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<!DOCTYPE html>
<html>
<head>
<title>Password Score</title>
<link rel="stylesheet" type="text/css" href="docs/css/bootstrap.css">
<link rel="stylesheet" type="text/css" href="docs/css/prettify.css">
<script type="text/javascript" src="docs/js/jquery.js"></script>
<script type="text/javascript" src="docs/js/jquery.tmpl.js"></script>
<script type="text/javascript" src="docs/js/prettify.js"></script>
<script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-MML-AM_CHTML'></script>
<script type="text/javascript">
MathJax.Hub.Config({
tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}
});
$(document).ready(function() {
window.prettyPrint() && prettyPrint();
});
</script>
</head>
<body>
<a href="https://github.com/davidstutz/password-score"><img style="position: absolute; top: 0; right: 0; border: 0;" src="https://s3.amazonaws.com/github/ribbons/forkme_right_red_aa0000.png" alt="Fork me on GitHub"></a>
<div class="container">
<div class="row">
<div class="col-md-8">
<h1>Password Score</h1>
<hr>
<ul class="nav nav-pills">
<li><a href="index.html">Demo</a></li>
<li><a href="statistics.html">Statistics</a></li>
<li><a href="api.html">API</a></li>
<li class="active"><a href="#">Documentation</a></li>
<li><a href="tests/SpecRunner.html" target="_blank">Tests</a></li>
</ul>
<hr>
<h2><a id="introduction"></a>Introduction</h2>
<p>
Password Score is designed to give a realistic estimation of the strength of a password. When speaking of "strength" we must ask for a measure. A common measure for this purpose is based on information theory and called entropy. We will define the entropy of a password as follows: when $N$ is the number of guesses needed to crack a password with certainty the entropy is given by the base-2 logarithm of $N$.
</p>
</div>
<div class="col-md-4">
<div class="well well-sm" style="margin-top:12px;">
<ul class="nav nav-list">
<li><a href="#introduction">Introduction</a></li>
<li><a href="#usage">Usage</a></li>
<li><a href="#pattern-matching">Pattern Matching</a></li>
<li><a href="#dictionaries">Dictionaries</a></li>
<li><a href="#leet-speak">1337 - Leet Speak</a></li>
<li><a href="#keyboard-patterns">Keyboard Patterns</a></li>
<li><a href="#dates">Dates</a></li>
<li><a href="#sequences-repetitions">Sequences and Repetitions</a></li>
<li><a href="#data-sources">Data Sources</a></li>
<li><a href="#references">References</a></li>
<li><a href="#license">License</a></li>
</ul>
</div>
</div>
</div>
</div>
<div class="container">
<p>
A naive approach of estimating the number of guesses needed is using a brute-force approach. Given a password $p$ we take $N := n^{|p|}$ where $|p|$ is the length of $p$ and $n$ is the number of possible characters. The brute-force approach simply tries all possible combinations of $|p|$ characters. But due to human nature assuming a password to be a random sequence of characters is far to idealistic. Most of us tend to choose passwords made up of common words, names, special numbers - passwords which are easy to remember. So the naive approach highly overestimates the strength of a password.
</p>
<p>
Therefore every password cracking software uses dictionaries, lists of common passwords and names to give better performance. Password Score will search a given password for common words, passwords or names - or in general Password Score searches for <i>patterns</i> within the password. Other possible patterns are keyboard patterns like `qwerty` or sequences like `1234`. Instead of using random numbers we tend to use numbers which have a meaning like dates - birthdays or anniversaries of any kind.
</p>
<h2><a id="usage"></a>Usage</h2>
<p>
Password Score can be used without dependencies. However, the <a href="index.html">Demonstration</a> uses <a href="http://jquery.com/" target="_blank">jQuery</a> to visualize the results. Include Password Score as follows:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
<!-- Main JS file (necessary). -->
<script type="text/javascript" src="dist/js/password-score.js"></script>
<!-- This file provides the default options (including dictionaries in english and german): -->
<script type="text/javascript" src="dist/js/password-score-options.js"></script>
</pre>
</div>
</div>
<div class="container">
<p>
The file <code>password-score.js</code> includes two classes: <code>Score</code> and <code>Keyboard</code>. See the <a href="api.html">API Documentation</a> for details.
</p>
<h2><a id="pattern-matching"></a>Pattern Matching</h2>
<p>
To use Password Score simply fetch a password and create a <code>new Score()</code>:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var password = 'qwerty';
var score = new Score(password);
</pre>
</div>
</div>
<div class="container">
<p>
To calculate the entropy we will use the <code>calculateEntropyScore(options)</code> method. This method requires some configuration, for example which dictionaries to search or whether to search for keyboard patterns. This may look as follows:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var options = [
{
'type': 'dictionary',
'leet': true,
'key': 'english',
'dictionary': englishDictionary
},
{
'type': 'dictionary',
'leet': false,
'key': 'passwords',
'dictionary': commonPasswords
},
{
'type': 'keyboard',
'key': 'qwerty',
'keyboard': QWERTY
}
];
// The calculateEntropyScore returns a score correpsonding to the calculated
// entropy of the password considering the above configuration.
console.log(score.calculateEntropyScore(options));
</pre>
</div>
</div>
<div class="container">
<p>
Based on the given options Password Score searches the password for all patterns it can find based on the given resources and calculates the entropy for all the patterns. Given a password consisting of $k$ non-overlapping patterns $p = p_1 \ldots p_k$ the entropy of $p$ is assumed to be the sum of the pattern entropies. Because we may have multiple overlapping patterns we then try to minimize the overall entropy as to underestimate the password rather than to overestimate it. Details on the different configuration options can be found int he next sections.
</p>
<p>
Password Score provides <b>default options</b> including several dictionaries: english, german, english country names, german country names, city names, last names, female first names, male first names, common passwords. See <a href="#date-sources">Data Sources</a> for details. In additiona, Password scores is initially configured to search all of these dictionaries for <a href="#leet-speak">Leet Speak</a> and searches the password for <a href="#repititions">Repititions</a>, <a href="#sequences">Sequences</a> and <a href="#dates">Dates</a>.
</p>
<p>
Beneath returning the password entropy, <code>score.calculateEntropyScore(options)</code> caches all found patterns and their entropies.
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var options = [
{
'type': 'dictionary',
'leet': true,
'key': 'english' // Key to access found patterns.
'dictionary': englishDictionary
}
];
// Returns the calculated entropy.
console.log(score.calculateEntropyScore(options));
// These are the patterns which contribute to the minimum entropy, that is all
// patterns found in the given resources which - taken together - result
// in minimum entropy.
console.log(score.cache.minimumMatches);
// The patterns found within the english dictionary can be accessed using
// the 'key' confiugraiton option used above:
console.log(score.cache.english);
</pre>
</div>
</div>
<div class='container'>
<h2><a id="dictionaries"></a>Dictionaries</h2>
<p>
As seen above Password Score can be configured to match against a given dictionary the following way:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var options = {
// For using different dictionaries different keys can be used.
'english' : {
'type': 'dictionary',
'key': 'english',
'dictionary': englishDictionary
},
};
</pre>
</div>
</div>
<div class="container">
<p>
A dictionary is simply an object where the keys represent the words, and the corresponding values represent scoring values which are used to calculate the entropy of the word when considered as pattern. Mostly these values will be a rank, that is more ocmmon words receive a higher rank than rare words, see the xample below. Dictionaries must not be common language dictionaries like english or german dictionaries. We can also use a list of common passwords or common names as dictionary:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var englishDictionary = {
'you': 1, // Most used english word ...
// ...
'housewife': 2154, // Higher rank -> less common word!
};
var commonPasswords = {
'password': 1, // Most common password ...
// ...
'd9ebk7': 8603, // Higher rank -> less common password!
};
</pre>
</div>
</div>
<div class="container">
<p>
As mentioned above the scoring value will be used to determine the entropy by simply taking the base-2 logarithm. We will use the scoring value as to differentiate between very common patterns and less common patterns - <code>password</code> is the most common password whereas <code>d9ebk7</code> is not that common.
</p>
<h2><a id="leet-speak"></a>1337 - Leet Speak</h2>
<p>
Using a leet speak translation table, Password Score can search dictionaries for words which occur in leet speak within the password. This translation table looks like this:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
leet = {
'1': ['i', 'l'],
'2': ['n', 'r', 'z'],
'3': ['e'],
'4': ['a'],
'5': ['s'],
'6': ['g'],
'7': ['t'],
'8': ['b'],
'9': ['g', 'o'],
'0': ['o'],
'@': ['a'],
'(': ['c'],
'[': ['c'],
'<': ['c'],
'&': ['g'],
'!': ['i'],
'|': ['i', 'l'],
'?': ['n', 'r'],
'$': ['s'],
'+': ['t'],
'%': ['x']
};
</pre>
</div>
</div>
<div class="container">
<p>
Given a word in leet speak, Password Score generates a list of all possible substitutions using the translation table. All possible substitutions are matched against a given dictionary. The entropy can be calculated by determining the number of possible leet speak versions of the dictionary word. To configure password score to apply leet speak detection on a given dictionary use:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var options = [
{
'type': 'dictionary',
'leet': true, // Enables leet speak matching for this dictionary.
'key': 'english',
'dictionary': englishDictionary
}
];
</pre>
</div>
</div>
<div class="container">
<h2><a id="keyboard-patterns"></a>Keyboard Patterns</h2>
<p>
<code>qwerty</code> will always be within the top ten of the most common passwords simply because it is easy to remember on the corresponding keyboard. We will assume a keyboard pattern to be a path on the keyboard when considered as undirected graph. They QWERTY and QWERTZ keyboards are includes in Password Score per default. However, additional keyboard layouts may be used as follows:
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
var options = {
{
'type': 'keyboard',
'keyboard': AZERTY // Your definition of the AZERTY keyboard ...
}
};
</pre>
</div>
</div>
<div class="container">
<p>
Theoretically the entropy of a keyboard pattern is given by the number of possible beginnings multiplied by the number of possible next characters for each character within the pattern.
</p>
<p>
Of course, it is possible to define additional keyboard layouts, see the definition of the QWERTY keyboard below. Each key is assumed to have a maximum of six neighbors.
</p>
</div>
<div class="stripe">
<div class="container">
<pre class="prettyprint">
QWERTY: new Keyboard({
'~': [null, null, null, '~`', '1!', null, null], // 1
'`': [null, null, null, '~`', '1!', null, null], // 1
'1': [null, null, '`~', '1!', '2@', null, 'qQ'], // 3
'!': [null, null, '`~', '1!', '2@', null, 'qQ'], // 3
'2': [null, null, '1!', '2@', '3#', 'qQ', 'wW'], // 4
'@': [null, null, '1!', '2@', '3#', 'qQ', 'wW'], //4
'3': [null, null, '2@', '3#', '4$', 'wW', 'eE'], //4
'#': [null, null, '2@', '3#', '4$', 'wW', 'eE'], //4
'4': [null, null, '3#', '4$', '5%', 'eE', 'rR'], //4
'$': [null, null, '3#', '4$', '5%', 'eE', 'rR'], //4
'5': [null, null, '4$', '5%', '6^', 'rR', 'tT'], //4
'%': [null, null, '4$', '5%', '6^', 'rR', 'tT'], //4
'6': [null, null, '5%', '6^', '7&', 'tT', 'yY'], //4
'^': [null, null, '5%', '6^', '7&', 'tT', 'yY'], //4
'7': [null, null, '6^', '7&', '8*', 'yY', 'uU'], //4
'&': [null, null, '6^', '7&', '8*', 'yY', 'uU'], //4
'8': [null, null, '7&', '8*', '9(', 'uU', 'iI'], // 4
'*': [null, null, '7&', '8*', '9(', 'uU', 'iI'], // 4
'9': [null, null, '8*', '9(', '0)', 'iI', 'oO'], // 4
'(': [null, null, '8*', '9(', '0)', 'iI', 'oO'], // 4
'0': [null, null, '9(', '0)', '-_', 'oO', 'pP'], // 4
')': [null, null, '9(', '0)', '-_', 'oO', 'pP'], // 4
'-': [null, null, '0)', '-_', '=+', 'pP', '[{'], // 4
'_': [null, null, '0)', '-_', '=+', 'pP', '[{'], // 4
'=': [null, null, '-_', '=+', '\\|', '{[', '}]'], // 4
'+': [null, null, '-_', '=+', '\\|', '{[', '}]'], // 4
'\\': [null, null, '=+', '\\|', null, '}]', null], // 2
'|': [null, null, '=+', '\\|', null, '}]', null], // 2
'q': ['1!', '2@', null, 'qQ', 'wW', null, 'aA'], // 4
'Q': ['1!', '2@', null, 'qQ', 'wW', null, 'aA'], // 4
'w': ['2@', '3#', 'qQ', 'wW','eE', 'aA', 'sS'], // 6
'W': ['2@', '3#', 'qQ', 'wW','eE', 'aA', 'sS'], // 6
'e': ['3#', '4$', 'wW', 'eE', 'rR', 'sS', 'dD'], // 6
'E': ['3#', '4$', 'wW', 'eE', 'rR', 'sS', 'dD'], // 6
'r': ['4$', '5%', 'eE', 'rR', 'tT', 'dD', 'fF'], // 6
'R': ['4$', '5%', 'eE', 'rR', 'tT', 'dD', 'fF'], // 6
't': ['5%', '6^', 'rR', 'tT', 'yY', 'fF', 'gG'], // 6
'T': ['5%', '6^', 'rR', 'tT', 'yY', 'fF', 'gG'], // 6
'y': ['6^', '7&', 'tT', 'yY', 'uU', 'gG', 'hH'], // 6
'Y': ['6^', '7&', 'tT', 'yY', 'uU', 'gG', 'hH'], // 6
'u': ['7&', '8*', 'yY', 'uU', 'iI', 'hH', 'jJ'], // 6
'U': ['7&', '8*', 'yY', 'uU', 'iI', 'hH', 'jJ'], // 6
'i': ['8*', '9(', 'uU', 'iI', 'oO', 'jJ', 'kK'], // 6
'I': ['8*', '9(', 'uU', 'iI', 'oO', 'jJ', 'kK'], // 6
'o': ['9(', '0)', 'iI', 'oO', 'pP', 'kK', 'lL'], // 6
'O': ['9(', '0)', 'iI', 'oO', 'pP', 'kK', 'lL'], // 6
'p': ['0)', '-_', 'oO', 'pP', '[{', 'lL', ':;'], // 6
'P': ['0)', '-_', 'oO', 'pP', '[{', 'lL', ':;'], // 6
'[': ['-_', '=+', 'pP', '[{', ']}', ':;', '\'"'], // 6
'{': ['-_', '=+', 'pP', '[{', ']}', ':;', '\'"'], // 6
']': ['=+', '\\|', '[{', ']}', null, '\'"', null], // 4
'}': ['=+', '\\|', '[{', ']}', null, '\'"', null], // 4
'a': ['qQ', 'wW', null, 'aA', 'sS', null, 'zZ'], // 4
'A': ['qQ', 'wW', null, 'aA', 'sS', null, 'zZ'], // 4
's': ['wW', 'eE', 'aA', 'sS', 'dD', 'zZ', 'xX'], // 6
'S': ['wW', 'eE', 'aA', 'sS', 'dD', 'zZ', 'xX'], // 6
'd': ['eE', 'rR', 'sS', 'dD', 'fF', 'xX', 'cC'], // 6
'D': ['eE', 'rR', 'sS', 'dD', 'fF', 'xX', 'cC'], // 6
'f': ['rR', 'tT', 'dD', 'fF', 'gG', 'cC', 'vV'], // 6
'F': ['rR', 'tT', 'dD', 'fF', 'gG', 'cC', 'vV'], // 6
'g': ['tT', 'yY', 'fF', 'gG', 'hH', 'vV', 'bB'], // 6
'G': ['tT', 'yY', 'fF', 'gG', 'hH', 'vV', 'bB'], // 6
'h': ['yY', 'uU', 'gG', 'hH', 'jJ', 'bB', 'nN'], // 6
'H': ['yY', 'uU', 'gG', 'hH', 'jJ', 'bB', 'nN'], // 6
'j': ['uU', 'iI', 'hH', 'jJ', 'kK', 'nN', 'mM'], // 6
'J': ['uU', 'iI', 'hH', 'jJ', 'kK', 'nN', 'mM'], // 6
'k': ['iI', 'oO', 'jJ', 'kK', 'lL', 'mM', ',;'], // 6
'K': ['iI', 'oO', 'jJ', 'kK', 'lL', 'mM', ',;'], // 6
'l': ['oO', 'pP', 'kK', 'lL', ':;', ',<', '.>'], // 6
'L': ['oO', 'pP', 'kK', 'lL', ':;', ',<', '.>'], // 6
':': ['pP', '[{', 'lL', ':;', '\'"', '.>', '?/'], // 6
';': ['pP', '[{', 'lL', ':;', '\'"', '.>', '?/'], // 6
'\'': ['[{', ']}', ':;', '\'"', null, '?/', null], // 5
'"': ['[{', ']}', ':;', '\'"', null, '?/', null], // 5
'z': ['aA', 'sS', null, 'zZ', 'xX', null, null], // 4
'Z': ['aA', 'sS', null, 'zZ', 'xX', null, null], // 4
'x': ['sS', 'dD', 'zZ', 'xX', 'cC', null, null], // 4
'X': ['sS', 'dD', 'zZ', 'xX', 'cC', null, null], // 4
'c': ['dD', 'fF', 'xX', 'cC', 'vV', null, null], // 4
'C': ['dD', 'fF', 'xX', 'cC', 'vV', null, null], // 4
'v': ['fF', 'gG', 'cC', 'vV', 'bB', null, null], // 4
'V': ['fF', 'gG', 'cC', 'vV', 'bB', null, null], // 4
'b': ['gG', 'hH', 'vV', 'bB', 'nN', null, null], // 4
'B': ['gG', 'hH', 'vV', 'bB', 'nN', null, null], // 4
'n': ['hH', 'jJ', 'bB', 'nN', 'mM', null, null], // 4
'N': ['hH', 'jJ', 'bB', 'nN', 'mM', null, null], // 4
'm': ['jJ', 'kK', 'nN', 'mM', ',<', null, null], // 4
'M': ['jJ', 'kK', 'nN', 'mM', ',<', null, null], // 4
',': ['kK', 'lL', 'mM', ',<', '.>', null, null], // 4
'<': ['kK', 'lL', 'mM', ',<', '.>', null, null], // 4
'.': ['lL', ':;', ',<', '.>', '/?', null, null], // 4
'>': ['lL', ':;', ',<', '.>', '/?', null, null], // 4
'/': [':;', '\'"', '.>', '/?', null, null, null], // 3
'?': [':;', '\'"', '.>', '/?', null, null, null] // 3
}, 4.571428571), // Average number of neighbors.
</pre>
</div>
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<h2><a id="dates"></a>Dates</h2>
<p>
Per default, Password Score searches the given password for dates. However, to configure Password Score to do so manually, use:
</p>
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<pre class="prettyprint">
var options = {
{
'type': 'dates'
}
};
</pre>
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<p>
Dates are hard to catch because they may occur in many different formats. They may consist only of a day and a month or only of a month and a year. Years on its own are common, too - my first passwords contained the last two digits of my year of birth. Fortunately regular expressions can be used to scan efficiently for the different formats of dates:
</p>
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<pre class="prettyprint">
'(0?[1-9]|1[012])([\- \/.])?(0?[1-9]|[12][0-9]|3[01])([\- \/.])?([0-9]{4})' // Middle-endian, four digit year.
'(0?[1-9]|[12][0-9]|3[01])([\- \/.])?(0?[1-9]|1[012])([\- \/.])?([0-9]{2})' // Little-endian, two digit year.
// ...
</pre>
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<p>
The number of possible dates is dependent on the format. In general we simply take $31 \cdot 12 \cdot y$ where $y$ is the number of years being considered. When assuming $y$ to be too large we will not get any difference from considering a random eight (or six) digit number with $10^8$ respectively $10^6$ possible combinations. Therefore, choosing $y$ to be around $100$ or $200$ will be a good and realistic choice.
</p>
<h2><a id="sequences-repetitions"></a>Sequences and Repetitions</h2>
<p>
Password Score is able to search for number sequences and substrings of the alphabet (and does so per default):
</p>
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<pre class="prettyprint">
var options = [
{
'type': 'sequences'
}
];
</pre>
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<p>
Reversed sequences are checked as well. The entropy of a sequence is only influenced by the possibilities for the first character and the length.
</p>
<p>
In addition, Password score searches for repititions (also per default):
</p>
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<pre class="prettyprint">
var options = [
{
'type': 'repetition'
}
];
</pre>
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<p>
The entropy of single character repetitions is determined the same way as for sequences. When repeating multiple characters the entropy is determined by the length of the sequence to be repeated and the number of repetitions.
</p>
<h2><a id="data-sources"></a>Data Sources</h2>
<p>
See below for the data used for the dictionaries:
</p>
<ul>
<li><a href="http://invokeit.wordpress.com/frequency-word-lists/" target="_blank">Hermit Dave's "Frequency Word Lists"</a> are quite useful as a replacement for usual dictionaries as they also include spoken language:
<li><a href="https://xato.net/passwords/more-top-worst-passwords/" target="_blank">Mark Burnett's "10,000 Top Passwords"</a> can be used to identify common passwords.</li>
<li>Lists of common female and male names as well as last names can be taken from the <a href="http://deron.meranda.us/data/" target="_blank">US Census Data</a> from 1990.</li>
<li>Lists of countries in all languages can be found <a href="http://www.countries-list.info/" target="_blank">here</a>.
<li><a href="http://www.geonames.org/" target="_blank">GeoNames.org</a> provides lists of cities <a href="http://download.geonames.org/export/dump/" target="_blank">here</a>. As only a few city names are being translated among languages these lists will work language independent.</li>
</ul>
<p>
For using the raw data a simple PHP script can be used to generate JSON files with the appropriate format.
</p>
<h2><a id="references"></a>References</h2>
<p>Mainly inspired by <a href="https://tech.dropbox.com/2012/04/zxcvbn-realistic-password-strength-estimation/" target="_blank">"zxcvbn: realistic password strength estimation"</a>, Dropbox Tech Blog.</p>
</div>
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<a href="http://davidstutz.de">David Stutz</a> - <a href="http://opensource.org/licenses/BSD-3-Clause">BSD 3-Clause License</a> - <a href="https://davidstutz.de/impressum/">Impressum</a> - <a href="https://davidstutz.de/datenschutz/">Datenschutz</a>
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