src/js/entropy.js

   1 /*
   2  * Detects entropy from a string.
   3  *
   4  * Formats include:
   5  * binary [0-1]
   6  * base 6 [0-5]
   7  * dice 6 [1-6]
   8  * decimal [0-9]
   9  * hexadecimal [0-9A-F]
  10  *
  11  * Automatically uses lowest entropy to avoid issues such as interpretting 0101
  12  * as hexadecimal which would be 16 bits when really it's only 4 bits of binary
  13  * entropy.
  14  */
  15
  16 window.Entropy = new (function() {
  17
  18     // matchers returns an array of the matched events for each type of entropy.
  19     // eg
  20     // matchers.binary("010") returns ["0", "1", "0"]
  21     // matchers.binary("a10") returns ["1", "0"]
  22     // matchers.hex("a10") returns ["a", "1", "0"]
  23     var matchers = {
  24         binary: function(str) {
  25             return str.match(/[0-1]/gi) || [];
  26         },
  27         base6: function(str) {
  28             return str.match(/[0-5]/gi) || [];
  29         },
  30         dice: function(str) {
  31             return str.match(/[1-6]/gi) || []; // ie dice numbers
  32         },
  33         base10: function(str) {
  34             return str.match(/[0-9]/gi) || [];
  35         },
  36         hex: function(str) {
  37             return str.match(/[0-9A-F]/gi) || [];
  38         },
  39         card: function(str) {
  40             // Format is NumberSuit, eg
  41             // AH ace of hearts
  42             // 8C eight of clubs
  43             // TD ten of diamonds
  44             // JS jack of spades
  45             // QH queen of hearts
  46             // KC king of clubs
  47             return str.match(/([A2-9TJQK][CDHS])/gi) || [];
  48         }
  49     }
  50
  51     // Convert array of cards from ["ac", "4d", "ks"]
  52     // to numbers between 0 and 51 [0, 16, 51]
  53     function convertCardsToInts(cards) {
  54         var ints = [];
  55         var values = "a23456789tjqk";
  56         var suits = "cdhs";
  57         for (var i=0; i<cards.length; i++) {
  58             var card = cards[i].toLowerCase();
  59             var value = card[0];
  60             var suit = card[1];
  61             var asInt = 13 * suits.indexOf(suit) + values.indexOf(value);
  62             ints.push(asInt);
  63         }
  64         return ints;
  65     }
  66
  67     this.fromString = function(rawEntropyStr) {
  68         // Find type of entropy being used (binary, hex, dice etc)
  69         var base = getBase(rawEntropyStr);
  70         // Convert dice to base6 entropy (ie 1-6 to 0-5)
  71         // This is done by changing all 6s to 0s
  72         if (base.str == "dice") {
  73             var newParts = [];
  74             var newInts = [];
  75             for (var i=0; i<base.parts.length; i++) {
  76                 var c = base.parts[i];
  77                 if ("12345".indexOf(c) > -1) {
  78                     newParts[i] = base.parts[i];
  79                     newInts[i] = base.ints[i];
  80                 }
  81                 else {
  82                     newParts[i] = "0";
  83                     newInts[i] = 0;
  84                 }
  85             }
  86             base.str = "base 6 (dice)";
  87             base.ints = newInts;
  88             base.parts = newParts;
  89             base.matcher = matchers.base6;
  90         }
  91         // Detect empty entropy
  92         if (base.parts.length == 0) {
  93             return {
  94                 binaryStr: "",
  95                 cleanStr: "",
  96                 cleanHtml: "",
  97                 base: base,
  98             };
  99         }
 100         // Convert base.ints to BigInteger.
 101         // Due to using unusual bases, eg cards of base52, this is not as simple as
 102         // using BigInteger.parse()
 103         var entropyInt = BigInteger.ZERO;
 104         for (var i=base.ints.length-1; i>=0; i--) {
 105             var thisInt = BigInteger.parse(base.ints[i]);
 106             var power = (base.ints.length - 1) - i;
 107             var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
 108             entropyInt = entropyInt.add(additionalEntropy);
 109         }
 110         // Convert entropy to binary
 111         var entropyBin = entropyInt.toString(2);
 112         // If the first integer is small, it must be padded with zeros.
 113         // Otherwise the chance of the first bit being 1 is 100%, which is
 114         // obviously incorrect.
 115         // This is not perfect for non-2^n bases.
 116         var expectedBits = Math.floor(base.parts.length * Math.log2(base.asInt));
 117         while (entropyBin.length < expectedBits) {
 118             entropyBin = "0" + entropyBin;
 119         }
 120         // Assume cards are NOT replaced.
 121         // Additional entropy decreases as more cards are used. This means
 122         // entropy is measured using n!, not base^n.
 123         // eg the second last card can be only one of two, not one of fifty two
 124         // so the added entropy for that card is only one bit at most
 125         if (base.asInt == 52) {
 126             // Get the maximum value without replacement
 127             var totalDecks = Math.ceil(base.parts.length / 52);
 128             var totalCards = totalDecks * 52;
 129             var totalCombos = factorial(52).pow(totalDecks);
 130             var totalRemainingCards = totalCards - base.parts.length;
 131             var remainingDecks = Math.floor(totalRemainingCards / 52);
 132             var remainingCards = totalRemainingCards % 52;
 133             var remainingCombos = factorial(52).pow(remainingDecks).multiply(factorial(remainingCards));
 134             var currentCombos = totalCombos.divide(remainingCombos);
 135             var numberOfBits = Math.log2(currentCombos);
 136             var maxWithoutReplace = BigInteger.pow(2, numberOfBits);
 137             // aggresive flooring of numberOfBits by BigInteger.pow means a
 138             // more accurate result can be had for small numbers using the
 139             // built-in Math.pow function.
 140             if (numberOfBits < 32) {
 141                 maxWithoutReplace = BigInteger(Math.round(Math.pow(2, numberOfBits)));
 142             }
 143             // Get the maximum value with replacement
 144             var maxWithReplace = BigInteger.pow(52, base.parts.length);
 145             // Calculate the new value by scaling the original value down
 146             var withoutReplace = entropyInt.multiply(maxWithoutReplace).divide(maxWithReplace);
 147             // Left pad with zeros based on number of bits
 148             var entropyBin = withoutReplace.toString(2);
 149             var numberOfBitsInt = Math.floor(numberOfBits);
 150             while (entropyBin.length < numberOfBitsInt) {
 151                 entropyBin = "0" + entropyBin;
 152             }
 153         }
 154         // Supply a 'filtered' entropy string for display purposes
 155         var entropyClean = base.parts.join("");
 156         var entropyHtml = base.parts.join("");
 157         if (base.asInt == 52) {
 158             entropyClean = base.parts.join(" ").toUpperCase();
 159             entropyClean = entropyClean.replace(/C/g, "\u2663");
 160             entropyClean = entropyClean.replace(/D/g, "\u2666");
 161             entropyClean = entropyClean.replace(/H/g, "\u2665");
 162             entropyClean = entropyClean.replace(/S/g, "\u2660");
 163             entropyHtml = base.parts.join(" ").toUpperCase();
 164             entropyHtml = entropyHtml.replace(/C/g, "<span class='card-suit club'>\u2663</span>");
 165             entropyHtml = entropyHtml.replace(/D/g, "<span class='card-suit diamond'>\u2666</span>");
 166             entropyHtml = entropyHtml.replace(/H/g, "<span class='card-suit heart'>\u2665</span>");
 167             entropyHtml = entropyHtml.replace(/S/g, "<span class='card-suit spade'>\u2660</span>");
 168         }
 169         var e = {
 170             binaryStr: entropyBin,
 171             cleanStr: entropyClean,
 172             cleanHtml: entropyHtml,
 173             base: base,
 174         }
 175         return e;
 176     }
 177
 178     function getBase(str) {
 179         // Need to get the lowest base for the supplied entropy.
 180         // This prevents interpreting, say, dice rolls as hexadecimal.
 181         var binaryMatches = matchers.binary(str);
 182         var hexMatches = matchers.hex(str);
 183         // Find the lowest base that can be used, whilst ignoring any irrelevant chars
 184         if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) {
 185             var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
 186             return {
 187                 ints: ints,
 188                 parts: binaryMatches,
 189                 matcher: matchers.binary,
 190                 asInt: 2,
 191                 str: "binary",
 192             }
 193         }
 194         var cardMatches = matchers.card(str);
 195         if (cardMatches.length >= hexMatches.length / 2) {
 196             var ints = convertCardsToInts(cardMatches);
 197             return {
 198                 ints: ints,
 199                 parts: cardMatches,
 200                 matcher: matchers.card,
 201                 asInt: 52,
 202                 str: "card",
 203             }
 204         }
 205         var diceMatches = matchers.dice(str);
 206         if (diceMatches.length == hexMatches.length && hexMatches.length > 0) {
 207             var ints = diceMatches.map(function(i) { return parseInt(i) });
 208             return {
 209                 ints: ints,
 210                 parts: diceMatches,
 211                 matcher: matchers.dice,
 212                 asInt: 6,
 213                 str: "dice",
 214             }
 215         }
 216         var base6Matches = matchers.base6(str);
 217         if (base6Matches.length == hexMatches.length && hexMatches.length > 0) {
 218             var ints = base6Matches.map(function(i) { return parseInt(i) });
 219             return {
 220                 ints: ints,
 221                 parts: base6Matches,
 222                 matcher: matchers.base6,
 223                 asInt: 6,
 224                 str: "base 6",
 225             }
 226         }
 227         var base10Matches = matchers.base10(str);
 228         if (base10Matches.length == hexMatches.length && hexMatches.length > 0) {
 229             var ints = base10Matches.map(function(i) { return parseInt(i) });
 230             return {
 231                 ints: ints,
 232                 parts: base10Matches,
 233                 matcher: matchers.base10,
 234                 asInt: 10,
 235                 str: "base 10",
 236             }
 237         }
 238         var ints = hexMatches.map(function(i) { return parseInt(i, 16) });
 239         return {
 240             ints: ints,
 241             parts: hexMatches,
 242             matcher: matchers.hex,
 243             asInt: 16,
 244             str: "hexadecimal",
 245         }
 246     }
 247
 248     // Polyfill for Math.log2
 249     // See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill
 250     Math.log2 = Math.log2 || function(x) {
 251         // The polyfill isn't good enough because of the poor accuracy of
 252         // Math.LOG2E
 253         // log2(8) gave 2.9999999999999996 which when floored causes issues.
 254         // So instead use the BigInteger library to get it right.
 255         return BigInteger.log(x) / BigInteger.log(2);
 256     };
 257
 258     // Depends on BigInteger
 259     function factorial(n) {
 260         if (n == 0) {
 261             return 1;
 262         }
 263         f = BigInteger.ONE;
 264         for (var i=1; i<=n; i++) {
 265             f = f.multiply(new BigInteger(i));
 266         }
 267         return f;
 268     }
 269
 270 })();