* 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 BigInteger(2);
+
// matchers returns an array of the matched events for each type of entropy.
// eg
// matchers.binary("010") returns ["0", "1", "0"]
while (entropyBin.length < expectedBits) {
entropyBin = "0" + entropyBin;
}
+ // 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
+ if (base.asInt == 52) {
+ var totalDecks = Math.ceil(base.parts.length / 52);
+ var totalCards = totalDecks * 52;
+ var totalCombos = factorial(52).pow(totalDecks);
+ var totalRemainingCards = totalCards - base.parts.length;
+ var remainingDecks = Math.floor(totalRemainingCards / 52);
+ var remainingCards = totalRemainingCards % 52;
+ var remainingCombos = factorial(52).pow(remainingDecks).multiply(factorial(remainingCards));
+ var currentCombos = totalCombos.divide(remainingCombos);
+ var numberOfBits = Math.log2(currentCombos);
+ var maxWithoutReplace = BigInteger.pow(2, numberOfBits);
+ // Use a bunch of sorted decks to measure entropy from, populated
+ // as needed.
+ var sortedDecks = [];
+ // Initialize the final entropy value for these cards
+ var entropyInt = BigInteger.ZERO;
+ // Track how many instances of each card have been used, and thus
+ // how many decks are in use.
+ var cardCounts = {};
+ // Track the total bits of entropy that remain, which diminishes as
+ // each card is drawn.
+ var totalBitsLeft = numberOfBits;
+ // Work out entropy contribution of each card drawn
+ for (var i=0; i<base.parts.length; i++) {
+ // Get the card that was drawn
+ var cardLower = base.parts[i];
+ var card = cardLower.toUpperCase();
+ // Initialize the deck for this card if needed, to track how
+ // much entropy it adds.
+ if (!(card in cardCounts)) {
+ cardCounts[card] = 0;
+ }
+ // Get the deck this card is from
+ var deckIndex = cardCounts[card];
+ while (deckIndex > sortedDecks.length-1) {
+ sortedDecks.push(getSortedDeck());
+ }
+ // See how many bits this card contributes (depends on how many
+ // are left in the deck it's from)
+ var deckForCard = sortedDecks[deckIndex];
+ var cardsLeftInDeck = deckForCard.length;
+ var additionalBits = Math.log2(cardsLeftInDeck);
+ // Work out the min and max value for this card
+ var nextTotalBitsLeft = totalBitsLeft - additionalBits;
+ var minPossibleNewEntropy = TWO.pow(nextTotalBitsLeft).subtract(1);
+ var maxPossibleNewEntropy = TWO.pow(totalBitsLeft).subtract(1);
+ var diff = maxPossibleNewEntropy.subtract(minPossibleNewEntropy);
+ // BigInteger aggresively floors numbers which greatly affects
+ // the small numbers. In that case, use native Math library
+ var useBigInt = totalBitsLeft >= 32;
+ if (!useBigInt) {
+ minPossibleNewEntropy = Math.round(Math.pow(2, nextTotalBitsLeft)-1);
+ maxPossibleNewEntropy = Math.round(Math.pow(2, totalBitsLeft)-1);
+ diff = maxPossibleNewEntropy - minPossibleNewEntropy;
+ }
+ // Scale the value between possible min and max depending on
+ // this card value
+ var thisCardIndex = deckForCard.indexOf(card);
+ var toAdd = BigInteger.ZERO;
+ if (cardsLeftInDeck > 1) {
+ if (useBigInt) {
+ toAdd = diff.multiply(thisCardIndex)
+ .divide(deckForCard.length - 1)
+ .add(minPossibleNewEntropy);
+ }
+ else {
+ var ratio = thisCardIndex / (deckForCard.length -1);
+ var f = diff * ratio;
+ toAdd = new BigInteger(f).add(minPossibleNewEntropy);
+ }
+ }
+ // Add this card entropy to existing entropy
+ entropyInt = entropyInt.add(toAdd);
+ // Remove this card from the deck it comes from
+ deckForCard.splice(thisCardIndex,1);
+ // Ensure the next insance of this card uses the next deck
+ cardCounts[card] = cardCounts[card] + 1;
+ // Next card drawn has less total remaining bits to work with
+ totalBitsLeft = nextTotalBitsLeft;
+ }
+ // Convert to binary
+ var entropyBin = entropyInt.toString(2);
+ var numberOfBitsInt = Math.floor(numberOfBits);
+ while (entropyBin.length < numberOfBitsInt) {
+ entropyBin = "0" + entropyBin;
+ }
+ }
// 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,
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) {
// Need to get the lowest base for the supplied entropy.
// This prevents interpreting, say, dice rolls as hexadecimal.
return BigInteger.log(x) / BigInteger.log(2);
};
+ // Depends on BigInteger
+ function factorial(n) {
+ if (n == 0) {
+ return 1;
+ }
+ f = BigInteger.ONE;
+ for (var i=1; i<=n; i++) {
+ f = f.multiply(new BigInteger(i));
+ }
+ return f;
+ }
+
})();
projects / perso / Immae / Projets / Cryptomonnaies / BIP39.git / blobdiff