Entropy can be supplied by user

1 files changed, 1929 insertions, 7 deletions

diff --git a/bip39-standalone.html b/bip39-standalone.html
index 5993b86..e3af3a6 100644
--- a/bip39-standalone.html
+++ b/bip39-standalone.html
@@ -69,12 +69,14 @@
                 <div class="col-md-12">
                     <h2>Mnemonic</h2>
                     <form class="form-horizontal" role="form">
-                        <div class="col-sm-2"></div>
-                        <div class="col-sm-10">
-                            <p>You can enter an existing BIP39 mnemonic, or generate a new random one. Typing your own twelve words will probably not work how you expect, since the words require a particular structure (the last word is a checksum)</p>
-                            <p>For more info see the <a href="https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki" target="_blank">BIP39 spec</a></p>
-                        </div>
                         <div class="form-group">
+                            <div class="col-sm-2"></div>
+                            <div class="col-sm-10">
+                                <p>You can enter an existing BIP39 mnemonic, or generate a new random one. Typing your own twelve words will probably not work how you expect, since the words require a particular structure (the last word is a checksum)</p>
+                                <p>For more info see the <a href="https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki" target="_blank">BIP39 spec</a></p>
+                            </div>
+                        </div>
+                        <div class="form-group generate-container">
                             <label class="col-sm-2 control-label"></label>
                             <div class="col-sm-10">
                                 <div class="form-inline">
@@ -96,7 +98,30 @@
                                 </div>
                             </div>
                         </div>
-                            <div class="form-group">
+                        <div class="entropy-container hidden">
+                            <label for="entropy" class="col-sm-2 control-label">Entropy</label>
+                            <div class="col-sm-10">
+                                <input id="entropy" class="entropy form-control" placeholder="Accepts binary, base 6, 6-sided dice, base 10, hexadecimal">
+                                <span class="help-block">
+                                    <div class="text-danger">
+                                    This is an advanced feature.
+                                    Your mnemonic may be insecure if this feature is used incorrectly.
+                                    <a href="#entropy-notes">Read more</a>
+                                    </div>
+                                    <div class="text-danger entropy-error"></div>
+                               </span>
+                            </div>
+                        </div>
+                        <div class="form-group">
+                            <div class="col-sm-2"></div>
+                            <div class="col-sm-10 checkbox">
+                                <label>
+                                    <input type="checkbox" class="use-entropy">
+                                    Supply my own source of entropy
+                                </label>
+                            </div>
+                        </div>
+                        <div class="form-group">
                             <label class="col-sm-2 control-label"></label>
                             <div class="col-sm-10 languages">
                                 <a href="#english">English</a>
@@ -357,6 +382,24 @@
                         but be careful - it can be easy to make mistakes if you
                         don't know what you're doing
                     </p>
+                    <h3 id="entropy-notes">Entropy</h3>
+                    <p>
+                    Entropy values must be sourced from a
+                    <a href="https://en.wikipedia.org/wiki/Random_number_generation" target="_blank">strong source of randomness</a>.
+                    This means flipping a fair coin, rolling a fair dice, noise measurements etc. Do <strong>NOT</strong> use
+                    phrases from books, lyrics from songs, your birthday or steet address, keyboard mashing, or anything you <i>think</i>
+                    is random, because chances are <em>overwhelming</em> that it isn't random enough for the needs of this tool.
+                    </p>
+                    <p>
+                    The random mnemonic generator on this page uses a
+                    <a href="https://developer.mozilla.org/en-US/docs/Web/API/RandomSource/getRandomValues" target="_blank">cryptographically secure random number generator</a>,
+                    and can generally be trusted more than your own intuition about randomness.
+                    If cryptographic randomness isn't available in your browser, this page will show a warning and <i>will not generate
+                    random mnemonics</i>.
+                    </p>
+                    <p>
+                    <a href="https://bitcointalk.org/index.php?topic=311000.msg3345309#msg3345309" target="_blank">You are not a good source of entropy.</a>
+                    </p>
                 </div>
             </div>
 
@@ -16169,6 +16212,1781 @@ var Mnemonic = function(language) {
 
 }
 </script>
+        <script>window.Entropy = new (function() {
+
+    var matchers = {
+        binary: /[0-1]/gi,
+        base6: /[0-5]/gi,
+        dice: /[1-6]/gi, // ie dice numbers
+        base10: /[0-9]/gi,
+        hex: /[0-9A-F]/gi,
+    }
+
+    this.fromString = function(rawEntropyStr) {
+        // Find type of entropy being used (binary, hex, dice etc)
+        var base = getBase(rawEntropyStr);
+        // Convert dice to base6 entropy (ie 1-6 to 0-5)
+        if (base.str == "dice") {
+            var newRawEntropyStr = "";
+            for (var i=0; i<rawEntropyStr.length; i++) {
+                var c = rawEntropyStr[i];
+                if ("123456".indexOf(c) > -1) {
+                    newRawEntropyStr += (parseInt(c) - 1).toString();
+                }
+                else {
+                    newRawEntropyStr += c
+                }
+            }
+            rawEntropyStr = newRawEntropyStr;
+            base.str = "base 6 (dice)";
+            base.matcher = matchers.base6;
+        }
+        var entropyParts = rawEntropyStr.match(base.matcher) || [];
+        var entropyStr = entropyParts.join("");
+        // Detect empty entropy
+        if (entropyStr.length == 0) {
+            return {
+                binaryStr: "",
+                hexStr: "",
+                cleanStr: "",
+                base: base,
+            };
+        }
+        // Pull leading zeros off
+        var leadingZeros = "";
+        while (entropyStr[0] == "0") {
+            leadingZeros += "0";
+            entropyStr = entropyStr.substring(1);
+        }
+        // Convert leading zeros to binary equivalent
+        var numBinLeadingZeros = Math.ceil(Math.log2(base.asInt) * leadingZeros.length);
+        var binLeadingZeros = "";
+        for (var i=0; i<numBinLeadingZeros; i++) {
+            binLeadingZeros += "0";
+        }
+        // Convert leading zeros to hex equivalent
+        var numHexLeadingZeros = Math.floor(numBinLeadingZeros / 4);
+        var hexLeadingZeros = "";
+        for (var i=0; i<numHexLeadingZeros; i++) {
+            hexLeadingZeros += "0";
+        }
+        // Handle entropy of zero
+        if (entropyStr == "") {
+            return {
+                binaryStr: binLeadingZeros,
+                hexStr: hexLeadingZeros || "0",
+                cleanStr: leadingZeros,
+                base: base,
+            }
+        }
+        // If using hex, should always be multiples of 4 bits, which can get
+        // out of sync if first number has leading 0 bits, eg 2 in hex is 0010
+        // which would show up as 10, thus missing 2 bits it should have.
+        if (base.asInt == 16) {
+            var firstDigit = parseInt(entropyStr[0], 16);
+            if (firstDigit >= 4 && firstDigit < 8) {
+                binLeadingZeros += "0";
+            }
+            else if (firstDigit >= 2 && firstDigit < 4) {
+                binLeadingZeros += "00";
+            }
+            else if (firstDigit >= 1 && firstDigit < 2) {
+                binLeadingZeros += "000";
+            }
+        }
+        // Convert entropy to different foramts
+        var entropyInt = BigInteger.parse(entropyStr, base.asInt);
+        var entropyBin = binLeadingZeros + entropyInt.toString(2);
+        var entropyHex = hexLeadingZeros + entropyInt.toString(16);
+        var entropyClean = leadingZeros + entropyStr;
+        var e = {
+            binaryStr: entropyBin,
+            hexStr: entropyHex,
+            cleanStr: entropyClean,
+            base: base,
+        }
+        return e;
+    }
+
+    function getBase(str) {
+        // Need to get the lowest base for the supplied entropy.
+        // This prevents interpreting, say, dice rolls as hexadecimal.
+        var binaryMatches = str.match(matchers.binary) || [];
+        var base6Matches = str.match(matchers.base6) || [];
+        var diceMatches = str.match(matchers.dice) || [];
+        var base10Matches = str.match(matchers.base10) || [];
+        var hexMatches = str.match(matchers.hex) || [];
+        // Find the lowest base that can be used, whilst ignoring any irrelevant chars
+        if (binaryMatches.length == hexMatches.length) {
+            return {
+                matcher: matchers.binary,
+                asInt: 2,
+                str: "binary",
+            }
+        }
+        if (diceMatches.length == hexMatches.length) {
+            return {
+                matcher: matchers.dice,
+                asInt: 6,
+                str: "dice",
+            }
+        }
+        if (base6Matches.length == hexMatches.length) {
+            return {
+                matcher: matchers.base6,
+                asInt: 6,
+                str: "base 6",
+            }
+        }
+        if (base10Matches.length == hexMatches.length) {
+            return {
+                matcher: matchers.base10,
+                asInt: 10,
+                str: "base 10",
+            }
+        }
+        return {
+            matcher: matchers.hex,
+            asInt: 16,
+            str: "hexadecimal",
+        }
+    }
+
+    // Polyfill for Math.log2
+    // See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill
+    Math.log2 = Math.log2 || function(x) {
+        return Math.log(x) * Math.LOG2E;
+    };
+
+})();
+
+
+// BigInteger library included here because
+// only the entropy library depends on it
+// so if entropy detection is removed so is the dependency
+
+
+/*
+        JavaScript BigInteger library version 0.9.1
+        http://silentmatt.com/biginteger/
+
+        Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
+        Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
+        Licensed under the MIT license.
+
+        Support for arbitrary internal representation base was added by
+        Vitaly Magerya.
+*/
+
+/*
+        File: biginteger.js
+
+        Exports:
+
+                <BigInteger>
+*/
+(function(exports) {
+"use strict";
+/*
+        Class: BigInteger
+        An arbitrarily-large integer.
+
+        <BigInteger> objects should be considered immutable. None of the "built-in"
+        methods modify *this* or their arguments. All properties should be
+        considered private.
+
+        All the methods of <BigInteger> instances can be called "statically". The
+        static versions are convenient if you don't already have a <BigInteger>
+        object.
+
+        As an example, these calls are equivalent.
+
+        > BigInteger(4).multiply(5); // returns BigInteger(20);
+        > BigInteger.multiply(4, 5); // returns BigInteger(20);
+
+        > var a = 42;
+        > var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
+*/
+
+var CONSTRUCT = {}; // Unique token to call "private" version of constructor
+
+/*
+        Constructor: BigInteger()
+        Convert a value to a <BigInteger>.
+
+        Although <BigInteger()> is the constructor for <BigInteger> objects, it is
+        best not to call it as a constructor. If *n* is a <BigInteger> object, it is
+        simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
+        without a radix argument.
+
+        > var n0 = BigInteger();      // Same as <BigInteger.ZERO>
+        > var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
+        > var n2 = BigInteger(123);   // Create a new <BigInteger> with value 123
+        > var n3 = BigInteger(n2);    // Return n2, unchanged
+
+        The constructor form only takes an array and a sign. *n* must be an
+        array of numbers in little-endian order, where each digit is between 0
+        and BigInteger.base.  The second parameter sets the sign: -1 for
+        negative, +1 for positive, or 0 for zero. The array is *not copied and
+        may be modified*. If the array contains only zeros, the sign parameter
+        is ignored and is forced to zero.
+
+        > new BigInteger([5], -1): create a new BigInteger with value -5
+
+        Parameters:
+
+                n - Value to convert to a <BigInteger>.
+
+        Returns:
+
+                A <BigInteger> value.
+
+        See Also:
+
+                <parse>, <BigInteger>
+*/
+function BigInteger(n, s, token) {
+        if (token !== CONSTRUCT) {
+                if (n instanceof BigInteger) {
+                        return n;
+                }
+                else if (typeof n === "undefined") {
+                        return ZERO;
+                }
+                return BigInteger.parse(n);
+        }
+
+        n = n || [];  // Provide the nullary constructor for subclasses.
+        while (n.length && !n[n.length - 1]) {
+                --n.length;
+        }
+        this._d = n;
+        this._s = n.length ? (s || 1) : 0;
+}
+
+BigInteger._construct = function(n, s) {
+        return new BigInteger(n, s, CONSTRUCT);
+};
+
+// Base-10 speedup hacks in parse, toString, exp10 and log functions
+// require base to be a power of 10. 10^7 is the largest such power
+// that won't cause a precision loss when digits are multiplied.
+var BigInteger_base = 10000000;
+var BigInteger_base_log10 = 7;
+
+BigInteger.base = BigInteger_base;
+BigInteger.base_log10 = BigInteger_base_log10;
+
+var ZERO = new BigInteger([], 0, CONSTRUCT);
+// Constant: ZERO
+// <BigInteger> 0.
+BigInteger.ZERO = ZERO;
+
+var ONE = new BigInteger([1], 1, CONSTRUCT);
+// Constant: ONE
+// <BigInteger> 1.
+BigInteger.ONE = ONE;
+
+var M_ONE = new BigInteger(ONE._d, -1, CONSTRUCT);
+// Constant: M_ONE
+// <BigInteger> -1.
+BigInteger.M_ONE = M_ONE;
+
+// Constant: _0
+// Shortcut for <ZERO>.
+BigInteger._0 = ZERO;
+
+// Constant: _1
+// Shortcut for <ONE>.
+BigInteger._1 = ONE;
+
+/*
+        Constant: small
+        Array of <BigIntegers> from 0 to 36.
+
+        These are used internally for parsing, but useful when you need a "small"
+        <BigInteger>.
+
+        See Also:
+
+                <ZERO>, <ONE>, <_0>, <_1>
+*/
+BigInteger.small = [
+        ZERO,
+        ONE,
+        /* Assuming BigInteger_base > 36 */
+        new BigInteger( [2], 1, CONSTRUCT),
+        new BigInteger( [3], 1, CONSTRUCT),
+        new BigInteger( [4], 1, CONSTRUCT),
+        new BigInteger( [5], 1, CONSTRUCT),
+        new BigInteger( [6], 1, CONSTRUCT),
+        new BigInteger( [7], 1, CONSTRUCT),
+        new BigInteger( [8], 1, CONSTRUCT),
+        new BigInteger( [9], 1, CONSTRUCT),
+        new BigInteger([10], 1, CONSTRUCT),
+        new BigInteger([11], 1, CONSTRUCT),
+        new BigInteger([12], 1, CONSTRUCT),
+        new BigInteger([13], 1, CONSTRUCT),
+        new BigInteger([14], 1, CONSTRUCT),
+        new BigInteger([15], 1, CONSTRUCT),
+        new BigInteger([16], 1, CONSTRUCT),
+        new BigInteger([17], 1, CONSTRUCT),
+        new BigInteger([18], 1, CONSTRUCT),
+        new BigInteger([19], 1, CONSTRUCT),
+        new BigInteger([20], 1, CONSTRUCT),
+        new BigInteger([21], 1, CONSTRUCT),
+        new BigInteger([22], 1, CONSTRUCT),
+        new BigInteger([23], 1, CONSTRUCT),
+        new BigInteger([24], 1, CONSTRUCT),
+        new BigInteger([25], 1, CONSTRUCT),
+        new BigInteger([26], 1, CONSTRUCT),
+        new BigInteger([27], 1, CONSTRUCT),
+        new BigInteger([28], 1, CONSTRUCT),
+        new BigInteger([29], 1, CONSTRUCT),
+        new BigInteger([30], 1, CONSTRUCT),
+        new BigInteger([31], 1, CONSTRUCT),
+        new BigInteger([32], 1, CONSTRUCT),
+        new BigInteger([33], 1, CONSTRUCT),
+        new BigInteger([34], 1, CONSTRUCT),
+        new BigInteger([35], 1, CONSTRUCT),
+        new BigInteger([36], 1, CONSTRUCT)
+];
+
+// Used for parsing/radix conversion
+BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
+
+/*
+        Method: toString
+        Convert a <BigInteger> to a string.
+
+        When *base* is greater than 10, letters are upper case.
+
+        Parameters:
+
+                base - Optional base to represent the number in (default is base 10).
+                       Must be between 2 and 36 inclusive, or an Error will be thrown.
+
+        Returns:
+
+                The string representation of the <BigInteger>.
+*/
+BigInteger.prototype.toString = function(base) {
+        base = +base || 10;
+        if (base < 2 || base > 36) {
+                throw new Error("illegal radix " + base + ".");
+        }
+        if (this._s === 0) {
+                return "0";
+        }
+        if (base === 10) {
+                var str = this._s < 0 ? "-" : "";
+                str += this._d[this._d.length - 1].toString();
+                for (var i = this._d.length - 2; i >= 0; i--) {
+                        var group = this._d[i].toString();
+                        while (group.length < BigInteger_base_log10) group = '0' + group;
+                        str += group;
+                }
+                return str;
+        }
+        else {
+                var numerals = BigInteger.digits;
+                base = BigInteger.small[base];
+                var sign = this._s;
+
+                var n = this.abs();
+                var digits = [];
+                var digit;
+
+                while (n._s !== 0) {
+                        var divmod = n.divRem(base);
+                        n = divmod[0];
+                        digit = divmod[1];
+                        // TODO: This could be changed to unshift instead of reversing at the end.
+                        // Benchmark both to compare speeds.
+                        digits.push(numerals[digit.valueOf()]);
+                }
+                return (sign < 0 ? "-" : "") + digits.reverse().join("");
+        }
+};
+
+// Verify strings for parsing
+BigInteger.radixRegex = [
+        /^$/,
+        /^$/,
+        /^[01]*$/,
+        /^[012]*$/,
+        /^[0-3]*$/,
+        /^[0-4]*$/,
+        /^[0-5]*$/,
+        /^[0-6]*$/,
+        /^[0-7]*$/,
+        /^[0-8]*$/,
+        /^[0-9]*$/,
+        /^[0-9aA]*$/,
+        /^[0-9abAB]*$/,
+        /^[0-9abcABC]*$/,
+        /^[0-9a-dA-D]*$/,
+        /^[0-9a-eA-E]*$/,
+        /^[0-9a-fA-F]*$/,
+        /^[0-9a-gA-G]*$/,
+        /^[0-9a-hA-H]*$/,
+        /^[0-9a-iA-I]*$/,
+        /^[0-9a-jA-J]*$/,
+        /^[0-9a-kA-K]*$/,
+        /^[0-9a-lA-L]*$/,
+        /^[0-9a-mA-M]*$/,
+        /^[0-9a-nA-N]*$/,
+        /^[0-9a-oA-O]*$/,
+        /^[0-9a-pA-P]*$/,
+        /^[0-9a-qA-Q]*$/,
+        /^[0-9a-rA-R]*$/,
+        /^[0-9a-sA-S]*$/,
+        /^[0-9a-tA-T]*$/,
+        /^[0-9a-uA-U]*$/,
+        /^[0-9a-vA-V]*$/,
+        /^[0-9a-wA-W]*$/,
+        /^[0-9a-xA-X]*$/,
+        /^[0-9a-yA-Y]*$/,
+        /^[0-9a-zA-Z]*$/
+];
+
+/*
+        Function: parse
+        Parse a string into a <BigInteger>.
+
+        *base* is optional but, if provided, must be from 2 to 36 inclusive. If
+        *base* is not provided, it will be guessed based on the leading characters
+        of *s* as follows:
+
+        - "0x" or "0X": *base* = 16
+        - "0c" or "0C": *base* = 8
+        - "0b" or "0B": *base* = 2
+        - else: *base* = 10
+
+        If no base is provided, or *base* is 10, the number can be in exponential
+        form. For example, these are all valid:
+
+        > BigInteger.parse("1e9");              // Same as "1000000000"
+        > BigInteger.parse("1.234*10^3");       // Same as 1234
+        > BigInteger.parse("56789 * 10 ** -2"); // Same as 567
+
+        If any characters fall outside the range defined by the radix, an exception
+        will be thrown.
+
+        Parameters:
+
+                s - The string to parse.
+                base - Optional radix (default is to guess based on *s*).
+
+        Returns:
+
+                a <BigInteger> instance.
+*/
+BigInteger.parse = function(s, base) {
+        // Expands a number in exponential form to decimal form.
+        // expandExponential("-13.441*10^5") === "1344100";
+        // expandExponential("1.12300e-1") === "0.112300";
+        // expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
+        function expandExponential(str) {
+                str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
+
+                return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function(x, s, n, f, c) {
+                        c = +c;
+                        var l = c < 0;
+                        var i = n.length + c;
+                        x = (l ? n : f).length;
+                        c = ((c = Math.abs(c)) >= x ? c - x + l : 0);
+                        var z = (new Array(c + 1)).join("0");
+                        var r = n + f;
+                        return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : "");
+                });
+        }
+
+        s = s.toString();
+        if (typeof base === "undefined" || +base === 10) {
+                s = expandExponential(s);
+        }
+
+        var prefixRE;
+        if (typeof base === "undefined") {
+                prefixRE = '0[xcb]';
+        }
+        else if (base == 16) {
+                prefixRE = '0x';
+        }
+        else if (base == 8) {
+                prefixRE = '0c';
+        }
+        else if (base == 2) {
+                prefixRE = '0b';
+        }
+        else {
+                prefixRE = '';
+        }
+        var parts = new RegExp('^([+\\-]?)(' + prefixRE + ')?([0-9a-z]*)(?:\\.\\d*)?$', 'i').exec(s);
+        if (parts) {
+                var sign = parts[1] || "+";
+                var baseSection = parts[2] || "";
+                var digits = parts[3] || "";
+
+                if (typeof base === "undefined") {
+                        // Guess base
+                        if (baseSection === "0x" || baseSection === "0X") { // Hex
+                                base = 16;
+                        }
+                        else if (baseSection === "0c" || baseSection === "0C") { // Octal
+                                base = 8;
+                        }
+                        else if (baseSection === "0b" || baseSection === "0B") { // Binary
+                                base = 2;
+                        }
+                        else {
+                                base = 10;
+                        }
+                }
+                else if (base < 2 || base > 36) {
+                        throw new Error("Illegal radix " + base + ".");
+                }
+
+                base = +base;
+
+                // Check for digits outside the range
+                if (!(BigInteger.radixRegex[base].test(digits))) {
+                        throw new Error("Bad digit for radix " + base);
+                }
+
+                // Strip leading zeros, and convert to array
+                digits = digits.replace(/^0+/, "").split("");
+                if (digits.length === 0) {
+                        return ZERO;
+                }
+
+                // Get the sign (we know it's not zero)
+                sign = (sign === "-") ? -1 : 1;
+
+                // Optimize 10
+                if (base == 10) {
+                        var d = [];
+                        while (digits.length >= BigInteger_base_log10) {
+                                d.push(parseInt(digits.splice(digits.length-BigInteger.base_log10, BigInteger.base_log10).join(''), 10));
+                        }
+                        d.push(parseInt(digits.join(''), 10));
+                        return new BigInteger(d, sign, CONSTRUCT);
+                }
+
+                // Do the conversion
+                var d = ZERO;
+                base = BigInteger.small[base];
+                var small = BigInteger.small;
+                for (var i = 0; i < digits.length; i++) {
+                        d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
+                }
+                return new BigInteger(d._d, sign, CONSTRUCT);
+        }
+        else {
+                throw new Error("Invalid BigInteger format: " + s);
+        }
+};
+
+/*
+        Function: add
+        Add two <BigIntegers>.
+
+        Parameters:
+
+                n - The number to add to *this*. Will be converted to a <BigInteger>.
+
+        Returns:
+
+                The numbers added together.
+
+        See Also:
+
+                <subtract>, <multiply>, <quotient>, <next>
+*/
+BigInteger.prototype.add = function(n) {
+        if (this._s === 0) {
+                return BigInteger(n);
+        }
+
+        n = BigInteger(n);
+        if (n._s === 0) {
+                return this;
+        }
+        if (this._s !== n._s) {
+                n = n.negate();
+                return this.subtract(n);
+        }
+
+        var a = this._d;
+        var b = n._d;
+        var al = a.length;
+        var bl = b.length;
+        var sum = new Array(Math.max(al, bl) + 1);
+        var size = Math.min(al, bl);
+        var carry = 0;
+        var digit;
+
+        for (var i = 0; i < size; i++) {
+                digit = a[i] + b[i] + carry;
+                sum[i] = digit % BigInteger_base;
+                carry = (digit / BigInteger_base) | 0;
+        }
+        if (bl > al) {
+                a = b;
+                al = bl;
+        }
+        for (i = size; carry && i < al; i++) {
+                digit = a[i] + carry;
+                sum[i] = digit % BigInteger_base;
+                carry = (digit / BigInteger_base) | 0;
+        }
+        if (carry) {
+                sum[i] = carry;
+        }
+
+        for ( ; i < al; i++) {
+                sum[i] = a[i];
+        }
+
+        return new BigInteger(sum, this._s, CONSTRUCT);
+};
+
+/*
+        Function: negate
+        Get the additive inverse of a <BigInteger>.
+
+        Returns:
+
+                A <BigInteger> with the same magnatude, but with the opposite sign.
+
+        See Also:
+
+                <abs>
+*/
+BigInteger.prototype.negate = function() {
+        return new BigInteger(this._d, (-this._s) | 0, CONSTRUCT);
+};
+
+/*
+        Function: abs
+        Get the absolute value of a <BigInteger>.
+
+        Returns:
+
+                A <BigInteger> with the same magnatude, but always positive (or zero).
+
+        See Also:
+
+                <negate>
+*/
+BigInteger.prototype.abs = function() {
+        return (this._s < 0) ? this.negate() : this;
+};
+
+/*
+        Function: subtract
+        Subtract two <BigIntegers>.
+
+        Parameters:
+
+                n - The number to subtract from *this*. Will be converted to a <BigInteger>.
+
+        Returns:
+
+                The *n* subtracted from *this*.
+
+        See Also:
+
+                <add>, <multiply>, <quotient>, <prev>
+*/
+BigInteger.prototype.subtract = function(n) {
+        if (this._s === 0) {
+                return BigInteger(n).negate();
+        }
+
+        n = BigInteger(n);
+        if (n._s === 0) {
+                return this;
+        }
+        if (this._s !== n._s) {
+                n = n.negate();
+                return this.add(n);
+        }
+
+        var m = this;
+        // negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a|
+        if (this._s < 0) {
+                m = new BigInteger(n._d, 1, CONSTRUCT);
+                n = new BigInteger(this._d, 1, CONSTRUCT);
+        }
+
+        // Both are positive => a - b
+        var sign = m.compareAbs(n);
+        if (sign === 0) {
+                return ZERO;
+        }
+        else if (sign < 0) {
+                // swap m and n
+                var t = n;
+                n = m;
+                m = t;
+        }
+
+        // a > b
+        var a = m._d;
+        var b = n._d;
+        var al = a.length;
+        var bl = b.length;
+        var diff = new Array(al); // al >= bl since a > b
+        var borrow = 0;
+        var i;
+        var digit;
+
+        for (i = 0; i < bl; i++) {
+                digit = a[i] - borrow - b[i];
+                if (digit < 0) {
+                        digit += BigInteger_base;
+                        borrow = 1;
+                }
+                else {
+                        borrow = 0;
+                }
+                diff[i] = digit;
+        }
+        for (i = bl; i < al; i++) {
+                digit = a[i] - borrow;
+                if (digit < 0) {
+                        digit += BigInteger_base;
+                }
+                else {
+                        diff[i++] = digit;
+                        break;
+                }
+                diff[i] = digit;
+        }
+        for ( ; i < al; i++) {
+                diff[i] = a[i];
+        }
+
+        return new BigInteger(diff, sign, CONSTRUCT);
+};
+
+(function() {
+        function addOne(n, sign) {
+                var a = n._d;
+                var sum = a.slice();
+                var carry = true;
+                var i = 0;
+
+                while (true) {
+                        var digit = (a[i] || 0) + 1;
+                        sum[i] = digit % BigInteger_base;
+                        if (digit <= BigInteger_base - 1) {
+                                break;
+                        }
+                        ++i;
+                }
+
+                return new BigInteger(sum, sign, CONSTRUCT);
+        }
+
+        function subtractOne(n, sign) {
+                var a = n._d;
+                var sum = a.slice();
+                var borrow = true;
+                var i = 0;
+
+                while (true) {
+                        var digit = (a[i] || 0) - 1;
+                        if (digit < 0) {
+                                sum[i] = digit + BigInteger_base;
+                        }
+                        else {
+                                sum[i] = digit;
+                                break;
+                        }
+                        ++i;
+                }
+
+                return new BigInteger(sum, sign, CONSTRUCT);
+        }
+
+        /*
+                Function: next
+                Get the next <BigInteger> (add one).
+
+                Returns:
+
+                        *this* + 1.
+
+                See Also:
+
+                        <add>, <prev>
+        */
+        BigInteger.prototype.next = function() {
+                switch (this._s) {
+                case 0:
+                        return ONE;
+                case -1:
+                        return subtractOne(this, -1);
+                // case 1:
+                default:
+                        return addOne(this, 1);
+                }
+        };
+
+        /*
+                Function: prev
+                Get the previous <BigInteger> (subtract one).
+
+                Returns:
+
+                        *this* - 1.
+
+                See Also:
+
+                        <next>, <subtract>
+        */
+        BigInteger.prototype.prev = function() {
+                switch (this._s) {
+                case 0:
+                        return M_ONE;
+                case -1:
+                        return addOne(this, -1);
+                // case 1:
+                default:
+                        return subtractOne(this, 1);
+                }
+        };
+})();
+
+/*
+        Function: compareAbs
+        Compare the absolute value of two <BigIntegers>.
+
+        Calling <compareAbs> is faster than calling <abs> twice, then <compare>.
+
+        Parameters:
+
+                n - The number to compare to *this*. Will be converted to a <BigInteger>.
+
+        Returns:
+
+                -1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*.
+
+        See Also:
+
+                <compare>, <abs>
+*/
+BigInteger.prototype.compareAbs = function(n) {
+        if (this === n) {
+                return 0;
+        }
+
+        if (!(n instanceof BigInteger)) {
+                if (!isFinite(n)) {
+                        return(isNaN(n) ? n : -1);
+                }
+                n = BigInteger(n);
+        }
+
+        if (this._s === 0) {
+                return (n._s !== 0) ? -1 : 0;
+        }
+        if (n._s === 0) {
+                return 1;
+        }
+
+        var l = this._d.length;
+        var nl = n._d.length;
+        if (l < nl) {
+                return -1;
+        }
+        else if (l > nl) {
+                return 1;
+        }
+
+        var a = this._d;
+        var b = n._d;
+        for (var i = l-1; i >= 0; i--) {
+                if (a[i] !== b[i]) {
+                        return a[i] < b[i] ? -1 : 1;
+                }
+        }
+
+        return 0;
+};
+
+/*
+        Function: compare
+        Compare two <BigIntegers>.
+
+        Parameters:
+
+                n - The number to compare to *this*. Will be converted to a <BigInteger>.
+
+        Returns:
+
+                -1, 0, or +1 if *this* is less than, equal to, or greater than *n*.
+
+        See Also:
+
+                <compareAbs>, <isPositive>, <isNegative>, <isUnit>
+*/
+BigInteger.prototype.compare = function(n) {
+        if (this === n) {
+                return 0;
+        }
+
+        n = BigInteger(n);
+
+        if (this._s === 0) {
+                return -n._s;
+        }
+
+        if (this._s === n._s) { // both positive or both negative
+                var cmp = this.compareAbs(n);
+                return cmp * this._s;
+        }
+        else {
+                return this._s;
+        }
+};
+
+/*
+        Function: isUnit
+        Return true iff *this* is either 1 or -1.
+
+        Returns:
+
+                true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>.
+
+        See Also:
+
+                <isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>,
+                <BigInteger.ONE>, <BigInteger.M_ONE>
+*/
+BigInteger.prototype.isUnit = function() {
+        return this === ONE ||
+                this === M_ONE ||
+                (this._d.length === 1 && this._d[0] === 1);
+};
+
+/*
+        Function: multiply
+        Multiply two <BigIntegers>.
+
+        Parameters:
+
+                n - The number to multiply *this* by. Will be converted to a
+                <BigInteger>.
+
+        Returns:
+
+                The numbers multiplied together.
+
+        See Also:
+
+                <add>, <subtract>, <quotient>, <square>
+*/
+BigInteger.prototype.multiply = function(n) {
+        // TODO: Consider adding Karatsuba multiplication for large numbers
+        if (this._s === 0) {
+                return ZERO;
+        }
+
+        n = BigInteger(n);
+        if (n._s === 0) {
+                return ZERO;
+        }
+        if (this.isUnit()) {
+                if (this._s < 0) {
+                        return n.negate();
+                }
+                return n;
+        }
+        if (n.isUnit()) {
+                if (n._s < 0) {
+                        return this.negate();
+                }
+                return this;
+        }
+        if (this === n) {
+                return this.square();
+        }
+
+        var r = (this._d.length >= n._d.length);
+        var a = (r ? this : n)._d; // a will be longer than b
+        var b = (r ? n : this)._d;
+        var al = a.length;
+        var bl = b.length;
+
+        var pl = al + bl;
+        var partial = new Array(pl);
+        var i;
+        for (i = 0; i < pl; i++) {
+                partial[i] = 0;
+        }
+
+        for (i = 0; i < bl; i++) {
+                var carry = 0;
+                var bi = b[i];
+                var jlimit = al + i;
+                var digit;
+                for (var j = i; j < jlimit; j++) {
+                        digit = partial[j] + bi * a[j - i] + carry;
+                        carry = (digit / BigInteger_base) | 0;
+                        partial[j] = (digit % BigInteger_base) | 0;
+                }
+                if (carry) {
+                        digit = partial[j] + carry;
+                        carry = (digit / BigInteger_base) | 0;
+                        partial[j] = digit % BigInteger_base;
+                }
+        }
+        return new BigInteger(partial, this._s * n._s, CONSTRUCT);
+};
+
+// Multiply a BigInteger by a single-digit native number
+// Assumes that this and n are >= 0
+// This is not really intended to be used outside the library itself
+BigInteger.prototype.multiplySingleDigit = function(n) {
+        if (n === 0 || this._s === 0) {
+                return ZERO;
+        }
+        if (n === 1) {
+                return this;
+        }
+
+        var digit;
+        if (this._d.length === 1) {
+                digit = this._d[0] * n;
+                if (digit >= BigInteger_base) {
+                        return new BigInteger([(digit % BigInteger_base)|0,
+                                        (digit / BigInteger_base)|0], 1, CONSTRUCT);
+                }
+                return new BigInteger([digit], 1, CONSTRUCT);
+        }
+
+        if (n === 2) {
+                return this.add(this);
+        }
+        if (this.isUnit()) {
+                return new BigInteger([n], 1, CONSTRUCT);
+        }
+
+        var a = this._d;
+        var al = a.length;
+
+        var pl = al + 1;
+        var partial = new Array(pl);
+        for (var i = 0; i < pl; i++) {
+                partial[i] = 0;
+        }
+
+        var carry = 0;
+        for (var j = 0; j < al; j++) {
+                digit = n * a[j] + carry;
+                carry = (digit / BigInteger_base) | 0;
+                partial[j] = (digit % BigInteger_base) | 0;
+        }
+        if (carry) {
+                partial[j] = carry;
+        }
+
+        return new BigInteger(partial, 1, CONSTRUCT);
+};
+
+/*
+        Function: square
+        Multiply a <BigInteger> by itself.
+
+        This is slightly faster than regular multiplication, since it removes the
+        duplicated multiplcations.
+
+        Returns:
+
+                > this.multiply(this)
+
+        See Also:
+                <multiply>
+*/
+BigInteger.prototype.square = function() {
+        // Normally, squaring a 10-digit number would take 100 multiplications.
+        // Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated.
+        // This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies).
+        // Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org
+
+        if (this._s === 0) {
+                return ZERO;
+        }
+        if (this.isUnit()) {
+                return ONE;
+        }
+
+        var digits = this._d;
+        var length = digits.length;
+        var imult1 = new Array(length + length + 1);
+        var product, carry, k;
+        var i;
+
+        // Calculate diagonal
+        for (i = 0; i < length; i++) {
+                k = i * 2;
+                product = digits[i] * digits[i];
+                carry = (product / BigInteger_base) | 0;
+                imult1[k] = product % BigInteger_base;
+                imult1[k + 1] = carry;
+        }
+
+        // Calculate repeating part
+        for (i = 0; i < length; i++) {
+                carry = 0;
+                k = i * 2 + 1;
+                for (var j = i + 1; j < length; j++, k++) {
+                        product = digits[j] * digits[i] * 2 + imult1[k] + carry;
+                        carry = (product / BigInteger_base) | 0;
+                        imult1[k] = product % BigInteger_base;
+                }
+                k = length + i;
+                var digit = carry + imult1[k];
+                carry = (digit / BigInteger_base) | 0;
+                imult1[k] = digit % BigInteger_base;
+                imult1[k + 1] += carry;
+        }
+
+        return new BigInteger(imult1, 1, CONSTRUCT);
+};
+
+/*
+        Function: quotient
+        Divide two <BigIntegers> and truncate towards zero.
+
+        <quotient> throws an exception if *n* is zero.
+
+        Parameters:
+
+                n - The number to divide *this* by. Will be converted to a <BigInteger>.
+
+        Returns:
+
+                The *this* / *n*, truncated to an integer.
+
+        See Also:
+
+                <add>, <subtract>, <multiply>, <divRem>, <remainder>
+*/
+BigInteger.prototype.quotient = function(n) {
+        return this.divRem(n)[0];
+};
+
+/*
+        Function: divide
+        Deprecated synonym for <quotient>.
+*/
+BigInteger.prototype.divide = BigInteger.prototype.quotient;
+
+/*
+        Function: remainder
+        Calculate the remainder of two <BigIntegers>.
+
+        <remainder> throws an exception if *n* is zero.
+
+        Parameters:
+
+                n - The remainder after *this* is divided *this* by *n*. Will be
+                    converted to a <BigInteger>.
+
+        Returns:
+
+                *this* % *n*.
+
+        See Also:
+
+                <divRem>, <quotient>
+*/
+BigInteger.prototype.remainder = function(n) {
+        return this.divRem(n)[1];
+};
+
+/*
+        Function: divRem
+        Calculate the integer quotient and remainder of two <BigIntegers>.
+
+        <divRem> throws an exception if *n* is zero.
+
+        Parameters:
+
+                n - The number to divide *this* by. Will be converted to a <BigInteger>.
+
+        Returns:
+
+                A two-element array containing the quotient and the remainder.
+
+                > a.divRem(b)
+
+                is exactly equivalent to
+
+                > [a.quotient(b), a.remainder(b)]
+
+                except it is faster, because they are calculated at the same time.
+
+        See Also:
+
+                <quotient>, <remainder>
+*/
+BigInteger.prototype.divRem = function(n) {
+        n = BigInteger(n);
+        if (n._s === 0) {
+                throw new Error("Divide by zero");
+        }
+        if (this._s === 0) {
+                return [ZERO, ZERO];
+        }
+        if (n._d.length === 1) {
+                return this.divRemSmall(n._s * n._d[0]);
+        }
+
+        // Test for easy cases -- |n1| <= |n2|
+        switch (this.compareAbs(n)) {
+        case 0: // n1 == n2
+                return [this._s === n._s ? ONE : M_ONE, ZERO];
+        case -1: // |n1| < |n2|
+                return [ZERO, this];
+        }
+
+        var sign = this._s * n._s;
+        var a = n.abs();
+        var b_digits = this._d;
+        var b_index = b_digits.length;
+        var digits = n._d.length;
+        var quot = [];
+        var guess;
+
+        var part = new BigInteger([], 0, CONSTRUCT);
+
+        while (b_index) {
+                part._d.unshift(b_digits[--b_index]);
+                part = new BigInteger(part._d, 1, CONSTRUCT);
+
+                if (part.compareAbs(n) < 0) {
+                        quot.push(0);
+                        continue;
+                }
+                if (part._s === 0) {
+                        guess = 0;
+                }
+                else {
+                        var xlen = part._d.length, ylen = a._d.length;
+                        var highx = part._d[xlen-1]*BigInteger_base + part._d[xlen-2];
+                        var highy = a._d[ylen-1]*BigInteger_base + a._d[ylen-2];
+                        if (part._d.length > a._d.length) {
+                                // The length of part._d can either match a._d length,
+                                // or exceed it by one.
+                                highx = (highx+1)*BigInteger_base;
+                        }
+                        guess = Math.ceil(highx/highy);
+                }
+                do {
+                        var check = a.multiplySingleDigit(guess);
+                        if (check.compareAbs(part) <= 0) {
+                                break;
+                        }
+                        guess--;
+                } while (guess);
+
+                quot.push(guess);
+                if (!guess) {
+                        continue;
+                }
+                var diff = part.subtract(check);
+                part._d = diff._d.slice();
+        }
+
+        return [new BigInteger(quot.reverse(), sign, CONSTRUCT),
+                   new BigInteger(part._d, this._s, CONSTRUCT)];
+};
+
+// Throws an exception if n is outside of (-BigInteger.base, -1] or
+// [1, BigInteger.base).  It's not necessary to call this, since the
+// other division functions will call it if they are able to.
+BigInteger.prototype.divRemSmall = function(n) {
+        var r;
+        n = +n;
+        if (n === 0) {
+                throw new Error("Divide by zero");
+        }
+
+        var n_s = n < 0 ? -1 : 1;
+        var sign = this._s * n_s;
+        n = Math.abs(n);
+
+        if (n < 1 || n >= BigInteger_base) {
+                throw new Error("Argument out of range");
+        }
+
+        if (this._s === 0) {
+                return [ZERO, ZERO];
+        }
+
+        if (n === 1 || n === -1) {
+                return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign, CONSTRUCT), ZERO];
+        }
+
+        // 2 <= n < BigInteger_base
+
+        // divide a single digit by a single digit
+        if (this._d.length === 1) {
+                var q = new BigInteger([(this._d[0] / n) | 0], 1, CONSTRUCT);
+                r = new BigInteger([(this._d[0] % n) | 0], 1, CONSTRUCT);
+                if (sign < 0) {
+                        q = q.negate();
+                }
+                if (this._s < 0) {
+                        r = r.negate();
+                }
+                return [q, r];
+        }
+
+        var digits = this._d.slice();
+        var quot = new Array(digits.length);
+        var part = 0;
+        var diff = 0;
+        var i = 0;
+        var guess;
+
+        while (digits.length) {
+                part = part * BigInteger_base + digits[digits.length - 1];
+                if (part < n) {
+                        quot[i++] = 0;
+                        digits.pop();
+                        diff = BigInteger_base * diff + part;
+                        continue;
+                }
+                if (part === 0) {
+                        guess = 0;
+                }
+                else {
+                        guess = (part / n) | 0;
+                }
+
+                var check = n * guess;
+                diff = part - check;
+                quot[i++] = guess;
+                if (!guess) {
+                        digits.pop();
+                        continue;
+                }
+
+                digits.pop();
+                part = diff;
+        }
+
+        r = new BigInteger([diff], 1, CONSTRUCT);
+        if (this._s < 0) {
+                r = r.negate();
+        }
+        return [new BigInteger(quot.reverse(), sign, CONSTRUCT), r];
+};
+
+/*
+        Function: isEven
+        Return true iff *this* is divisible by two.
+
+        Note that <BigInteger.ZERO> is even.
+
+        Returns:
+
+                true if *this* is even, false otherwise.
+
+        See Also:
+
+                <isOdd>
+*/
+BigInteger.prototype.isEven = function() {
+        var digits = this._d;
+        return this._s === 0 || digits.length === 0 || (digits[0] % 2) === 0;
+};
+
+/*
+        Function: isOdd
+        Return true iff *this* is not divisible by two.
+
+        Returns:
+
+                true if *this* is odd, false otherwise.
+
+        See Also:
+
+                <isEven>
+*/
+BigInteger.prototype.isOdd = function() {
+        return !this.isEven();
+};
+
+/*
+        Function: sign
+        Get the sign of a <BigInteger>.
+
+        Returns:
+
+                * -1 if *this* < 0
+                * 0 if *this* == 0
+                * +1 if *this* > 0
+
+        See Also:
+
+                <isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.sign = function() {
+        return this._s;
+};
+
+/*
+        Function: isPositive
+        Return true iff *this* > 0.
+
+        Returns:
+
+                true if *this*.compare(<BigInteger.ZERO>) == 1.
+
+        See Also:
+
+                <sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.isPositive = function() {
+        return this._s > 0;
+};
+
+/*
+        Function: isNegative
+        Return true iff *this* < 0.
+
+        Returns:
+
+                true if *this*.compare(<BigInteger.ZERO>) == -1.
+
+        See Also:
+
+                <sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.isNegative = function() {
+        return this._s < 0;
+};
+
+/*
+        Function: isZero
+        Return true iff *this* == 0.
+
+        Returns:
+
+                true if *this*.compare(<BigInteger.ZERO>) == 0.
+
+        See Also:
+
+                <sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO>
+*/
+BigInteger.prototype.isZero = function() {
+        return this._s === 0;
+};
+
+/*
+        Function: exp10
+        Multiply a <BigInteger> by a power of 10.
+
+        This is equivalent to, but faster than
+
+        > if (n >= 0) {
+        >     return this.multiply(BigInteger("1e" + n));
+        > }
+        > else { // n <= 0
+        >     return this.quotient(BigInteger("1e" + -n));
+        > }
+
+        Parameters:
+
+                n - The power of 10 to multiply *this* by. *n* is converted to a
+                javascipt number and must be no greater than <BigInteger.MAX_EXP>
+                (0x7FFFFFFF), or an exception will be thrown.
+
+        Returns:
+
+                *this* * (10 ** *n*), truncated to an integer if necessary.
+
+        See Also:
+
+                <pow>, <multiply>
+*/
+BigInteger.prototype.exp10 = function(n) {
+        n = +n;
+        if (n === 0) {
+                return this;
+        }
+        if (Math.abs(n) > Number(MAX_EXP)) {
+                throw new Error("exponent too large in BigInteger.exp10");
+        }
+        // Optimization for this == 0. This also keeps us from having to trim zeros in the positive n case
+        if (this._s === 0) {
+                return ZERO;
+        }
+        if (n > 0) {
+                var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
+
+                for (; n >= BigInteger_base_log10; n -= BigInteger_base_log10) {
+                        k._d.unshift(0);
+                }
+                if (n == 0)
+                        return k;
+                k._s = 1;
+                k = k.multiplySingleDigit(Math.pow(10, n));
+                return (this._s < 0 ? k.negate() : k);
+        } else if (-n >= this._d.length*BigInteger_base_log10) {
+                return ZERO;
+        } else {
+                var k = new BigInteger(this._d.slice(), this._s, CONSTRUCT);
+
+                for (n = -n; n >= BigInteger_base_log10; n -= BigInteger_base_log10) {
+                        k._d.shift();
+                }
+                return (n == 0) ? k : k.divRemSmall(Math.pow(10, n))[0];
+        }
+};
+
+/*
+        Function: pow
+        Raise a <BigInteger> to a power.
+
+        In this implementation, 0**0 is 1.
+
+        Parameters:
+
+                n - The exponent to raise *this* by. *n* must be no greater than
+                <BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown.
+
+        Returns:
+
+                *this* raised to the *nth* power.
+
+        See Also:
+
+                <modPow>
+*/
+BigInteger.prototype.pow = function(n) {
+        if (this.isUnit()) {
+                if (this._s > 0) {
+                        return this;
+                }
+                else {
+                        return BigInteger(n).isOdd() ? this : this.negate();
+                }
+        }
+
+        n = BigInteger(n);
+        if (n._s === 0) {
+                return ONE;
+        }
+        else if (n._s < 0) {
+                if (this._s === 0) {
+                        throw new Error("Divide by zero");
+                }
+                else {
+                        return ZERO;
+                }
+        }
+        if (this._s === 0) {
+                return ZERO;
+        }
+        if (n.isUnit()) {
+                return this;
+        }
+
+        if (n.compareAbs(MAX_EXP) > 0) {
+                throw new Error("exponent too large in BigInteger.pow");
+        }
+        var x = this;
+        var aux = ONE;
+        var two = BigInteger.small[2];
+
+        while (n.isPositive()) {
+                if (n.isOdd()) {
+                        aux = aux.multiply(x);
+                        if (n.isUnit()) {
+                                return aux;
+                        }
+                }
+                x = x.square();
+                n = n.quotient(two);
+        }
+
+        return aux;
+};
+
+/*
+        Function: modPow
+        Raise a <BigInteger> to a power (mod m).
+
+        Because it is reduced by a modulus, <modPow> is not limited by
+        <BigInteger.MAX_EXP> like <pow>.
+
+        Parameters:
+
+                exponent - The exponent to raise *this* by. Must be positive.
+                modulus - The modulus.
+
+        Returns:
+
+                *this* ^ *exponent* (mod *modulus*).
+
+        See Also:
+
+                <pow>, <mod>
+*/
+BigInteger.prototype.modPow = function(exponent, modulus) {
+        var result = ONE;
+        var base = this;
+
+        while (exponent.isPositive()) {
+                if (exponent.isOdd()) {
+                        result = result.multiply(base).remainder(modulus);
+                }
+
+                exponent = exponent.quotient(BigInteger.small[2]);
+                if (exponent.isPositive()) {
+                        base = base.square().remainder(modulus);
+                }
+        }
+
+        return result;
+};
+
+/*
+        Function: log
+        Get the natural logarithm of a <BigInteger> as a native JavaScript number.
+
+        This is equivalent to
+
+        > Math.log(this.toJSValue())
+
+        but handles values outside of the native number range.
+
+        Returns:
+
+                log( *this* )
+
+        See Also:
+
+                <toJSValue>
+*/
+BigInteger.prototype.log = function() {
+        switch (this._s) {
+        case 0:  return -Infinity;
+        case -1: return NaN;
+        default: // Fall through.
+        }
+
+        var l = this._d.length;
+
+        if (l*BigInteger_base_log10 < 30) {
+                return Math.log(this.valueOf());
+        }
+
+        var N = Math.ceil(30/BigInteger_base_log10);
+        var firstNdigits = this._d.slice(l - N);
+        return Math.log((new BigInteger(firstNdigits, 1, CONSTRUCT)).valueOf()) + (l - N) * Math.log(BigInteger_base);
+};
+
+/*
+        Function: valueOf
+        Convert a <BigInteger> to a native JavaScript integer.
+
+        This is called automatically by JavaScipt to convert a <BigInteger> to a
+        native value.
+
+        Returns:
+
+                > parseInt(this.toString(), 10)
+
+        See Also:
+
+                <toString>, <toJSValue>
+*/
+BigInteger.prototype.valueOf = function() {
+        return parseInt(this.toString(), 10);
+};
+
+/*
+        Function: toJSValue
+        Convert a <BigInteger> to a native JavaScript integer.
+
+        This is the same as valueOf, but more explicitly named.
+
+        Returns:
+
+                > parseInt(this.toString(), 10)
+
+        See Also:
+
+                <toString>, <valueOf>
+*/
+BigInteger.prototype.toJSValue = function() {
+        return parseInt(this.toString(), 10);
+};
+
+var MAX_EXP = BigInteger(0x7FFFFFFF);
+// Constant: MAX_EXP
+// The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
+BigInteger.MAX_EXP = MAX_EXP;
+
+(function() {
+        function makeUnary(fn) {
+                return function(a) {
+                        return fn.call(BigInteger(a));
+                };
+        }
+
+        function makeBinary(fn) {
+                return function(a, b) {
+                        return fn.call(BigInteger(a), BigInteger(b));
+                };
+        }
+
+        function makeTrinary(fn) {
+                return function(a, b, c) {
+                        return fn.call(BigInteger(a), BigInteger(b), BigInteger(c));
+                };
+        }
+
+        (function() {
+                var i, fn;
+                var unary = "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(",");
+                var binary = "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(",");
+                var trinary = ["modPow"];
+
+                for (i = 0; i < unary.length; i++) {
+                        fn = unary[i];
+                        BigInteger[fn] = makeUnary(BigInteger.prototype[fn]);
+                }
+
+                for (i = 0; i < binary.length; i++) {
+                        fn = binary[i];
+                        BigInteger[fn] = makeBinary(BigInteger.prototype[fn]);
+                }
+
+                for (i = 0; i < trinary.length; i++) {
+                        fn = trinary[i];
+                        BigInteger[fn] = makeTrinary(BigInteger.prototype[fn]);
+                }
+
+                BigInteger.exp10 = function(x, n) {
+                        return BigInteger(x).exp10(n);
+                };
+        })();
+})();
+
+exports.BigInteger = BigInteger;
+})(typeof exports !== 'undefined' ? exports : this);
+</script>
         <script>(function() {
 
     // mnemonics is populated as required by getLanguage
@@ -16185,14 +18003,20 @@ var Mnemonic = function(language) {
     var showPubKey = true;
     var showPrivKey = true;
 
+    var entropyChangeTimeoutEvent = null;
     var phraseChangeTimeoutEvent = null;
     var rootKeyChangedTimeoutEvent = null;
 
     var DOM = {};
     DOM.network = $(".network");
     DOM.phraseNetwork = $("#network-phrase");
+    DOM.useEntropy = $(".use-entropy");
+    DOM.entropyContainer = $(".entropy-container");
+    DOM.entropy = $(".entropy");
+    DOM.entropyError = $(".entropy-error");
     DOM.phrase = $(".phrase");
     DOM.passphrase = $(".passphrase");
+    DOM.generateContainer = $(".generate-container");
     DOM.generate = $(".generate");
     DOM.seed = $(".seed");
     DOM.rootKey = $(".root-key");
@@ -16224,6 +18048,8 @@ var Mnemonic = function(language) {
     function init() {
         // Events
         DOM.network.on("change", networkChanged);
+        DOM.useEntropy.on("change", setEntropyVisibility);
+        DOM.entropy.on("input", delayedEntropyChanged);
         DOM.phrase.on("input", delayedPhraseChanged);
         DOM.passphrase.on("input", delayedPhraseChanged);
         DOM.generate.on("click", generateClicked);
@@ -16260,6 +18086,21 @@ var Mnemonic = function(language) {
         }
     }
 
+    function setEntropyVisibility() {
+        if (isUsingOwnEntropy()) {
+            DOM.entropyContainer.removeClass("hidden");
+            DOM.generateContainer.addClass("hidden");
+            DOM.phrase.prop("readonly", true);
+            DOM.entropy.focus();
+            entropyChanged();
+        }
+        else {
+            DOM.entropyContainer.addClass("hidden");
+            DOM.generateContainer.removeClass("hidden");
+            DOM.phrase.prop("readonly", false);
+        }
+    }
+
     function delayedPhraseChanged() {
         hideValidationError();
         showPending();
@@ -16287,6 +18128,20 @@ var Mnemonic = function(language) {
         hidePending();
     }
 
+    function delayedEntropyChanged() {
+        hideValidationError();
+        showPending();
+        if (entropyChangeTimeoutEvent != null) {
+            clearTimeout(entropyChangeTimeoutEvent);
+        }
+        entropyChangeTimeoutEvent = setTimeout(entropyChanged, 400);
+    }
+
+    function entropyChanged() {
+        setMnemonicFromEntropy();
+        phraseChanged();
+    }
+
     function delayedRootKeyChanged() {
         // Warn if there is an existing mnemonic or passphrase.
         if (DOM.phrase.val().length > 0 || DOM.passphrase.val().length > 0) {
@@ -16339,6 +18194,9 @@ var Mnemonic = function(language) {
     }
 
     function generateClicked() {
+        if (isUsingOwnEntropy()) {
+            return;
+        }
         clearDisplay();
         showPending();
         setTimeout(function() {
@@ -16770,7 +18628,12 @@ var Mnemonic = function(language) {
     }
 
     function getLanguageFromUrl() {
-        return window.location.hash.substring(1);
+        for (var language in WORDLISTS) {
+            if (window.location.hash.indexOf(language) > -1) {
+                return language;
+            }
+        }
+        return "";
     }
 
     function setMnemonicLanguage() {
@@ -16821,6 +18684,65 @@ var Mnemonic = function(language) {
         return phrase;
     }
 
+    function isUsingOwnEntropy() {
+        return DOM.useEntropy.prop("checked");
+    }
+
+    function setMnemonicFromEntropy() {
+        hideEntropyError();
+        // Work out minimum base for entropy
+        var entropyStr = DOM.entropy.val();
+        var entropy = Entropy.fromString(entropyStr);
+        if (entropy.hexStr.length == 0) {
+            return;
+        }
+        // Show entropy details
+        var extraBits = 32 - (entropy.binaryStr.length % 32);
+        var extraChars = Math.ceil(extraBits * Math.log(2) / Math.log(entropy.base.asInt));
+        var strength = "an extremely weak";
+        if (entropy.hexStr.length >= 8) {
+            strength = "a very weak";
+        }
+        if (entropy.hexStr.length >= 12) {
+            strength = "a weak";
+        }
+        if (entropy.hexStr.length >= 24) {
+            strength = "a strong";
+        }
+        if (entropy.hexStr.length >= 32) {
+            strength = "a very strong";
+        }
+        if (entropy.hexStr.length >= 40) {
+            strength = "an extremely strong";
+        }
+        if (entropy.hexStr.length >=48) {
+            strength = "an even stronger"
+        }
+        var msg = "Have " + entropy.binaryStr.length + " bits of entropy, " + extraChars + " more " + entropy.base.str + " chars required to generate " + strength + " mnemonic: " + entropy.cleanStr;
+        showEntropyError(msg);
+        // Discard trailing entropy
+        var hexStr = entropy.hexStr.substring(0, Math.floor(entropy.hexStr.length / 8) * 8);
+        // Convert entropy string to numeric array
+        var entropyArr = [];
+        for (var i=0; i<hexStr.length / 2; i++) {
+            var entropyByte = parseInt(hexStr[i*2].concat(hexStr[i*2+1]), 16);
+            entropyArr.push(entropyByte)
+        }
+        // Convert entropy array to mnemonic
+        var phrase = mnemonic.toMnemonic(entropyArr);
+        // Set the mnemonic in the UI
+        DOM.phrase.val(phrase);
+    }
+
+    function hideEntropyError() {
+        DOM.entropyError.addClass("hidden");
+    }
+
+    function showEntropyError(msg) {
+        DOM.entropyError.text(msg);
+        DOM.entropyError.removeClass("hidden");
+    }
+
     var networks = [
         {
             name: "Bitcoin",