From: Ian Coleman <coleman.ian@gmail.com>
Date: Wed, 16 Nov 2016 01:21:17 +0000 (+1100)
Subject: Multiple decks of cards are possible
X-Git-Url: https://git.immae.eu/?a=commitdiff_plain;h=fc8c40413313d83c3bce334fbab2fa866751713e;p=perso%2FImmae%2FProjets%2FCryptomonnaies%2FBIP39.git

Multiple decks of cards are possible

but also a needless oversupply of entropy
---

diff --git a/src/js/index.js b/src/js/index.js
index dbbd382..f354399 100644
--- a/src/js/index.js
+++ b/src/js/index.js
@@ -846,9 +846,13 @@
         // 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 (entropy.base.asInt == 52) {
-            var totalCombos = factorial(52);
-            var remainingCards = 52 - entropy.base.parts.length;
-            var remainingCombos = factorial(remainingCards);
+            var totalDecks = Math.ceil(entropy.base.parts.length / 52);
+            var totalCards = totalDecks * 52;
+            var totalCombos = factorial(52).pow(totalDecks);
+            var totalRemainingCards = totalCards - entropy.base.parts.length;
+            var remainingDecks = Math.floor(totalRemainingCards / 52);
+            var remainingCards = totalRemainingCards % 52;
+            var remainingCombos = factorial(52).pow(remainingDecks) * factorial(remainingCards);
             var currentCombos = totalCombos.divide(remainingCombos);
             bitsStr = currentCombos.toString(2).length.toString();
         }
diff --git a/tests.js b/tests.js
index 1b1d445..189f1ea 100644
--- a/tests.js
+++ b/tests.js
@@ -2644,7 +2644,7 @@ page.open(url, function(status) {
             entropy: "ac2c3c4c5c6c7c8c9ctcjcqckcad2d3d4d5d6d7d8d9dtdjdqdkdah2h3h4h5h6h7h8h9hthjhqhkhas2s3s4s5s6s7s8s9stsjsqsks3d",
             type: "card (full deck, 1 duplicate: 3d)",
             events: 53,
-            bits: 226,
+            bits: 232,
             words: 27,
             strength: "extremely strong",
         },
@@ -2652,7 +2652,7 @@ page.open(url, function(status) {
             entropy: "ac2c3c4c5c6c7c8c9ctcjcqckcad2d3d4d5d6d7d8d9dtdjdqdkdah2h3h4h5h6h7h8h9hthjhqhkhas2s3s4s5s6s7s8s9stsjsqs3d4d",
             type: "card (2 duplicates: 3d 4d)",
             events: 53,
-            bits: 226,
+            bits: 232,
             words: 27,
             strength: "extremely strong",
         },
@@ -2660,7 +2660,7 @@ page.open(url, function(status) {
             entropy: "ac2c3c4c5c6c7c8c9ctcjcqckcad2d3d4d5d6d7d8d9dtdjdqdkdah2h3h4h5h6h7h8h9hthjhqhkhas2s3s4s5s6s7s8s9stsjsqs3d4d5d6d",
             type: "card (4 duplicates: 3d 4d 5d...)",
             events: 53,
-            bits: 226,
+            bits: 243,
             words: 27,
             strength: "extremely strong",
         },
@@ -2669,7 +2669,7 @@ page.open(url, function(status) {
             entropy: "ac2c3c4c5c6c7c8c9ctcjcqckcad2d3d4d5d6d7d8d9dtdjdqdkdah2h3h4h5h6h7h8h9hthjhqhkhas2s3s4s5s6s7s8s9stsjsqsksac2c3c4c5c6c7c8c9ctcjcqckcad2d3d4d5d6d7d8d9dtdjdqdkdah2h3h4h5h6h7h8h9hthjhqhkhas2s3s4s5s6s7s8s9stsjsqsks",
             type: "card (full deck, 52 duplicates: ac 2c 3c...)",
             events: 104,
-            bits: 226,
+            bits: 452,
             words: 54,
             strength: "extremely strong",
         },