window.Entropy = new (function() {
- var TWO = new libs.BigInteger.BigInteger(2);
+ let eventBits = {
+
+ "binary": {
+ "0": "0",
+ "1": "1",
+ },
+
+ // log2(6) = 2.58496 bits per roll, with bias
+ // 4 rolls give 2 bits each
+ // 2 rolls give 1 bit each
+ // Average (4*2 + 2*1) / 6 = 1.66 bits per roll without bias
+ "base 6": {
+ "0": "00",
+ "1": "01",
+ "2": "10",
+ "3": "11",
+ "4": "0",
+ "5": "1",
+ },
+
+ // log2(6) = 2.58496 bits per roll, with bias
+ // 4 rolls give 2 bits each
+ // 2 rolls give 1 bit each
+ // Average (4*2 + 2*1) / 6 = 1.66 bits per roll without bias
+ "base 6 (dice)": {
+ "0": "00", // equivalent to 0 in base 6
+ "1": "01",
+ "2": "10",
+ "3": "11",
+ "4": "0",
+ "5": "1",
+ },
+
+ // log2(10) = 3.321928 bits per digit, with bias
+ // 8 digits give 3 bits each
+ // 2 digits give 1 bit each
+ // Average (8*3 + 2*1) / 10 = 2.6 bits per digit without bias
+ "base 10": {
+ "0": "000",
+ "1": "001",
+ "2": "010",
+ "3": "011",
+ "4": "100",
+ "5": "101",
+ "6": "110",
+ "7": "111",
+ "8": "0",
+ "9": "1",
+ },
+
+ "hexadecimal": {
+ "0": "0000",
+ "1": "0001",
+ "2": "0010",
+ "3": "0011",
+ "4": "0100",
+ "5": "0101",
+ "6": "0110",
+ "7": "0111",
+ "8": "1000",
+ "9": "1001",
+ "a": "1010",
+ "b": "1011",
+ "c": "1100",
+ "d": "1101",
+ "e": "1110",
+ "f": "1111",
+ },
+
+ // log2(52) = 5.7004 bits per card, with bias
+ // 32 cards give 5 bits each
+ // 16 cards give 4 bits each
+ // 4 cards give 2 bits each
+ // Average (32*5 + 16*4 + 4*2) / 52 = 4.46 bits per card without bias
+ "card": {
+ "ac": "00000",
+ "2c": "00001",
+ "3c": "00010",
+ "4c": "00011",
+ "5c": "00100",
+ "6c": "00101",
+ "7c": "00110",
+ "8c": "00111",
+ "9c": "01000",
+ "tc": "01001",
+ "jc": "01010",
+ "qc": "01011",
+ "kc": "01100",
+ "ad": "01101",
+ "2d": "01110",
+ "3d": "01111",
+ "4d": "10000",
+ "5d": "10001",
+ "6d": "10010",
+ "7d": "10011",
+ "8d": "10100",
+ "9d": "10101",
+ "td": "10110",
+ "jd": "10111",
+ "qd": "11000",
+ "kd": "11001",
+ "ah": "11010",
+ "2h": "11011",
+ "3h": "11100",
+ "4h": "11101",
+ "5h": "11110",
+ "6h": "11111",
+ "7h": "0000",
+ "8h": "0001",
+ "9h": "0010",
+ "th": "0011",
+ "jh": "0100",
+ "qh": "0101",
+ "kh": "0110",
+ "as": "0111",
+ "2s": "1000",
+ "3s": "1001",
+ "4s": "1010",
+ "5s": "1011",
+ "6s": "1100",
+ "7s": "1101",
+ "8s": "1110",
+ "9s": "1111",
+ "ts": "00",
+ "js": "01",
+ "qs": "10",
+ "ks": "11",
+ },
+
+ }
// matchers returns an array of the matched events for each type of entropy.
// eg
}
}
- // Convert array of cards from ["ac", "4d", "ks"]
- // to numbers between 0 and 51 [0, 16, 51]
- function convertCardsToInts(cards) {
- var ints = [];
- var values = "a23456789tjqk";
- var suits = "cdhs";
- for (var i=0; i<cards.length; i++) {
- var card = cards[i].toLowerCase();
- var value = card[0];
- var suit = card[1];
- var asInt = 13 * suits.indexOf(suit) + values.indexOf(value);
- ints.push(asInt);
- }
- return ints;
- }
-
this.fromString = function(rawEntropyStr, baseStr) {
// Find type of entropy being used (binary, hex, dice etc)
var base = getBase(rawEntropyStr, baseStr);
// Convert dice to base6 entropy (ie 1-6 to 0-5)
// This is done by changing all 6s to 0s
if (base.str == "dice") {
- var newParts = [];
- var newInts = [];
- for (var i=0; i<base.parts.length; i++) {
- var c = base.parts[i];
+ var newEvents = [];
+ for (var i=0; i<base.events.length; i++) {
+ var c = base.events[i];
if ("12345".indexOf(c) > -1) {
- newParts[i] = base.parts[i];
- newInts[i] = base.ints[i];
+ newEvents[i] = base.events[i];
}
else {
- newParts[i] = "0";
- newInts[i] = 0;
+ newEvents[i] = "0";
}
}
base.str = "base 6 (dice)";
- base.ints = newInts;
- base.parts = newParts;
+ base.events = newEvents;
base.matcher = matchers.base6;
}
// Detect empty entropy
- if (base.parts.length == 0) {
+ if (base.events.length == 0) {
return {
binaryStr: "",
cleanStr: "",
base: base,
};
}
- // Convert base.ints to BigInteger.
- // Due to using unusual bases, eg cards of base52, this is not as simple as
- // using BigInteger.parse()
- var entropyInt = libs.BigInteger.BigInteger.ZERO;
- for (var i=base.ints.length-1; i>=0; i--) {
- var thisInt = libs.BigInteger.BigInteger.parse(base.ints[i]);
- var power = (base.ints.length - 1) - i;
- var additionalEntropy = libs.BigInteger.BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
- entropyInt = entropyInt.add(additionalEntropy);
- }
- // Convert entropy to binary
- var entropyBin = entropyInt.toString(2);
- // If the first integer is small, it must be padded with zeros.
- // Otherwise the chance of the first bit being 1 is 100%, which is
- // obviously incorrect.
- // This is not perfect for non-2^n bases.
- var expectedBits = Math.floor(base.parts.length * Math.log2(base.asInt));
- while (entropyBin.length < expectedBits) {
- entropyBin = "0" + entropyBin;
- }
- // Calculate the number of bits per event
- var bitsPerEvent = Math.log2(base.asInt);
- // Cards binary must be handled differently, since they're not replaced
- if (base.asInt == 52) {
- var cardEntropy = processCardEntropy(base.parts);
- entropyBin = cardEntropy.binaryStr;
- bitsPerEvent = cardEntropy.bitsPerEvent;
- }
+ // Convert entropy events to binary
+ var entropyBin = base.events.map(function(e) {
+ return eventBits[base.str][e.toLowerCase()];
+ }).join("");
+ // Get average bits per event
+ // which may be adjusted for bias if log2(base) is fractional
+ var bitsPerEvent = base.bitsPerEvent;
// Supply a 'filtered' entropy string for display purposes
- var entropyClean = base.parts.join("");
- var entropyHtml = base.parts.join("");
+ var entropyClean = base.events.join("");
+ var entropyHtml = base.events.join("");
if (base.asInt == 52) {
- entropyClean = base.parts.join(" ").toUpperCase();
+ entropyClean = base.events.join(" ").toUpperCase();
entropyClean = entropyClean.replace(/C/g, "\u2663");
entropyClean = entropyClean.replace(/D/g, "\u2666");
entropyClean = entropyClean.replace(/H/g, "\u2665");
entropyClean = entropyClean.replace(/S/g, "\u2660");
- entropyHtml = base.parts.join(" ").toUpperCase();
+ entropyHtml = base.events.join(" ").toUpperCase();
entropyHtml = entropyHtml.replace(/C/g, "<span class='card-suit club'>\u2663</span>");
entropyHtml = entropyHtml.replace(/D/g, "<span class='card-suit diamond'>\u2666</span>");
entropyHtml = entropyHtml.replace(/H/g, "<span class='card-suit heart'>\u2665</span>");
return e;
}
- function getSortedDeck() {
- var s = [];
- var suits = "CDHS";
- var values = "A23456789TJQK";
- for (var i=0; i<suits.length; i++) {
- for (var j=0; j<values.length; j++) {
- s.push(values[j]+suits[i]);
- }
- }
- return s;
- }
-
function getBase(str, baseStr) {
// Need to get the lowest base for the supplied entropy.
// This prevents interpreting, say, dice rolls as hexadecimal.
var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
return {
ints: ints,
- parts: binaryMatches,
+ events: binaryMatches,
matcher: matchers.binary,
asInt: 2,
+ bitsPerEvent: 1,
str: "binary",
}
}
var cardMatches = matchers.card(str);
if ((cardMatches.length >= hexMatches.length / 2 && autodetect) || baseStr === "card") {
- var ints = convertCardsToInts(cardMatches);
return {
ints: ints,
- parts: cardMatches,
+ events: cardMatches,
matcher: matchers.card,
asInt: 52,
+ bitsPerEvent: (32*5 + 16*4 + 4*2) / 52, // see cardBits
str: "card",
}
}
var ints = diceMatches.map(function(i) { return parseInt(i) });
return {
ints: ints,
- parts: diceMatches,
+ events: diceMatches,
matcher: matchers.dice,
asInt: 6,
+ bitsPerEvent: (4*2 + 2*1) / 6, // see diceBits
str: "dice",
}
}
var ints = base6Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
- parts: base6Matches,
+ events: base6Matches,
matcher: matchers.base6,
asInt: 6,
+ bitsPerEvent: (4*2 + 2*1) / 6, // see diceBits
str: "base 6",
}
}
var ints = base10Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
- parts: base10Matches,
+ events: base10Matches,
matcher: matchers.base10,
asInt: 10,
+ bitsPerEvent: (8*3 + 2*1) / 10, // see b10Bits
str: "base 10",
}
}
var ints = hexMatches.map(function(i) { return parseInt(i, 16) });
return {
ints: ints,
- parts: hexMatches,
+ events: hexMatches,
matcher: matchers.hex,
asInt: 16,
+ bitsPerEvent: 4,
str: "hexadecimal",
}
}
- // Assume cards are NOT replaced.
- // Additional entropy decreases as more cards are used. This means
- // total possible entropy is measured using n!, not base^n.
- // eg the second last card can be only one of two, not one of fifty two
- // so the added entropy for that card is only one bit at most
- function processCardEntropy(cards) {
- // Track how many instances of each card have been used, and thus
- // how many decks are in use.
- var cardCounts = {};
- var numberOfDecks = 0;
- // Work out number of decks by max(duplicates)
- for (var i=0; i<cards.length; i++) {
- // Get the card that was drawn
- var cardLower = cards[i];
- var card = cardLower.toUpperCase();
- // Initialize the count for this card if needed
- if (!(card in cardCounts)) {
- cardCounts[card] = 0;
- }
- cardCounts[card] += 1;
- // See if this is max(duplicates)
- if (cardCounts[card] > numberOfDecks) {
- numberOfDecks = cardCounts[card];
- }
- }
- // Work out the total number of bits for this many decks
- // See http://crypto.stackexchange.com/q/41886
- var gainedBits = 0;
- // Equivalent of Math.log2(factorial(52*numberOfDecks))
- // which becomes infinity for numberOfDecks > 4
- for (var i=1; i<=52*numberOfDecks; i++) {
- gainedBits = gainedBits + Math.log2(i);
- }
- var lostBits = 52 * Math.log2(factorial(numberOfDecks));
- var maxBits = gainedBits - lostBits;
- // Convert the drawn cards to a binary representation.
- // The exact technique for doing this is unclear.
- // See
- // http://crypto.stackexchange.com/a/41896
- // "I even doubt that this is well defined (only the average entropy
- // is, I believe)."
- // See
- // https://github.com/iancoleman/bip39/issues/33#issuecomment-263021856
- // "The binary representation can be the first log(permutations,2) bits
- // of the sha-2 hash of the normalized deck string."
- //
- // In this specific implementation, the first N bits of the hash of the
- // normalized cards string is being used. Uppercase, no spaces; eg
- // sha256("AH8DQSTC2H")
- var totalCards = numberOfDecks * 52;
- var percentUsed = cards.length / totalCards;
- // Calculate the average number of bits of entropy for the number of
- // cards drawn.
- var numberOfBits = Math.floor(maxBits * percentUsed);
- // Create a normalized string of the selected cards
- var normalizedCards = cards.join("").toUpperCase();
- // Convert to binary using the SHA256 hash of the normalized cards.
- // If the number of bits is more than 256, multiple hashes
- // are used until the required number of bits is reached.
- var entropyBin = "";
- var iterations = 0;
- while (entropyBin.length < numberOfBits) {
- var hashedCards = sjcl.hash.sha256.hash(normalizedCards + ":" + iterations);
- var hashHex = sjcl.codec.hex.fromBits(hashedCards);
- for (var i=0; i<hashHex.length; i++) {
- var decimal = parseInt(hashHex[i], 16);
- var binary = decimal.toString(2);
- while (binary.length < 4) {
- binary = "0" + binary;
- }
- entropyBin = entropyBin + binary;
- }
- iterations = iterations + 1;
- }
- // Truncate to the appropriate number of bits.
- entropyBin = entropyBin.substring(0, numberOfBits);
- // Get the number of bits per event
- bitsPerEvent = maxBits / totalCards;
- return {
- binaryStr: entropyBin,
- bitsPerEvent: bitsPerEvent,
- }
- }
-
- // 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) {
- // The polyfill isn't good enough because of the poor accuracy of
- // Math.LOG2E
- // log2(8) gave 2.9999999999999996 which when floored causes issues.
- // So instead use the BigInteger library to get it right.
- return libs.BigInteger.BigInteger.log(x) / libs.BigInteger.BigInteger.log(2);
- };
-
- // Depends on BigInteger
- function factorial(n) {
- if (n == 0) {
- return 1;
- }
- f = libs.BigInteger.BigInteger.ONE;
- for (var i=1; i<=n; i++) {
- f = f.multiply(new libs.BigInteger.BigInteger(i));
- }
- return f;
- }
-
})();
projects / perso / Immae / Projets / Cryptomonnaies / BIP39.git / blobdiff