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| author | Andrey Andreev <narf@devilix.net> | 2018-01-13 12:57:11 +0100 |
|---|---|---|
| committer | Andrey Andreev <narf@devilix.net> | 2018-01-13 12:57:11 +0100 |
| commit | 02a0518e1c56ba3506f370362ac5ebdb8a138312 (patch) | |
| tree | 8b4684192b403dcae17d298eb4fc9e7ab001acad /user_guide/libraries/encryption.html | |
| parent | f0b9735d5857e6c07c8f5824b13cff4828db3cfe (diff) | |
[ci skip] 3.1.7 release
Diffstat (limited to 'user_guide/libraries/encryption.html')
| -rw-r--r-- | user_guide/libraries/encryption.html | 1405 |
1 files changed, 1405 insertions, 0 deletions
diff --git a/user_guide/libraries/encryption.html b/user_guide/libraries/encryption.html new file mode 100644 index 000000000..4904c496b --- /dev/null +++ b/user_guide/libraries/encryption.html @@ -0,0 +1,1405 @@ + + +<!DOCTYPE html> +<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]--> +<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]--> +<head> + <meta charset="utf-8"> + <meta name="viewport" content="width=device-width, initial-scale=1.0"> + + <title>Encryption Library — CodeIgniter 3.1.7 documentation</title> + + + + + <link rel="shortcut icon" href="../_static/ci-icon.ico"/> + + + + <link href='https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic|Roboto+Slab:400,700|Inconsolata:400,700&subset=latin,cyrillic' rel='stylesheet' type='text/css'> + + + + + + + + + + <link rel="stylesheet" href="../_static/css/citheme.css" type="text/css" /> + + + + <link rel="index" title="Index" + href="../genindex.html"/> + <link rel="search" 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</div> + </ul> + <hr/> +</div> + <div role="main" class="document"> + + <div class="section" id="encryption-library"> +<h1>Encryption Library<a class="headerlink" href="#encryption-library" title="Permalink to this headline">¶</a></h1> +<div class="admonition important"> +<p class="first admonition-title">Important</p> +<p class="last">DO NOT use this or any other <em>encryption</em> library for +user password storage! Passwords must be <em>hashed</em> instead, and you +should do that via PHP’s own <a class="reference external" href="http://php.net/password">Password Hashing extension</a>.</p> +</div> +<p>The Encryption Library provides two-way data encryption. To do so in +a cryptographically secure way, it utilizes PHP extensions that are +unfortunately not always available on all systems. +You must meet one of the following dependencies in order to use this +library:</p> +<ul class="simple"> +<li><a class="reference external" href="http://php.net/openssl">OpenSSL</a></li> +<li><a class="reference external" href="http://php.net/mcrypt">MCrypt</a> (and <cite>MCRYPT_DEV_URANDOM</cite> availability)</li> +</ul> +<p>If neither of the above dependencies is met, we simply cannot offer +you a good enough implementation to meet the high standards required +for proper cryptography.</p> +<div class="contents local topic" id="contents"> +<ul class="simple"> +<li><a class="reference internal" href="#using-the-encryption-library" id="id2">Using the Encryption Library</a><ul> +<li><a class="reference internal" href="#initializing-the-class" id="id3">Initializing the Class</a></li> +<li><a class="reference internal" href="#default-behavior" id="id4">Default behavior</a></li> +<li><a class="reference internal" href="#setting-your-encryption-key" id="id5">Setting your encryption_key</a></li> +<li><a class="reference internal" href="#supported-encryption-ciphers-and-modes" id="id6">Supported encryption ciphers and modes</a><ul> +<li><a class="reference internal" href="#portable-ciphers" id="id7">Portable ciphers</a></li> +<li><a class="reference internal" href="#driver-specific-ciphers" id="id8">Driver-specific ciphers</a></li> +<li><a class="reference internal" href="#encryption-modes" id="id9">Encryption modes</a></li> +</ul> +</li> +<li><a class="reference internal" href="#message-length" id="id10">Message Length</a></li> +<li><a class="reference internal" href="#configuring-the-library" id="id11">Configuring the library</a></li> +<li><a class="reference internal" href="#encrypting-and-decrypting-data" id="id12">Encrypting and decrypting data</a><ul> +<li><a class="reference internal" href="#how-it-works" id="id13">How it works</a></li> +<li><a class="reference internal" href="#using-custom-parameters" id="id14">Using custom parameters</a></li> +<li><a class="reference internal" href="#supported-hmac-authentication-algorithms" id="id15">Supported HMAC authentication algorithms</a></li> +</ul> +</li> +</ul> +</li> +<li><a class="reference internal" href="#class-reference" id="id16">Class Reference</a></li> +</ul> +</div> +<div class="custom-index container"></div><div class="section" id="using-the-encryption-library"> +<h2><a class="toc-backref" href="#id2">Using the Encryption Library</a><a class="headerlink" href="#using-the-encryption-library" title="Permalink to this headline">¶</a></h2> +<div class="section" id="initializing-the-class"> +<h3><a class="toc-backref" href="#id3">Initializing the Class</a><a class="headerlink" href="#initializing-the-class" title="Permalink to this headline">¶</a></h3> +<p>Like most other classes in CodeIgniter, the Encryption library is +initialized in your controller using the <code class="docutils literal"><span class="pre">$this->load->library()</span></code> +method:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$this</span><span class="o">-></span><span class="na">load</span><span class="o">-></span><span class="na">library</span><span class="p">(</span><span class="s1">'encryption'</span><span class="p">);</span> +</pre></div> +</div> +<p>Once loaded, the Encryption library object will be available using:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span> +</pre></div> +</div> +</div> +<div class="section" id="default-behavior"> +<h3><a class="toc-backref" href="#id4">Default behavior</a><a class="headerlink" href="#default-behavior" title="Permalink to this headline">¶</a></h3> +<p>By default, the Encryption Library will use the AES-128 cipher in CBC +mode, using your configured <em>encryption_key</em> and SHA512 HMAC authentication.</p> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">AES-128 is chosen both because it is proven to be strong and +because of its wide availability across different cryptographic +software and programming languages’ APIs.</p> +</div> +<p>However, the <em>encryption_key</em> is not used as is.</p> +<p>If you are somewhat familiar with cryptography, you should already know +that a HMAC also requires a secret key and using the same key for both +encryption and authentication is a bad practice.</p> +<p>Because of that, two separate keys are derived from your already configured +<em>encryption_key</em>: one for encryption and one for authentication. This is +done via a technique called <a class="reference external" href="http://en.wikipedia.org/wiki/HKDF">HMAC-based Key Derivation Function</a> (HKDF).</p> +</div> +<div class="section" id="setting-your-encryption-key"> +<h3><a class="toc-backref" href="#id5">Setting your encryption_key</a><a class="headerlink" href="#setting-your-encryption-key" title="Permalink to this headline">¶</a></h3> +<p>An <em>encryption key</em> is a piece of information that controls the +cryptographic process and permits a plain-text string to be encrypted, +and afterwards - decrypted. It is the secret “ingredient” in the whole +process that allows you to be the only one who is able to decrypt data +that you’ve decided to hide from the eyes of the public. +After one key is used to encrypt data, that same key provides the <strong>only</strong> +means to decrypt it, so not only must you chose one carefully, but you +must not lose it or you will also lose access to the data.</p> +<p>It must be noted that to ensure maximum security, such key <em>should</em> not +only be as strong as possible, but also often changed. Such behavior +however is rarely practical or possible to implement, and that is why +CodeIgniter gives you the ability to configure a single key that is to be +used (almost) every time.</p> +<p>It goes without saying that you should guard your key carefully. Should +someone gain access to your key, the data will be easily decrypted. If +your server is not totally under your control it’s impossible to ensure +key security so you may want to think carefully before using it for +anything that requires high security, like storing credit card numbers.</p> +<p>Your encryption key <strong>must</strong> be as long as the encyption algorithm in use +allows. For AES-128, that’s 128 bits or 16 bytes (charcters) long. +You will find a table below that shows the supported key lengths of +different ciphers.</p> +<p>The key should be as random as possible and it <strong>must not</strong> be a regular +text string, nor the output of a hashing function, etc. In order to create +a proper key, you must use the Encryption library’s <code class="docutils literal"><span class="pre">create_key()</span></code> method</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="c1">// $key will be assigned a 16-byte (128-bit) random key</span> +<span class="nv">$key</span> <span class="o">=</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">create_key</span><span class="p">(</span><span class="mi">16</span><span class="p">);</span> +</pre></div> +</div> +<p>The key can be either stored in your <em>application/config/config.php</em>, or +you can design your own storage mechanism and pass the key dynamically +when encrypting/decrypting.</p> +<p>To save your key to your <em>application/config/config.php</em>, open the file +and set:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$config</span><span class="p">[</span><span class="s1">'encryption_key'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'YOUR KEY'</span><span class="p">;</span> +</pre></div> +</div> +<p>You’ll notice that the <code class="docutils literal"><span class="pre">create_key()</span></code> method outputs binary data, which +is hard to deal with (i.e. a copy-paste may damage it), so you may use +<code class="docutils literal"><span class="pre">bin2hex()</span></code>, <code class="docutils literal"><span class="pre">hex2bin()</span></code> or Base64-encoding to work with the key in +a more friendly manner. For example:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="c1">// Get a hex-encoded representation of the key:</span> +<span class="nv">$key</span> <span class="o">=</span> <span class="nb">bin2hex</span><span class="p">(</span><span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">create_key</span><span class="p">(</span><span class="mi">16</span><span class="p">));</span> + +<span class="c1">// Put the same value in your config with hex2bin(),</span> +<span class="c1">// so that it is still passed as binary to the library:</span> +<span class="nv">$config</span><span class="p">[</span><span class="s1">'encryption_key'</span><span class="p">]</span> <span class="o">=</span> <span class="nb">hex2bin</span><span class="p">(</span><span class="o"><</span><span class="nx">your</span> <span class="nx">hex</span><span class="o">-</span><span class="nx">encoded</span> <span class="nb">key</span><span class="o">></span><span class="p">);</span> +</pre></div> +</div> +</div> +<div class="section" id="supported-encryption-ciphers-and-modes"> +<span id="ciphers-and-modes"></span><h3><a class="toc-backref" href="#id6">Supported encryption ciphers and modes</a><a class="headerlink" href="#supported-encryption-ciphers-and-modes" title="Permalink to this headline">¶</a></h3> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">The terms ‘cipher’ and ‘encryption algorithm’ are interchangeable.</p> +</div> +<div class="section" id="portable-ciphers"> +<h4><a class="toc-backref" href="#id7">Portable ciphers</a><a class="headerlink" href="#portable-ciphers" title="Permalink to this headline">¶</a></h4> +<p>Because MCrypt and OpenSSL (also called drivers throughout this document) +each support different sets of encryption algorithms and often implement +them in different ways, our Encryption library is designed to use them in +a portable fashion, or in other words - it enables you to use them +interchangeably, at least for the ciphers supported by both drivers.</p> +<p>It is also implemented in a way that aims to match the standard +implementations in other programming languages and libraries.</p> +<p>Here’s a list of the so called “portable” ciphers, where +“CodeIgniter name” is the string value that you’d have to pass to the +Encryption library to use that cipher:</p> +<table border="1" class="docutils"> +<colgroup> +<col width="24%" /> +<col width="18%" /> +<col width="28%" /> +<col width="31%" /> +</colgroup> +<thead valign="bottom"> +<tr class="row-odd"><th class="head">Cipher name</th> +<th class="head">CodeIgniter name</th> +<th class="head">Key lengths (bits / bytes)</th> +<th class="head">Supported modes</th> +</tr> +</thead> +<tbody valign="top"> +<tr class="row-even"><td>AES-128 / Rijndael-128</td> +<td>aes-128</td> +<td>128 / 16</td> +<td>CBC, CTR, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-odd"><td>AES-192</td> +<td>aes-192</td> +<td>192 / 24</td> +<td>CBC, CTR, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-even"><td>AES-256</td> +<td>aes-256</td> +<td>256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-odd"><td>DES</td> +<td>des</td> +<td>56 / 7</td> +<td>CBC, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-even"><td>TripleDES</td> +<td>tripledes</td> +<td>56 / 7, 112 / 14, 168 / 21</td> +<td>CBC, CFB, CFB8, OFB</td> +</tr> +<tr class="row-odd"><td>Blowfish</td> +<td>blowfish</td> +<td>128-448 / 16-56</td> +<td>CBC, CFB, OFB, ECB</td> +</tr> +<tr class="row-even"><td>CAST5 / CAST-128</td> +<td>cast5</td> +<td>88-128 / 11-16</td> +<td>CBC, CFB, OFB, ECB</td> +</tr> +<tr class="row-odd"><td>RC4 / ARCFour</td> +<td>rc4</td> +<td>40-2048 / 5-256</td> +<td>Stream</td> +</tr> +</tbody> +</table> +<div class="admonition important"> +<p class="first admonition-title">Important</p> +<p class="last">Because of how MCrypt works, if you fail to provide a key +with the appropriate length, you might end up using a different +algorithm than the one configured, so be really careful with that!</p> +</div> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">In case it isn’t clear from the above table, Blowfish, CAST5 +and RC4 support variable length keys. That is, any number in the +shown ranges is valid, although in bit terms that only happens +in 8-bit increments.</p> +</div> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">Even though CAST5 supports key lengths lower than 128 bits +(16 bytes), in fact they will just be zero-padded to the +maximum length, as specified in <a class="reference external" href="http://tools.ietf.org/rfc/rfc2144.txt">RFC 2144</a>.</p> +</div> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">Blowfish supports key lengths as small as 32 bits (4 bytes), but +our tests have shown that only lengths of 128 bits (16 bytes) or +higher are properly supported by both MCrypt and OpenSSL. It is +also a bad practice to use such low-length keys anyway.</p> +</div> +</div> +<div class="section" id="driver-specific-ciphers"> +<h4><a class="toc-backref" href="#id8">Driver-specific ciphers</a><a class="headerlink" href="#driver-specific-ciphers" title="Permalink to this headline">¶</a></h4> +<p>As noted above, MCrypt and OpenSSL support different sets of encryption +ciphers. For portability reasons and because we haven’t tested them +properly, we do not advise you to use the ones that are driver-specific, +but regardless, here’s a list of most of them:</p> +<table border="1" class="docutils"> +<colgroup> +<col width="15%" /> +<col width="10%" /> +<col width="32%" /> +<col width="44%" /> +</colgroup> +<thead valign="bottom"> +<tr class="row-odd"><th class="head">Cipher name</th> +<th class="head">Driver</th> +<th class="head">Key lengths (bits / bytes)</th> +<th class="head">Supported modes</th> +</tr> +</thead> +<tbody valign="top"> +<tr class="row-even"><td>AES-128</td> +<td>OpenSSL</td> +<td>128 / 16</td> +<td>CBC, CTR, CFB, CFB8, OFB, ECB, XTS</td> +</tr> +<tr class="row-odd"><td>AES-192</td> +<td>OpenSSL</td> +<td>192 / 24</td> +<td>CBC, CTR, CFB, CFB8, OFB, ECB, XTS</td> +</tr> +<tr class="row-even"><td>AES-256</td> +<td>OpenSSL</td> +<td>256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, ECB, XTS</td> +</tr> +<tr class="row-odd"><td>Rijndael-128</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-even"><td>Rijndael-192</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-odd"><td>Rijndael-256</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-even"><td>GOST</td> +<td>MCrypt</td> +<td>256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-odd"><td>Twofish</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-even"><td>CAST-128</td> +<td>MCrypt</td> +<td>40-128 / 5-16</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-odd"><td>CAST-256</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-even"><td>Loki97</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-odd"><td>SaferPlus</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-even"><td>Serpent</td> +<td>MCrypt</td> +<td>128 / 16, 192 / 24, 256 / 32</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-odd"><td>XTEA</td> +<td>MCrypt</td> +<td>128 / 16</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-even"><td>RC2</td> +<td>MCrypt</td> +<td>8-1024 / 1-128</td> +<td>CBC, CTR, CFB, CFB8, OFB, OFB8, ECB</td> +</tr> +<tr class="row-odd"><td>RC2</td> +<td>OpenSSL</td> +<td>8-1024 / 1-128</td> +<td>CBC, CFB, OFB, ECB</td> +</tr> +<tr class="row-even"><td>Camellia-128</td> +<td>OpenSSL</td> +<td>128 / 16</td> +<td>CBC, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-odd"><td>Camellia-192</td> +<td>OpenSSL</td> +<td>192 / 24</td> +<td>CBC, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-even"><td>Camellia-256</td> +<td>OpenSSL</td> +<td>256 / 32</td> +<td>CBC, CFB, CFB8, OFB, ECB</td> +</tr> +<tr class="row-odd"><td>Seed</td> +<td>OpenSSL</td> +<td>128 / 16</td> +<td>CBC, CFB, OFB, ECB</td> +</tr> +</tbody> +</table> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">If you wish to use one of those ciphers, you’d have to pass +its name in lower-case to the Encryption library.</p> +</div> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">You’ve probably noticed that all AES cipers (and Rijndael-128) +are also listed in the portable ciphers list. This is because +drivers support different modes for these ciphers. Also, it is +important to note that AES-128 and Rijndael-128 are actually +the same cipher, but <strong>only</strong> when used with a 128-bit key.</p> +</div> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">CAST-128 / CAST-5 is also listed in both the portable and +driver-specific ciphers list. This is because OpenSSL’s +implementation doesn’t appear to be working correctly with +key sizes of 80 bits and lower.</p> +</div> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">RC2 is listed as supported by both MCrypt and OpenSSL. +However, both drivers implement them differently and they +are not portable. It is probably worth noting that we only +found one obscure source confirming that it is MCrypt that +is not properly implementing it.</p> +</div> +</div> +<div class="section" id="encryption-modes"> +<span id="id1"></span><h4><a class="toc-backref" href="#id9">Encryption modes</a><a class="headerlink" href="#encryption-modes" title="Permalink to this headline">¶</a></h4> +<p>Different modes of encryption have different characteristics and serve +for different purposes. Some are stronger than others, some are faster +and some offer extra features. +We are not going in depth into that here, we’ll leave that to the +cryptography experts. The table below is to provide brief informational +reference to our more experienced users. If you are a beginner, just +stick to the CBC mode - it is widely accepted as strong and secure for +general purposes.</p> +<table border="1" class="docutils"> +<colgroup> +<col width="6%" /> +<col width="9%" /> +<col width="9%" /> +<col width="76%" /> +</colgroup> +<thead valign="bottom"> +<tr class="row-odd"><th class="head">Mode name</th> +<th class="head">CodeIgniter name</th> +<th class="head">Driver support</th> +<th class="head">Additional info</th> +</tr> +</thead> +<tbody valign="top"> +<tr class="row-even"><td>CBC</td> +<td>cbc</td> +<td>MCrypt, OpenSSL</td> +<td>A safe default choice</td> +</tr> +<tr class="row-odd"><td>CTR</td> +<td>ctr</td> +<td>MCrypt, OpenSSL</td> +<td>Considered as theoretically better than CBC, but not as widely available</td> +</tr> +<tr class="row-even"><td>CFB</td> +<td>cfb</td> +<td>MCrypt, OpenSSL</td> +<td>N/A</td> +</tr> +<tr class="row-odd"><td>CFB8</td> +<td>cfb8</td> +<td>MCrypt, OpenSSL</td> +<td>Same as CFB, but operates in 8-bit mode (not recommended).</td> +</tr> +<tr class="row-even"><td>OFB</td> +<td>ofb</td> +<td>MCrypt, OpenSSL</td> +<td>N/A</td> +</tr> +<tr class="row-odd"><td>OFB8</td> +<td>ofb8</td> +<td>MCrypt</td> +<td>Same as OFB, but operates in 8-bit mode (not recommended).</td> +</tr> +<tr class="row-even"><td>ECB</td> +<td>ecb</td> +<td>MCrypt, OpenSSL</td> +<td>Ignores IV (not recommended).</td> +</tr> +<tr class="row-odd"><td>XTS</td> +<td>xts</td> +<td>OpenSSL</td> +<td>Usually used for encrypting random access data such as RAM or hard-disk storage.</td> +</tr> +<tr class="row-even"><td>Stream</td> +<td>stream</td> +<td>MCrypt, OpenSSL</td> +<td>This is not actually a mode, it just says that a stream cipher is being used. Required because of the general cipher+mode initialization process.</td> +</tr> +</tbody> +</table> +</div> +</div> +<div class="section" id="message-length"> +<h3><a class="toc-backref" href="#id10">Message Length</a><a class="headerlink" href="#message-length" title="Permalink to this headline">¶</a></h3> +<p>It’s probably important for you to know that an encrypted string is usually +longer than the original, plain-text string (depending on the cipher).</p> +<p>This is influenced by the cipher algorithm itself, the IV prepended to the +cipher-text and the HMAC authentication message that is also prepended. +Furthermore, the encrypted message is also Base64-encoded so that it is safe +for storage and transmission, regardless of a possible character set in use.</p> +<p>Keep this information in mind when selecting your data storage mechanism. +Cookies, for example, can only hold 4K of information.</p> +</div> +<div class="section" id="configuring-the-library"> +<span id="configuration"></span><h3><a class="toc-backref" href="#id11">Configuring the library</a><a class="headerlink" href="#configuring-the-library" title="Permalink to this headline">¶</a></h3> +<p>For usability, performance, but also historical reasons tied to our old +<a class="reference internal" href="encrypt.html"><span class="doc">Encrypt Class</span></a>, the Encryption library is designed to +use repeatedly the same driver, encryption cipher, mode and key.</p> +<p>As noted in the “Default behavior” section above, this means using an +auto-detected driver (OpenSSL has a higher priority), the AES-128 ciper +in CBC mode, and your <code class="docutils literal"><span class="pre">$config['encryption_key']</span></code> value.</p> +<p>If you wish to change that however, you need to use the <code class="docutils literal"><span class="pre">initialize()</span></code> +method. It accepts an associative array of parameters, all of which are +optional:</p> +<table border="1" class="docutils"> +<colgroup> +<col width="15%" /> +<col width="85%" /> +</colgroup> +<thead valign="bottom"> +<tr class="row-odd"><th class="head">Option</th> +<th class="head">Possible values</th> +</tr> +</thead> +<tbody valign="top"> +<tr class="row-even"><td>driver</td> +<td>‘mcrypt’, ‘openssl’</td> +</tr> +<tr class="row-odd"><td>cipher</td> +<td>Cipher name (see <a class="reference internal" href="#ciphers-and-modes"><span class="std std-ref">Supported encryption ciphers and modes</span></a>)</td> +</tr> +<tr class="row-even"><td>mode</td> +<td>Encryption mode (see <a class="reference internal" href="#encryption-modes"><span class="std std-ref">Encryption modes</span></a>)</td> +</tr> +<tr class="row-odd"><td>key</td> +<td>Encryption key</td> +</tr> +</tbody> +</table> +<p>For example, if you were to change the encryption algorithm and +mode to AES-256 in CTR mode, this is what you should do:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">initialize</span><span class="p">(</span> + <span class="k">array</span><span class="p">(</span> + <span class="s1">'cipher'</span> <span class="o">=></span> <span class="s1">'aes-256'</span><span class="p">,</span> + <span class="s1">'mode'</span> <span class="o">=></span> <span class="s1">'ctr'</span><span class="p">,</span> + <span class="s1">'key'</span> <span class="o">=></span> <span class="s1">'<a 32-character random string>'</span> + <span class="p">)</span> +<span class="p">);</span> +</pre></div> +</div> +<p>Note that we only mentioned that you want to change the ciper and mode, +but we also included a key in the example. As previously noted, it is +important that you choose a key with a proper size for the used algorithm.</p> +<p>There’s also the ability to change the driver, if for some reason you +have both, but want to use MCrypt instead of OpenSSL:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="c1">// Switch to the MCrypt driver</span> +<span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">initialize</span><span class="p">(</span><span class="k">array</span><span class="p">(</span><span class="s1">'driver'</span> <span class="o">=></span> <span class="s1">'mcrypt'</span><span class="p">));</span> + +<span class="c1">// Switch back to the OpenSSL driver</span> +<span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">initialize</span><span class="p">(</span><span class="k">array</span><span class="p">(</span><span class="s1">'driver'</span> <span class="o">=></span> <span class="s1">'openssl'</span><span class="p">));</span> +</pre></div> +</div> +</div> +<div class="section" id="encrypting-and-decrypting-data"> +<h3><a class="toc-backref" href="#id12">Encrypting and decrypting data</a><a class="headerlink" href="#encrypting-and-decrypting-data" title="Permalink to this headline">¶</a></h3> +<p>Encrypting and decrypting data with the already configured library +settings is simple. As simple as just passing the string to the +<code class="docutils literal"><span class="pre">encrypt()</span></code> and/or <code class="docutils literal"><span class="pre">decrypt()</span></code> methods:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$plain_text</span> <span class="o">=</span> <span class="s1">'This is a plain-text message!'</span><span class="p">;</span> +<span class="nv">$ciphertext</span> <span class="o">=</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">encrypt</span><span class="p">(</span><span class="nv">$plain_text</span><span class="p">);</span> + +<span class="c1">// Outputs: This is a plain-text message!</span> +<span class="k">echo</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">decrypt</span><span class="p">(</span><span class="nv">$ciphertext</span><span class="p">);</span> +</pre></div> +</div> +<p>And that’s it! The Encryption library will do everything necessary +for the whole process to be cryptographically secure out-of-the-box. +You don’t need to worry about it.</p> +<div class="admonition important"> +<p class="first admonition-title">Important</p> +<p class="last">Both methods will return FALSE in case of an error. +While for <code class="docutils literal"><span class="pre">encrypt()</span></code> this can only mean incorrect +configuration, you should always check the return value +of <code class="docutils literal"><span class="pre">decrypt()</span></code> in production code.</p> +</div> +<div class="section" id="how-it-works"> +<h4><a class="toc-backref" href="#id13">How it works</a><a class="headerlink" href="#how-it-works" title="Permalink to this headline">¶</a></h4> +<p>If you must know how the process works, here’s what happens under +the hood:</p> +<ul class="simple"> +<li><code class="docutils literal"><span class="pre">$this->encryption->encrypt($plain_text)</span></code><ol class="arabic"> +<li>Derive an encryption key and a HMAC key from your configured +<em>encryption_key</em> via HKDF, using the SHA-512 digest algorithm.</li> +<li>Generate a random initialization vector (IV).</li> +<li>Encrypt the data via AES-128 in CBC mode (or another previously +configured cipher and mode), using the above-mentioned derived +encryption key and IV.</li> +<li>Prepend said IV to the resulting cipher-text.</li> +<li>Base64-encode the resulting string, so that it can be safely +stored or transferred without worrying about character sets.</li> +<li>Create a SHA-512 HMAC authentication message using the derived +HMAC key to ensure data integrity and prepend it to the Base64 +string.</li> +</ol> +</li> +<li><code class="docutils literal"><span class="pre">$this->encryption->decrypt($ciphertext)</span></code><ol class="arabic"> +<li>Derive an encryption key and a HMAC key from your configured +<em>encryption_key</em> via HKDF, using the SHA-512 digest algorithm. +Because your configured <em>encryption_key</em> is the same, this +will produce the same result as in the <code class="docutils literal"><span class="pre">encrypt()</span></code> method +above - otherwise you won’t be able to decrypt it.</li> +<li>Check if the string is long enough, separate the HMAC out of +it and validate if it is correct (this is done in a way that +prevents timing attacks against it). Return FALSE if either of +the checks fails.</li> +<li>Base64-decode the string.</li> +<li>Separate the IV out of the cipher-text and decrypt the said +cipher-text using that IV and the derived encryption key.</li> +</ol> +</li> +</ul> +</div> +<div class="section" id="using-custom-parameters"> +<span id="custom-parameters"></span><h4><a class="toc-backref" href="#id14">Using custom parameters</a><a class="headerlink" href="#using-custom-parameters" title="Permalink to this headline">¶</a></h4> +<p>Let’s say you have to interact with another system that is out +of your control and uses another method to encrypt data. A +method that will most certainly not match the above-described +sequence and probably not use all of the steps either.</p> +<p>The Encryption library allows you to change how its encryption +and decryption processes work, so that you can easily tailor a +custom solution for such situations.</p> +<div class="admonition note"> +<p class="first admonition-title">Note</p> +<p class="last">It is possible to use the library in this way, without +setting an <em>encryption_key</em> in your configuration file.</p> +</div> +<p>All you have to do is to pass an associative array with a few +parameters to either the <code class="docutils literal"><span class="pre">encrypt()</span></code> or <code class="docutils literal"><span class="pre">decrypt()</span></code> method. +Here’s an example:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="c1">// Assume that we have $ciphertext, $key and $hmac_key</span> +<span class="c1">// from on outside source</span> + +<span class="nv">$message</span> <span class="o">=</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">decrypt</span><span class="p">(</span> + <span class="nv">$ciphertext</span><span class="p">,</span> + <span class="k">array</span><span class="p">(</span> + <span class="s1">'cipher'</span> <span class="o">=></span> <span class="s1">'blowfish'</span><span class="p">,</span> + <span class="s1">'mode'</span> <span class="o">=></span> <span class="s1">'cbc'</span><span class="p">,</span> + <span class="s1">'key'</span> <span class="o">=></span> <span class="nv">$key</span><span class="p">,</span> + <span class="s1">'hmac_digest'</span> <span class="o">=></span> <span class="s1">'sha256'</span><span class="p">,</span> + <span class="s1">'hmac_key'</span> <span class="o">=></span> <span class="nv">$hmac_key</span> + <span class="p">)</span> +<span class="p">);</span> +</pre></div> +</div> +<p>In the above example, we are decrypting a message that was encrypted +using the Blowfish cipher in CBC mode and authenticated via a SHA-256 +HMAC.</p> +<div class="admonition important"> +<p class="first admonition-title">Important</p> +<p class="last">Note that both ‘key’ and ‘hmac_key’ are used in this +example. When using custom parameters, encryption and HMAC keys +are not derived like the default behavior of the library is.</p> +</div> +<p>Below is a list of the available options.</p> +<p>However, unless you really need to and you know what you are doing, +we advise you to not change the encryption process as this could +impact security, so please do so with caution.</p> +<table border="1" class="docutils"> +<colgroup> +<col width="12%" /> +<col width="14%" /> +<col width="26%" /> +<col width="49%" /> +</colgroup> +<thead valign="bottom"> +<tr class="row-odd"><th class="head">Option</th> +<th class="head">Default value</th> +<th class="head">Mandatory / Optional</th> +<th class="head">Description</th> +</tr> +</thead> +<tbody valign="top"> +<tr class="row-even"><td>cipher</td> +<td>N/A</td> +<td>Yes</td> +<td>Encryption algorithm (see <a class="reference internal" href="#ciphers-and-modes"><span class="std std-ref">Supported encryption ciphers and modes</span></a>).</td> +</tr> +<tr class="row-odd"><td>mode</td> +<td>N/A</td> +<td>Yes</td> +<td>Encryption mode (see <a class="reference internal" href="#encryption-modes"><span class="std std-ref">Encryption modes</span></a>).</td> +</tr> +<tr class="row-even"><td>key</td> +<td>N/A</td> +<td>Yes</td> +<td>Encryption key.</td> +</tr> +<tr class="row-odd"><td>hmac</td> +<td>TRUE</td> +<td>No</td> +<td>Whether to use a HMAC. +Boolean. If set to FALSE, then <em>hmac_digest</em> and +<em>hmac_key</em> will be ignored.</td> +</tr> +<tr class="row-even"><td>hmac_digest</td> +<td>sha512</td> +<td>No</td> +<td>HMAC message digest algorithm (see <a class="reference internal" href="#digests"><span class="std std-ref">Supported HMAC authentication algorithms</span></a>).</td> +</tr> +<tr class="row-odd"><td>hmac_key</td> +<td>N/A</td> +<td>Yes, unless <em>hmac</em> is FALSE</td> +<td>HMAC key.</td> +</tr> +<tr class="row-even"><td>raw_data</td> +<td>FALSE</td> +<td>No</td> +<td>Whether the cipher-text should be raw. +Boolean. If set to TRUE, then Base64 encoding and +decoding will not be performed and HMAC will not +be a hexadecimal string.</td> +</tr> +</tbody> +</table> +<div class="admonition important"> +<p class="first admonition-title">Important</p> +<p class="last"><code class="docutils literal"><span class="pre">encrypt()</span></code> and <code class="docutils literal"><span class="pre">decrypt()</span></code> will return FALSE if +a mandatory parameter is not provided or if a provided +value is incorrect. This includes <em>hmac_key</em>, unless <em>hmac</em> +is set to FALSE.</p> +</div> +</div> +<div class="section" id="supported-hmac-authentication-algorithms"> +<span id="digests"></span><h4><a class="toc-backref" href="#id15">Supported HMAC authentication algorithms</a><a class="headerlink" href="#supported-hmac-authentication-algorithms" title="Permalink to this headline">¶</a></h4> +<p>For HMAC message authentication, the Encryption library supports +usage of the SHA-2 family of algorithms:</p> +<table border="1" class="docutils"> +<colgroup> +<col width="19%" /> +<col width="34%" /> +<col width="47%" /> +</colgroup> +<thead valign="bottom"> +<tr class="row-odd"><th class="head">Algorithm</th> +<th class="head">Raw length (bytes)</th> +<th class="head">Hex-encoded length (bytes)</th> +</tr> +</thead> +<tbody valign="top"> +<tr class="row-even"><td>sha512</td> +<td>64</td> +<td>128</td> +</tr> +<tr class="row-odd"><td>sha384</td> +<td>48</td> +<td>96</td> +</tr> +<tr class="row-even"><td>sha256</td> +<td>32</td> +<td>64</td> +</tr> +<tr class="row-odd"><td>sha224</td> +<td>28</td> +<td>56</td> +</tr> +</tbody> +</table> +<p>The reason for not including other popular algorithms, such as +MD5 or SHA1 is that they are no longer considered secure enough +and as such, we don’t want to encourage their usage. +If you absolutely need to use them, it is easy to do so via PHP’s +native <a class="reference external" href="http://php.net/manual/en/function.hash-hmac.php">hash_hmac()</a> function.</p> +<p>Stronger algorithms of course will be added in the future as they +appear and become widely available.</p> +</div> +</div> +</div> +<div class="section" id="class-reference"> +<h2><a class="toc-backref" href="#id16">Class Reference</a><a class="headerlink" href="#class-reference" title="Permalink to this headline">¶</a></h2> +<dl class="class"> +<dt id="CI_Encryption"> +<em class="property">class </em><code class="descname">CI_Encryption</code><a class="headerlink" href="#CI_Encryption" title="Permalink to this definition">¶</a></dt> +<dd><dl class="method"> +<dt id="CI_Encryption::initialize"> +<code class="descname">initialize</code><span class="sig-paren">(</span><em>$params</em><span class="sig-paren">)</span><a class="headerlink" href="#CI_Encryption::initialize" title="Permalink to this definition">¶</a></dt> +<dd><table class="docutils field-list" frame="void" rules="none"> +<col class="field-name" /> +<col class="field-body" /> +<tbody valign="top"> +<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> +<li><strong>$params</strong> (<em>array</em>) – Configuration parameters</li> +</ul> +</td> +</tr> +<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">CI_Encryption instance (method chaining)</p> +</td> +</tr> +<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">CI_Encryption</p> +</td> +</tr> +</tbody> +</table> +<p>Initializes (configures) the library to use a different +driver, cipher, mode or key.</p> +<p>Example:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">initialize</span><span class="p">(</span> + <span class="k">array</span><span class="p">(</span><span class="s1">'mode'</span> <span class="o">=></span> <span class="s1">'ctr'</span><span class="p">)</span> +<span class="p">);</span> +</pre></div> +</div> +<p>Please refer to the <a class="reference internal" href="#configuration"><span class="std std-ref">Configuring the library</span></a> section for detailed info.</p> +</dd></dl> + +<dl class="method"> +<dt id="CI_Encryption::encrypt"> +<code class="descname">encrypt</code><span class="sig-paren">(</span><em>$data</em><span class="optional">[</span>, <em>$params = NULL</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#CI_Encryption::encrypt" title="Permalink to this definition">¶</a></dt> +<dd><table class="docutils field-list" frame="void" rules="none"> +<col class="field-name" /> +<col class="field-body" /> +<tbody valign="top"> +<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> +<li><strong>$data</strong> (<em>string</em>) – Data to encrypt</li> +<li><strong>$params</strong> (<em>array</em>) – Optional parameters</li> +</ul> +</td> +</tr> +<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">Encrypted data or FALSE on failure</p> +</td> +</tr> +<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">string</p> +</td> +</tr> +</tbody> +</table> +<p>Encrypts the input data and returns its ciphertext.</p> +<p>Example:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$ciphertext</span> <span class="o">=</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">encrypt</span><span class="p">(</span><span class="s1">'My secret message'</span><span class="p">);</span> +</pre></div> +</div> +<p>Please refer to the <a class="reference internal" href="#custom-parameters"><span class="std std-ref">Using custom parameters</span></a> section for information +on the optional parameters.</p> +</dd></dl> + +<dl class="method"> +<dt id="CI_Encryption::decrypt"> +<code class="descname">decrypt</code><span class="sig-paren">(</span><em>$data</em><span class="optional">[</span>, <em>$params = NULL</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#CI_Encryption::decrypt" title="Permalink to this definition">¶</a></dt> +<dd><table class="docutils field-list" frame="void" rules="none"> +<col class="field-name" /> +<col class="field-body" /> +<tbody valign="top"> +<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> +<li><strong>$data</strong> (<em>string</em>) – Data to decrypt</li> +<li><strong>$params</strong> (<em>array</em>) – Optional parameters</li> +</ul> +</td> +</tr> +<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">Decrypted data or FALSE on failure</p> +</td> +</tr> +<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">string</p> +</td> +</tr> +</tbody> +</table> +<p>Decrypts the input data and returns it in plain-text.</p> +<p>Example:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="k">echo</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">decrypt</span><span class="p">(</span><span class="nv">$ciphertext</span><span class="p">);</span> +</pre></div> +</div> +<p>Please refer to the <a class="reference internal" href="#custom-parameters"><span class="std std-ref">Using custom parameters</span></a> secrion for information +on the optional parameters.</p> +</dd></dl> + +<dl class="method"> +<dt id="CI_Encryption::create_key"> +<code class="descname">create_key</code><span class="sig-paren">(</span><em>$length</em><span class="sig-paren">)</span><a class="headerlink" href="#CI_Encryption::create_key" title="Permalink to this definition">¶</a></dt> +<dd><table class="docutils field-list" frame="void" rules="none"> +<col class="field-name" /> +<col class="field-body" /> +<tbody valign="top"> +<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> +<li><strong>$length</strong> (<em>int</em>) – Output length</li> +</ul> +</td> +</tr> +<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">A pseudo-random cryptographic key with the specified length, or FALSE on failure</p> +</td> +</tr> +<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">string</p> +</td> +</tr> +</tbody> +</table> +<p>Creates a cryptographic key by fetching random data from +the operating system’s sources (i.e. /dev/urandom).</p> +</dd></dl> + +<dl class="method"> +<dt id="CI_Encryption::hkdf"> +<code class="descname">hkdf</code><span class="sig-paren">(</span><em>$key</em><span class="optional">[</span>, <em>$digest = 'sha512'</em><span class="optional">[</span>, <em>$salt = NULL</em><span class="optional">[</span>, <em>$length = NULL</em><span class="optional">[</span>, <em>$info = ''</em><span class="optional">]</span><span class="optional">]</span><span class="optional">]</span><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#CI_Encryption::hkdf" title="Permalink to this definition">¶</a></dt> +<dd><table class="docutils field-list" frame="void" rules="none"> +<col class="field-name" /> +<col class="field-body" /> +<tbody valign="top"> +<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> +<li><strong>$key</strong> (<em>string</em>) – Input key material</li> +<li><strong>$digest</strong> (<em>string</em>) – A SHA-2 family digest algorithm</li> +<li><strong>$salt</strong> (<em>string</em>) – Optional salt</li> +<li><strong>$length</strong> (<em>int</em>) – Optional output length</li> +<li><strong>$info</strong> (<em>string</em>) – Optional context/application-specific info</li> +</ul> +</td> +</tr> +<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">A pseudo-random key or FALSE on failure</p> +</td> +</tr> +<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">string</p> +</td> +</tr> +</tbody> +</table> +<p>Derives a key from another, presumably weaker key.</p> +<p>This method is used internally to derive an encryption and HMAC key +from your configured <em>encryption_key</em>.</p> +<p>It is publicly available due to its otherwise general purpose. It is +described in <a class="reference external" href="https://tools.ietf.org/rfc/rfc5869.txt">RFC 5869</a>.</p> +<p>However, as opposed to the description in RFC 5869, this implementation +doesn’t support SHA1.</p> +<p>Example:</p> +<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$hmac_key</span> <span class="o">=</span> <span class="nv">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">hkdf</span><span class="p">(</span> + <span class="nv">$key</span><span class="p">,</span> + <span class="s1">'sha512'</span><span class="p">,</span> + <span class="k">NULL</span><span class="p">,</span> + <span class="k">NULL</span><span class="p">,</span> + <span class="s1">'authentication'</span> +<span class="p">);</span> + +<span class="c1">// $hmac_key is a pseudo-random key with a length of 64 bytes</span> +</pre></div> +</div> +</dd></dl> + +</dd></dl> + +</div> +</div> + + + </div> + <footer> + + <div class="rst-footer-buttons" role="navigation" aria-label="footer navigation"> + + <a href="file_uploading.html" class="btn btn-neutral float-right" title="File Uploading Class">Next <span class="fa fa-arrow-circle-right"></span></a> + + + <a href="encrypt.html" class="btn btn-neutral" title="Encrypt Class"><span class="fa fa-arrow-circle-left"></span> Previous</a> + + </div> + + + <hr/> + + <div role="contentinfo"> + <p> + © Copyright 2014 - 2018, British Columbia Institute of Technology. + Last updated on Jan 13, 2018. + </p> + </div> + + Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. + +</footer> + </div> + </div> + + </section> + + </div> + + + + + + <script type="text/javascript"> + var DOCUMENTATION_OPTIONS = { + URL_ROOT:'../', + VERSION:'3.1.7', + COLLAPSE_INDEX:false, + FILE_SUFFIX:'.html', + HAS_SOURCE: false + }; + </script> + <script type="text/javascript" src="../_static/jquery.js"></script> + <script type="text/javascript" src="../_static/underscore.js"></script> + <script type="text/javascript" src="../_static/doctools.js"></script> + + + + + + <script type="text/javascript" src="../_static/js/theme.js"></script> + + + + + <script type="text/javascript"> + jQuery(function () { + SphinxRtdTheme.StickyNav.enable(); + }); + </script> + + +</body> +</html>
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