* dice 6 [1-6]
* decimal [0-9]
* hexadecimal [0-9A-F]
+ * card [A2-9TJQK][CDHS]
*
* Automatically uses lowest entropy to avoid issues such as interpretting 0101
* as hexadecimal which would be 16 bits when really it's only 4 bits of binary
window.Entropy = new (function() {
+ var TWO = new libs.BigInteger.BigInteger(2);
+
// matchers returns an array of the matched events for each type of entropy.
// eg
// matchers.binary("010") returns ["0", "1", "0"]
return ints;
}
- this.fromString = function(rawEntropyStr) {
+ this.fromString = function(rawEntropyStr, baseStr) {
// Find type of entropy being used (binary, hex, dice etc)
- var base = getBase(rawEntropyStr);
+ 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") {
// 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 = BigInteger.ZERO;
+ var entropyInt = libs.BigInteger.BigInteger.ZERO;
for (var i=base.ints.length-1; i>=0; i--) {
- var thisInt = BigInteger.parse(base.ints[i]);
+ var thisInt = libs.BigInteger.BigInteger.parse(base.ints[i]);
var power = (base.ints.length - 1) - i;
- var additionalEntropy = BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
+ var additionalEntropy = libs.BigInteger.BigInteger.parse(base.asInt).pow(power).multiply(thisInt);
entropyInt = entropyInt.add(additionalEntropy);
}
// Convert entropy to binary
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;
+ }
// Supply a 'filtered' entropy string for display purposes
var entropyClean = base.parts.join("");
var entropyHtml = base.parts.join("");
entropyHtml = entropyHtml.replace(/H/g, "<span class='card-suit heart'>\u2665</span>");
entropyHtml = entropyHtml.replace(/S/g, "<span class='card-suit spade'>\u2660</span>");
}
+ // Return the result
var e = {
binaryStr: entropyBin,
cleanStr: entropyClean,
cleanHtml: entropyHtml,
+ bitsPerEvent: bitsPerEvent,
base: base,
}
return e;
}
- function getBase(str) {
+ 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 binaryMatches = matchers.binary(str);
var hexMatches = matchers.hex(str);
+ var autodetect = baseStr === undefined;
// Find the lowest base that can be used, whilst ignoring any irrelevant chars
- if (binaryMatches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((binaryMatches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "binary") {
var ints = binaryMatches.map(function(i) { return parseInt(i, 2) });
return {
ints: ints,
}
}
var cardMatches = matchers.card(str);
- if (cardMatches.length >= hexMatches.length / 2) {
+ if ((cardMatches.length >= hexMatches.length / 2 && autodetect) || baseStr === "card") {
var ints = convertCardsToInts(cardMatches);
return {
ints: ints,
}
}
var diceMatches = matchers.dice(str);
- if (diceMatches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((diceMatches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "dice") {
var ints = diceMatches.map(function(i) { return parseInt(i) });
return {
ints: ints,
}
}
var base6Matches = matchers.base6(str);
- if (base6Matches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((base6Matches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "base 6") {
var ints = base6Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
}
}
var base10Matches = matchers.base10(str);
- if (base10Matches.length == hexMatches.length && hexMatches.length > 0) {
+ if ((base10Matches.length == hexMatches.length && hexMatches.length > 0 && autodetect) || baseStr === "base 10") {
var ints = base10Matches.map(function(i) { return parseInt(i) });
return {
ints: ints,
}
}
+ // 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) {
// Math.LOG2E
// log2(8) gave 2.9999999999999996 which when floored causes issues.
// So instead use the BigInteger library to get it right.
- return BigInteger.log(x) / BigInteger.log(2);
+ 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