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  * card [A2-9TJQK][CDHS]
  11  *
  12  * Automatically uses lowest entropy to avoid issues such as interpretting 0101
  13  * as hexadecimal which would be 16 bits when really it's only 4 bits of binary
  14  * entropy.
  15  */
  16
  17 window.Entropy = new (function() {
  18
  19     var TWO = new BigInteger(2);
  20
  21     // matchers returns an array of the matched events for each type of entropy.
  22     // eg
  23     // matchers.binary("010") returns ["0", "1", "0"]
  24     // matchers.binary("a10") returns ["1", "0"]
  25     // matchers.hex("a10") returns ["a", "1", "0"]
  26     var matchers = {
  27         binary: function(str) {
  28             return str.match(/[0-1]/gi) || [];
  29         },
  30         base6: function(str) {
  31             return str.match(/[0-5]/gi) || [];
  32         },
  33         dice: function(str) {
  34             return str.match(/[1-6]/gi) || []; // ie dice numbers
  35         },
  36         base10: function(str) {
  37             return str.match(/[0-9]/gi) || [];
  38         },
  39         hex: function(str) {
  40             return str.match(/[0-9A-F]/gi) || [];
  41         },
  42         card: function(str) {
  43             // Format is NumberSuit, eg
  44             // AH ace of hearts
  45             // 8C eight of clubs
  46             // TD ten of diamonds
  47             // JS jack of spades
  48             // QH queen of hearts
  49             // KC king of clubs
  50             return str.match(/([A2-9TJQK][CDHS])/gi) || [];
  51         }
  52     }
  53
  54     // Convert array of cards from ["ac", "4d", "ks"]
  55     // to numbers between 0 and 51 [0, 16, 51]
  56     function convertCardsToInts(cards) {
  57         var ints = [];
  58         var values = "a23456789tjqk";
  59         var suits = "cdhs";
  60         for (var i=0; i<cards.length; i++) {
  61             var card = cards[i].toLowerCase();
  62             var value = card[0];
  63             var suit = card[1];
  64             var asInt = 13 * suits.indexOf(suit) + values.indexOf(value);
  65             ints.push(asInt);
  66         }
  67         return ints;
  68     }
  69
  70     this.fromString = function(rawEntropyStr) {
  71         // Find type of entropy being used (binary, hex, dice etc)
  72         var base = getBase(rawEntropyStr);
  73         // Convert dice to base6 entropy (ie 1-6 to 0-5)
  74         // This is done by changing all 6s to 0s
  75         if (base.str == "dice") {
  76             var newParts = [];
  77             var newInts = [];
  78             for (var i=0; i<base.parts.length; i++) {
  79                 var c = base.parts[i];
  80                 if ("12345".indexOf(c) > -1) {
  81                     newParts[i] = base.parts[i];
  82                     newInts[i] = base.ints[i];
  83                 }
  84                 else {
  85                     newParts[i] = "0";
  86                     newInts[i] = 0;
  87                 }
  88             }
  89             base.str = "base 6 (dice)";
  90             base.ints = newInts;
  91             base.parts = newParts;
  92             base.matcher = matchers.base6;
  93         }
  94         // Detect empty entropy
  95         if (base.parts.length == 0) {
  96             return {
  97                 binaryStr: "",
  98                 cleanStr: "",
  99                 cleanHtml: "",
 100                 base: base,
 101             };
 102         }
 103         // Convert base.ints to BigInteger.
 104         // Due to using unusual bases, eg cards of base52, this is not as simple as
 105         // using BigInteger.parse()
 106         var entropyInt = BigInteger.ZERO;
 107         for (var i=base.ints.length-1; i>=0; i--) {
 108             var thisInt = BigInteger.parse(base.ints[i]);
 109             var power = (base.ints.length - 1) - i;
 110             var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
 111             entropyInt = entropyInt.add(additionalEntropy);
 112         }
 113         // Convert entropy to binary
 114         var entropyBin = entropyInt.toString(2);
 115         // If the first integer is small, it must be padded with zeros.
 116         // Otherwise the chance of the first bit being 1 is 100%, which is
 117         // obviously incorrect.
 118         // This is not perfect for non-2^n bases.
 119         var expectedBits = Math.floor(base.parts.length * Math.log2(base.asInt));
 120         while (entropyBin.length < expectedBits) {
 121             entropyBin = "0" + entropyBin;
 122         }
 123         // Cards binary must be handled differently, since they're not replaced
 124         if (base.asInt == 52) {
 125             entropyBin = getCardBinary(base.parts);
 126         }
 127         // Supply a 'filtered' entropy string for display purposes
 128         var entropyClean = base.parts.join("");
 129         var entropyHtml = base.parts.join("");
 130         if (base.asInt == 52) {
 131             entropyClean = base.parts.join(" ").toUpperCase();
 132             entropyClean = entropyClean.replace(/C/g, "\u2663");
 133             entropyClean = entropyClean.replace(/D/g, "\u2666");
 134             entropyClean = entropyClean.replace(/H/g, "\u2665");
 135             entropyClean = entropyClean.replace(/S/g, "\u2660");
 136             entropyHtml = base.parts.join(" ").toUpperCase();
 137             entropyHtml = entropyHtml.replace(/C/g, "<span class='card-suit club'>\u2663</span>");
 138             entropyHtml = entropyHtml.replace(/D/g, "<span class='card-suit diamond'>\u2666</span>");
 139             entropyHtml = entropyHtml.replace(/H/g, "<span class='card-suit heart'>\u2665</span>");
 140             entropyHtml = entropyHtml.replace(/S/g, "<span class='card-suit spade'>\u2660</span>");
 141         }
 142         // Return the result
 143         var e = {
 144             binaryStr: entropyBin,
 145             cleanStr: entropyClean,
 146             cleanHtml: entropyHtml,
 147             base: base,
 148         }
 149         return e;
 150     }
 151
 152     function getSortedDeck() {
 153         var s = [];
 154         var suits = "CDHS";
 155         var values = "A23456789TJQK";
 156         for (var i=0; i<suits.length; i++) {
 157             for (var j=0; j<values.length; j++) {
 158                 s.push(values[j]+suits[i]);
 159             }
 160         }
 161         return s;
 162     }
 163
 164     function getBase(str) {
 165         // Need to get the lowest base for the supplied entropy.
 166         // This prevents interpreting, say, dice rolls as hexadecimal.
 167         var binaryMatches = matchers.binary(str);
 168         var hexMatches = matchers.hex(str);
 169         // Find the lowest base that can be used, whilst ignoring any irrelevant chars
 170         if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) {
 171             var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
 172             return {
 173                 ints: ints,
 174                 parts: binaryMatches,
 175                 matcher: matchers.binary,
 176                 asInt: 2,
 177                 str: "binary",
 178             }
 179         }
 180         var cardMatches = matchers.card(str);
 181         if (cardMatches.length >= hexMatches.length / 2) {
 182             var ints = convertCardsToInts(cardMatches);
 183             return {
 184                 ints: ints,
 185                 parts: cardMatches,
 186                 matcher: matchers.card,
 187                 asInt: 52,
 188                 str: "card",
 189             }
 190         }
 191         var diceMatches = matchers.dice(str);
 192         if (diceMatches.length == hexMatches.length && hexMatches.length > 0) {
 193             var ints = diceMatches.map(function(i) { return parseInt(i) });
 194             return {
 195                 ints: ints,
 196                 parts: diceMatches,
 197                 matcher: matchers.dice,
 198                 asInt: 6,
 199                 str: "dice",
 200             }
 201         }
 202         var base6Matches = matchers.base6(str);
 203         if (base6Matches.length == hexMatches.length && hexMatches.length > 0) {
 204             var ints = base6Matches.map(function(i) { return parseInt(i) });
 205             return {
 206                 ints: ints,
 207                 parts: base6Matches,
 208                 matcher: matchers.base6,
 209                 asInt: 6,
 210                 str: "base 6",
 211             }
 212         }
 213         var base10Matches = matchers.base10(str);
 214         if (base10Matches.length == hexMatches.length && hexMatches.length > 0) {
 215             var ints = base10Matches.map(function(i) { return parseInt(i) });
 216             return {
 217                 ints: ints,
 218                 parts: base10Matches,
 219                 matcher: matchers.base10,
 220                 asInt: 10,
 221                 str: "base 10",
 222             }
 223         }
 224         var ints = hexMatches.map(function(i) { return parseInt(i, 16) });
 225         return {
 226             ints: ints,
 227             parts: hexMatches,
 228             matcher: matchers.hex,
 229             asInt: 16,
 230             str: "hexadecimal",
 231         }
 232     }
 233
 234     // Assume cards are NOT replaced.
 235     // Additional entropy decreases as more cards are used. This means
 236     // total possible entropy is measured using n!, not base^n.
 237     // eg the second last card can be only one of two, not one of fifty two
 238     // so the added entropy for that card is only one bit at most
 239     function getCardBinary(cards) {
 240         // Track how many instances of each card have been used, and thus
 241         // how many decks are in use.
 242         var cardCounts = {};
 243         var numberOfDecks = 0;
 244         // Work out number of decks by max(duplicates)
 245         for (var i=0; i<cards.length; i++) {
 246             // Get the card that was drawn
 247             var cardLower = cards[i];
 248             var card = cardLower.toUpperCase();
 249             // Initialize the count for this card if needed
 250             if (!(card in cardCounts)) {
 251                 cardCounts[card] = 0;
 252             }
 253             cardCounts[card] += 1;
 254             // See if this is max(duplicates)
 255             if (cardCounts[card] > numberOfDecks) {
 256                 numberOfDecks = cardCounts[card];
 257             }
 258         }
 259         // Work out the total number of bits for this many decks
 260         // See http://crypto.stackexchange.com/q/41886
 261         var gainedBits = Math.log2(factorial(52 * numberOfDecks));
 262         var lostBits = 52 * Math.log2(factorial(numberOfDecks));
 263         var maxBits = gainedBits - lostBits;
 264         // Convert the drawn cards to a binary representation.
 265         // The exact technique for doing this is unclear.
 266         // See
 267         // http://crypto.stackexchange.com/a/41896
 268         // "I even doubt that this is well defined (only the average entropy
 269         // is, I believe)."
 270         // See
 271         // https://github.com/iancoleman/bip39/issues/33#issuecomment-263021856
 272         // "The binary representation can be the first log(permutations,2) bits
 273         // of the sha-2 hash of the normalized deck string."
 274         //
 275         // In this specific implementation, the first N bits of the hash of the
 276         // normalized cards string is being used. Uppercase, no spaces; eg
 277         // sha256("AH8DQSTC2H")
 278         var totalCards = numberOfDecks * 52;
 279         var percentUsed = cards.length / totalCards;
 280         // Calculate the average number of bits of entropy for the number of
 281         // cards drawn.
 282         var numberOfBits = Math.floor(maxBits * percentUsed);
 283         // Create a normalized string of the selected cards
 284         var normalizedCards = cards.join("").toUpperCase();
 285         // Convert to binary using the SHA256 hash of the normalized cards.
 286         // If the number of bits is more than 256, multiple rounds of hashing
 287         // are used until the required number of bits is reached.
 288         var entropyBin = "";
 289         var iterations = 0;
 290         while (entropyBin.length < numberOfBits) {
 291             var hashedCards = sjcl.hash.sha256.hash(normalizedCards);
 292             for (var j=0; j<iterations; j++) {
 293                 hashedCards = sjcl.hash.sha256.hash(hashedCards);
 294             }
 295             var hashHex = sjcl.codec.hex.fromBits(hashedCards);
 296             for (var i=0; i<hashHex.length; i++) {
 297                 var decimal = parseInt(hashHex[i], 16);
 298                 var binary = decimal.toString(2);
 299                 while (binary.length < 4) {
 300                     binary = "0" + binary;
 301                 }
 302                 entropyBin = entropyBin + binary;
 303             }
 304             iterations = iterations + 1;
 305         }
 306         // Truncate to the appropriate number of bits.
 307         entropyBin = entropyBin.substring(0, numberOfBits);
 308         return entropyBin;
 309     }
 310
 311     // Polyfill for Math.log2
 312     // See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log2#Polyfill
 313     Math.log2 = Math.log2 || function(x) {
 314         // The polyfill isn't good enough because of the poor accuracy of
 315         // Math.LOG2E
 316         // log2(8) gave 2.9999999999999996 which when floored causes issues.
 317         // So instead use the BigInteger library to get it right.
 318         return BigInteger.log(x) / BigInteger.log(2);
 319     };
 320
 321     // Depends on BigInteger
 322     function factorial(n) {
 323         if (n == 0) {
 324             return 1;
 325         }
 326         f = BigInteger.ONE;
 327         for (var i=1; i<=n; i++) {
 328             f = f.multiply(new BigInteger(i));
 329         }
 330         return f;
 331     }
 332
 333 })();