		yBa.unshift(0);

		// Convert to BigIntegers
		var x = new BigInteger(xBa);
		var y = new BigInteger(yBa);

		// Return point
		return new ec.PointFp(curve, curve.fromBigInteger(x), curve.fromBigInteger(y));
	};

	ec.PointFp.prototype.add2D = function (b) {
		if (this.isInfinity()) return b;
		if (b.isInfinity()) return this;

		if (this.x.equals(b.x)) {
			if (this.y.equals(b.y)) {
				// this = b, i.e. this must be doubled
				return this.twice();
			}
			// this = -b, i.e. the result is the point at infinity
			return this.curve.getInfinity();
		}

		var x_x = b.x.subtract(this.x);
		var y_y = b.y.subtract(this.y);
		var gamma = y_y.divide(x_x);

		var x3 = gamma.square().subtract(this.x).subtract(b.x);
		var y3 = gamma.multiply(this.x.subtract(x3)).subtract(this.y);

		return new ec.PointFp(this.curve, x3, y3);
	};

	ec.PointFp.prototype.twice2D = function () {
		if (this.isInfinity()) return this;
		if (this.y.toBigInteger().signum() == 0) {
			// if y1 == 0, then (x1, y1) == (x1, -y1)
			// and hence this = -this and thus 2(x1, y1) == infinity
			return this.curve.getInfinity();
		}

		var TWO = this.curve.fromBigInteger(BigInteger.valueOf(2));
		var THREE = this.curve.fromBigInteger(BigInteger.valueOf(3));
		var gamma = this.x.square().multiply(THREE).add(this.curve.a).divide(this.y.multiply(TWO));

		var x3 = gamma.square().subtract(this.x.multiply(TWO));
		var y3 = gamma.multiply(this.x.subtract(x3)).subtract(this.y);

		return new ec.PointFp(this.curve, x3, y3);
	};

	ec.PointFp.prototype.multiply2D = function (k) {
		if (this.isInfinity()) return this;
		if (k.signum() == 0) return this.curve.getInfinity();

		var e = k;
		var h = e.multiply(new BigInteger("3"));

		var neg = this.negate();
		var R = this;

		var i;
		for (i = h.bitLength() - 2; i > 0; --i) {
			R = R.twice();

			var hBit = h.testBit(i);
			var eBit = e.testBit(i);

			if (hBit != eBit) {
				R = R.add2D(hBit ? this : neg);
			}
		}

		return R;
	};
	ec.PointFp.prototype.isOnCurve = function () {
		var x = this.getX().toBigInteger();
		var y = this.getY().toBigInteger();
		var a = this.curve.getA().toBigInteger();
		var b = this.curve.getB().toBigInteger();
		var n = this.curve.getQ();
		var lhs = y.multiply(y).mod(n);
		var rhs = x.multiply(x).multiply(x).add(a.multiply(x)).add(b).mod(n);
		return lhs.equals(rhs);
	};

	ec.PointFp.prototype.toString = function () {
		return '(' + this.getX().toBigInteger().toString() + ',' + this.getY().toBigInteger().toString() + ')';
	};

	/**
	* Validate an elliptic curve point.
	*
	* See SEC 1, section 3.2.2.1: Elliptic Curve Public Key Validation Primitive
	*/
	ec.PointFp.prototype.validate = function () {
		var n = this.curve.getQ();

		// Check Q != O
		if (this.isInfinity()) {
			throw new Error("Point is at infinity.");
		}

		// Check coordinate bounds
		var x = this.getX().toBigInteger();
		var y = this.getY().toBigInteger();
		if (x.compareTo(BigInteger.ONE) < 0 || x.compareTo(n.subtract(BigInteger.ONE)) > 0) {
			throw new Error('x coordinate out of bounds');
		}
		if (y.compareTo(BigInteger.ONE) < 0 || y.compareTo(n.subtract(BigInteger.ONE)) > 0) {
			throw new Error('y coordinate out of bounds');
		}

		// Check y^2 = x^3 + ax + b (mod n)
		if (!this.isOnCurve()) {
			throw new Error("Point is not on the curve.");
		}

		// Check nQ = 0 (Q is a scalar multiple of G)
		if (this.multiply(n).isInfinity()) {
			// TODO: This check doesn't work - fix.
			throw new Error("Point is not a scalar multiple of G.");
		}

		return true;
	};

	// ----------------
	// ECCurveFp constructor
	ec.CurveFp = function (q, a, b) {
		this.q = q;
		this.a = this.fromBigInteger(a);
		this.b = this.fromBigInteger(b);
		this.infinity = new ec.PointFp(this, null, null);
		this.reducer = new Barrett(this.q);
	}

	ec.CurveFp.prototype.getQ = function () {
		return this.q;
	};

	ec.CurveFp.prototype.getA = function () {
		return this.a;
	};

	ec.CurveFp.prototype.getB = function () {
		return this.b;
	};

	ec.CurveFp.prototype.equals = function (other) {
		if (other == this) return true;
		return (this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));
	};

	ec.CurveFp.prototype.getInfinity = function () {
		return this.infinity;
	};

	ec.CurveFp.prototype.fromBigInteger = function (x) {
		return new ec.FieldElementFp(this.q, x);
	};

	ec.CurveFp.prototype.reduce = function (x) {
		this.reducer.reduce(x);
	};

	// for now, work with hex strings because they're easier in JS
	// compressed support added by bitaddress.org
	ec.CurveFp.prototype.decodePointHex = function (s) {
		var firstByte = parseInt(s.substr(0, 2), 16);
		switch (firstByte) { // first byte
			case 0:
				return this.infinity;
			case 2: // compressed
			case 3: // compressed
				var yTilde = firstByte & 1;
				var xHex = s.substr(2, s.length - 2);
				var X1 = new BigInteger(xHex, 16);
				return this.decompressPoint(yTilde, X1);
			case 4: // uncompressed
			case 6: // hybrid
			case 7: // hybrid
				var len = (s.length - 2) / 2;
				var xHex = s.substr(2, len);
				var yHex = s.substr(len + 2, len);

				return new ec.PointFp(this,
					this.fromBigInteger(new BigInteger(xHex, 16)),
					this.fromBigInteger(new BigInteger(yHex, 16)));

			default: // unsupported
				return null;
		}
	};

	ec.CurveFp.prototype.encodePointHex = function (p) {
		if (p.isInfinity()) return "00";
		var xHex = p.getX().toBigInteger().toString(16);
		var yHex = p.getY().toBigInteger().toString(16);
		var oLen = this.getQ().toString(16).length;
		if ((oLen % 2) != 0) oLen++;
		while (xHex.length < oLen) {
			xHex = "0" + xHex;
		}
		while (yHex.length < oLen) {
			yHex = "0" + yHex;
		}
		return "04" + xHex + yHex;
	};

	/*
	* Copyright (c) 2000 - 2011 The Legion Of The Bouncy Castle (http://www.bouncycastle.org)
	* Ported to JavaScript by bitaddress.org
	*
	* Number yTilde
	* BigInteger X1
	*/
	ec.CurveFp.prototype.decompressPoint = function (yTilde, X1) {
		var x = this.fromBigInteger(X1);
		var alpha = x.multiply(x.square().add(this.getA())).add(this.getB());
		var beta = alpha.sqrt();
		// if we can't find a sqrt we haven't got a point on the curve - run!
		if (beta == null) throw new Error("Invalid point compression");
		var betaValue = beta.toBigInteger();
		var bit0 = betaValue.testBit(0) ? 1 : 0;
		if (bit0 != yTilde) {
			// Use the other root
			beta = this.fromBigInteger(this.getQ().subtract(betaValue));
		}
		return new ec.PointFp(this, x, beta, null, true);
	};


	ec.fromHex = function (s) { return new BigInteger(s, 16); };

	ec.integerToBytes = function (i, len) {
		var bytes = i.toByteArrayUnsigned();
		if (len < bytes.length) {
			bytes = bytes.slice(bytes.length - len);
		} else while (len > bytes.length) {
			bytes.unshift(0);
		}
		return bytes;
	};


	// Named EC curves
	// ----------------
	// X9ECParameters constructor
	ec.X9Parameters = function (curve, g, n, h) {
		this.curve = curve;
		this.g = g;
		this.n = n;
		this.h = h;
	}
	ec.X9Parameters.prototype.getCurve = function () { return this.curve; };
	ec.X9Parameters.prototype.getG = function () { return this.g; };
	ec.X9Parameters.prototype.getN = function () { return this.n; };
	ec.X9Parameters.prototype.getH = function () { return this.h; };

	// secp256k1 is the Curve used by Bitcoin
	ec.secNamedCurves = {
		// used by Bitcoin
		"secp256k1": function () {
			// p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1
			var p = ec.fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F");
			var a = BigInteger.ZERO;
			var b = ec.fromHex("7");
			var n = ec.fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
			var h = BigInteger.ONE;
			var curve = new ec.CurveFp(p, a, b);
			var G = curve.decodePointHex("04"
				+ "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798"
				+ "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8");
			return new ec.X9Parameters(curve, G, n, h);
		}
	};

	// secp256k1 called by Bitcoin's ECKEY
	ec.getSECCurveByName = function (name) {
		if (ec.secNamedCurves[name] == undefined) return null;
		return ec.secNamedCurves[name]();
	}

	if (typeof exports !== 'undefined') {
		exports = module.exports = {
			default: ec,
			EllipticCurve: ec,
			BigInteger: BigInteger
		};
	} else {
		this.ecbn = {
			EllipticCurve: ec,
			BigInteger: BigInteger
		};
	}

}).call(this);
