From fc7c248fafef4ba2aecf9dcf4718b3d4c91d94b0 Mon Sep 17 00:00:00 2001
From: Ian Coleman <coleman.ian@gmail.com>
Date: Wed, 30 Nov 2016 19:38:14 +1100
Subject: [PATCH 1/1] Entropy with more than 4 decks can be calculated

---
 bip39-standalone.html |  7 ++++-
 src/js/entropy.js     |  7 ++++-
 tests.js              | 59 ++++++++++++++++++++++++++++++++++++++-----
 3 files changed, 65 insertions(+), 8 deletions(-)

diff --git a/bip39-standalone.html b/bip39-standalone.html
index 4bad422..0da2443 100644
--- a/bip39-standalone.html
+++ b/bip39-standalone.html
@@ -18467,7 +18467,12 @@ window.Entropy = new (function() {
         }
         // Work out the total number of bits for this many decks
         // See http://crypto.stackexchange.com/q/41886
-        var gainedBits = Math.log2(factorial(52 * numberOfDecks));
+        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.
diff --git a/src/js/entropy.js b/src/js/entropy.js
index b7274bb..24fc21a 100644
--- a/src/js/entropy.js
+++ b/src/js/entropy.js
@@ -263,7 +263,12 @@ window.Entropy = new (function() {
         }
         // Work out the total number of bits for this many decks
         // See http://crypto.stackexchange.com/q/41886
-        var gainedBits = Math.log2(factorial(52 * numberOfDecks));
+        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.
diff --git a/tests.js b/tests.js
index 4f8f60f..843078f 100644
--- a/tests.js
+++ b/tests.js
@@ -2726,6 +2726,50 @@ page.open(url, function(status) {
             words: 18,
             strength: "extremely strong",
         },
+        // Multiple decks of cards increases bits per event
+        {
+            entropy: "3d",
+            events: 1,
+            bits: 4,
+            bitsPerEvent: 4.34,
+        },
+        {
+            entropy: "3d3d",
+            events: 2,
+            bits: 9,
+            bitsPerEvent: 4.80,
+        },
+        {
+            entropy: "3d3d3d",
+            events: 3,
+            bits: 15,
+            bitsPerEvent: 5.01,
+        },
+        {
+            entropy: "3d3d3d3d",
+            events: 4,
+            bits: 20,
+            bitsPerEvent: 5.14,
+        },
+        {
+            entropy: "3d3d3d3d3d",
+            events: 5,
+            bits: 26,
+            bitsPerEvent: 5.22,
+        },
+        {
+            entropy: "3d3d3d3d3d3d",
+            events: 6,
+            bits: 31,
+            bitsPerEvent: 5.28,
+        },
+        {
+            entropy: "3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d",
+            events: 33,
+            bits: 184,
+            bitsPerEvent: 5.59,
+            strength: 'easily cracked - Repeats like "abcabcabc" are only slightly harder to guess than "abc"',
+        },
     ];
     // use entropy
     page.evaluate(function() {
@@ -2737,18 +2781,21 @@ page.open(url, function(status) {
             if ("filtered" in expected && actual.indexOf(expected.filtered) == -1) {
                 return "Filtered value not in feedback";
             }
-            if (actual.indexOf(expected.type) == -1) {
+            if ("type" in expected && actual.indexOf(expected.type) == -1) {
                 return "Entropy type not in feedback";
             }
-            if (actual.indexOf(expected.events) == -1) {
+            if ("events" in expected && actual.indexOf(expected.events) == -1) {
                 return "Event count not in feedback";
             }
-            if (actual.indexOf(expected.bits) == -1) {
+            if ("bits" in expected && actual.indexOf(expected.bits) == -1) {
                 return "Bit count not in feedback";
             }
-            if (actual.indexOf(expected.strength) == -1) {
+            if ("strength" in expected && actual.indexOf(expected.strength) == -1) {
                 return "Strength not in feedback";
             }
+            if ("bitsPerEvent" in expected && actual.indexOf(expected.bitsPerEvent) == -1) {
+                return "bitsPerEvent not in feedback";
+            }
             return false;
         }
         test = tests[i];
@@ -2762,7 +2809,7 @@ page.open(url, function(status) {
                 return $(".phrase").val();
             });
             // Check mnemonic length
-            if (test.words == 0) {
+            if ("words" in test && test.words == 0) {
                 if (mnemonic.length > 0) {
                     console.log("Mnemonic length for " + test.strength + " strength is not " + test.words);
                     console.log("Entropy: " + test.entropy);
@@ -2770,7 +2817,7 @@ page.open(url, function(status) {
                     fail();
                 }
             }
-            else {
+            else if ("words" in test) {
                 if (mnemonic.split(" ").length != test.words) {
                     console.log("Mnemonic length for " + test.strength + " strength is not " + test.words);
                     console.log("Entropy: " + test.entropy);
-- 
2.41.0