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diff --git a/user_guide/libraries/encryption.html b/user_guide/libraries/encryption.html deleted file mode 100644 index 745509305..000000000 --- a/user_guide/libraries/encryption.html +++ /dev/null @@ -1,1406 +0,0 @@ - - -<!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 3.1.5 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="top" title="CodeIgniter 3.1.5 documentation" href="../index.html"/> - 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src="data:image/gif;base64,R0lGODlhFAAUAJEAAAAAADMzM////wAAACH5BAUUAAIALAAAAAAUABQAAAImlI+py+0PU5gRBRDM3DxbWoXis42X13USOLauUIqnlsaH/eY6UwAAOw==" /> - </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 <tt class="docutils literal"><span class="pre">$this->load->library()</span></tt> -method:</p> -<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$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 <tt class="docutils literal"><span class="pre">create_key()</span></tt> 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 <tt class="docutils literal"><span class="pre">create_key()</span></tt> method outputs binary data, which -is hard to deal with (i.e. a copy-paste may damage it), so you may use -<tt class="docutils literal"><span class="pre">bin2hex()</span></tt>, <tt class="docutils literal"><span class="pre">hex2bin()</span></tt> 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"><em>Encrypt Class</em></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 <tt class="docutils literal"><span class="pre">$config['encryption_key']</span></tt> value.</p> -<p>If you wish to change that however, you need to use the <tt class="docutils literal"><span class="pre">initialize()</span></tt> -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"><em>Supported encryption ciphers and modes</em></a>)</td> -</tr> -<tr class="row-even"><td>mode</td> -<td>Encryption mode (see <a class="reference internal" href="#encryption-modes"><em>Encryption modes</em></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">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">initialize</span><span class="p">(</span><span class="k">array</span><span class="p">(</span><span class="s1">'driver'</span> <span class="o">=></span> <span class="s1">'openssl'</span><span class="p">));</span> -</pre></div> -</div> -</div> -<div class="section" id="encrypting-and-decrypting-data"> -<h3><a class="toc-backref" href="#id12">Encrypting and decrypting data</a><a class="headerlink" href="#encrypting-and-decrypting-data" title="Permalink to this headline">¶</a></h3> -<p>Encrypting and decrypting data with the already configured library -settings is simple. As simple as just passing the string to the -<tt class="docutils literal"><span class="pre">encrypt()</span></tt> and/or <tt class="docutils literal"><span class="pre">decrypt()</span></tt> methods:</p> -<div class="highlight-ci"><div class="highlight"><pre><span></span><span class="nv">$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">$ciphertext</span><span class="p">);</span> -</pre></div> -</div> -<p>And that’s it! The Encryption library will do everything necessary -for the whole process to be cryptographically secure out-of-the-box. -You don’t need to worry about it.</p> -<div class="admonition important"> -<p class="first admonition-title">Important</p> -<p class="last">Both methods will return FALSE in case of an error. -While for <tt class="docutils literal"><span class="pre">encrypt()</span></tt> this can only mean incorrect -configuration, you should always check the return value -of <tt class="docutils literal"><span class="pre">decrypt()</span></tt> in production code.</p> -</div> -<div class="section" id="how-it-works"> -<h4><a class="toc-backref" href="#id13">How it works</a><a class="headerlink" href="#how-it-works" title="Permalink to this headline">¶</a></h4> -<p>If you must know how the process works, here’s what happens under -the hood:</p> -<ul class="simple"> -<li><tt class="docutils literal"><span class="pre">$this->encryption->encrypt($plain_text)</span></tt><ol class="arabic"> -<li>Derive an encryption key and a HMAC key from your configured -<em>encryption_key</em> via HKDF, using the SHA-512 digest algorithm.</li> -<li>Generate a random initialization vector (IV).</li> -<li>Encrypt the data via AES-128 in CBC mode (or another previously -configured cipher and mode), using the above-mentioned derived -encryption key and IV.</li> -<li>Prepend said IV to the resulting cipher-text.</li> -<li>Base64-encode the resulting string, so that it can be safely -stored or transferred without worrying about character sets.</li> -<li>Create a SHA-512 HMAC authentication message using the derived -HMAC key to ensure data integrity and prepend it to the Base64 -string.</li> -</ol> -</li> -<li><tt class="docutils literal"><span class="pre">$this->encryption->decrypt($ciphertext)</span></tt><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 <tt class="docutils literal"><span class="pre">encrypt()</span></tt> 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 <tt class="docutils literal"><span class="pre">encrypt()</span></tt> or <tt class="docutils literal"><span class="pre">decrypt()</span></tt> 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"><em>Supported encryption ciphers and modes</em></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"><em>Encryption modes</em></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"><em>Supported HMAC authentication algorithms</em></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"><tt class="docutils literal"><span class="pre">encrypt()</span></tt> and <tt class="docutils literal"><span class="pre">decrypt()</span></tt> 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><tt class="descname">CI_Encryption</tt><a class="headerlink" href="#CI_Encryption" title="Permalink to this definition">¶</a></dt> -<dd><dl class="method"> -<dt id="CI_Encryption::initialize"> -<tt class="descname">initialize</tt><big>(</big><em>$params</em><big>)</big><a class="headerlink" href="#CI_Encryption::initialize" title="Permalink to this definition">¶</a></dt> -<dd><table class="docutils field-list" frame="void" rules="none"> -<col class="field-name" /> -<col class="field-body" /> -<tbody valign="top"> -<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> -<li><strong>$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">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">initialize</span><span class="p">(</span> - <span class="k">array</span><span class="p">(</span><span class="s1">'mode'</span> <span class="o">=></span> <span class="s1">'ctr'</span><span class="p">)</span> -<span class="p">);</span> -</pre></div> -</div> -<p>Please refer to the <a class="reference internal" href="#configuration"><em>Configuring the library</em></a> section for detailed info.</p> -</dd></dl> - -<dl class="method"> -<dt id="CI_Encryption::encrypt"> -<tt class="descname">encrypt</tt><big>(</big><em>$data</em><span class="optional">[</span>, <em>$params = NULL</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#CI_Encryption::encrypt" title="Permalink to this definition">¶</a></dt> -<dd><table class="docutils field-list" frame="void" rules="none"> -<col class="field-name" /> -<col class="field-body" /> -<tbody valign="top"> -<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> -<li><strong>$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">$this</span><span class="o">-></span><span class="na">encryption</span><span class="o">-></span><span class="na">encrypt</span><span class="p">(</span><span class="s1">'My secret message'</span><span class="p">);</span> -</pre></div> -</div> -<p>Please refer to the <a class="reference internal" href="#custom-parameters"><em>Using custom parameters</em></a> section for information -on the optional parameters.</p> -</dd></dl> - -<dl class="method"> -<dt id="CI_Encryption::decrypt"> -<tt class="descname">decrypt</tt><big>(</big><em>$data</em><span class="optional">[</span>, <em>$params = NULL</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#CI_Encryption::decrypt" title="Permalink to this definition">¶</a></dt> -<dd><table class="docutils field-list" frame="void" rules="none"> -<col class="field-name" /> -<col class="field-body" /> -<tbody valign="top"> -<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> -<li><strong>$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">$ciphertext</span><span class="p">);</span> -</pre></div> -</div> -<p>Please refer to the <a class="reference internal" href="#custom-parameters"><em>Using custom parameters</em></a> secrion for information -on the optional parameters.</p> -</dd></dl> - -<dl class="method"> -<dt id="CI_Encryption::create_key"> -<tt class="descname">create_key</tt><big>(</big><em>$length</em><big>)</big><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>$length</strong> (<em>int</em>) – Output length</li> -</ul> -</td> -</tr> -<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">A pseudo-random cryptographic key with the specified length, or FALSE on failure</p> -</td> -</tr> -<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">string</p> -</td> -</tr> -</tbody> -</table> -<p>Creates a cryptographic key by fetching random data from -the operating system’s sources (i.e. /dev/urandom).</p> -</dd></dl> - -<dl class="method"> -<dt id="CI_Encryption::hkdf"> -<tt class="descname">hkdf</tt><big>(</big><em>$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><big>)</big><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 - 2017, British Columbia Institute of Technology. - Last updated on Jun 19, 2017. - </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:'3.1.5', - 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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