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<div class="title">GF128 Class Reference</div> </div>
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<p>Operations in the Galois field GF(2^128).
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<a href="classGF128.html#details">More...</a></p>
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<p><code>#include <<a class="el" href="GF128_8h_source.html">GF128.h</a>></code></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
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Static Public Member Functions</h2></td></tr>
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<tr class="memitem:a43adbd72619e4f97ce427a60e7c0a248"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="classGF128.html#a43adbd72619e4f97ce427a60e7c0a248">mulInit</a> (uint32_t H[4], const void *key)</td></tr>
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<tr class="memdesc:a43adbd72619e4f97ce427a60e7c0a248"><td class="mdescLeft"> </td><td class="mdescRight">Initialize multiplication in the GF(2^128) field. <a href="#a43adbd72619e4f97ce427a60e7c0a248">More...</a><br/></td></tr>
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<tr class="separator:a43adbd72619e4f97ce427a60e7c0a248"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a7d9a341a1715d37d25feba21627bc3ab"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="classGF128.html#a7d9a341a1715d37d25feba21627bc3ab">mul</a> (uint32_t Y[4], const uint32_t H[4])</td></tr>
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<tr class="memdesc:a7d9a341a1715d37d25feba21627bc3ab"><td class="mdescLeft"> </td><td class="mdescRight">Perform a multiplication in the GF(2^128) field. <a href="#a7d9a341a1715d37d25feba21627bc3ab">More...</a><br/></td></tr>
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<tr class="separator:a7d9a341a1715d37d25feba21627bc3ab"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aef22f6b7be5937f60ed2b7bcf831e52d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d">dbl</a> (uint32_t V[4])</td></tr>
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<tr class="memdesc:aef22f6b7be5937f60ed2b7bcf831e52d"><td class="mdescLeft"> </td><td class="mdescRight">Doubles a value in the GF(2^128) field. <a href="#aef22f6b7be5937f60ed2b7bcf831e52d">More...</a><br/></td></tr>
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<tr class="separator:aef22f6b7be5937f60ed2b7bcf831e52d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a56000a4cd7d436de42360e9d43eecde4"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="classGF128.html#a56000a4cd7d436de42360e9d43eecde4">dblEAX</a> (uint32_t V[4])</td></tr>
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<tr class="memdesc:a56000a4cd7d436de42360e9d43eecde4"><td class="mdescLeft"> </td><td class="mdescRight">Doubles a value in the GF(2^128) field using <a class="el" href="classEAX.html" title="Implementation of the EAX authenticated cipher. ">EAX</a> conventions. <a href="#a56000a4cd7d436de42360e9d43eecde4">More...</a><br/></td></tr>
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<tr class="separator:a56000a4cd7d436de42360e9d43eecde4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3732c9471771c36ac1b518e974d46b3e"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="classGF128.html#a3732c9471771c36ac1b518e974d46b3e">dblXTS</a> (uint32_t V[4])</td></tr>
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<tr class="memdesc:a3732c9471771c36ac1b518e974d46b3e"><td class="mdescLeft"> </td><td class="mdescRight">Doubles a value in the GF(2^128) field using <a class="el" href="classXTS.html" title="Implementation of the XTS mode for 128-bit block ciphers. ">XTS</a> conventions. <a href="#a3732c9471771c36ac1b518e974d46b3e">More...</a><br/></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Operations in the Galois field GF(2^128). </p>
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<p>This class contains helper functions for performing operations in the Galois field GF(2^128) which is used as the basis of <a class="el" href="classGCM.html" title="Implementation of the Galois Counter Mode (GCM). ">GCM</a> and <a class="el" href="classGHASH.html" title="Implementation of the GHASH message authenticator. ">GHASH</a>. These functions are provided for use by other cryptographic protocols that make use of GF(2^128).</p>
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<p>Most of the functions in this class use the field, polynomial, and byte ordering conventions described in NIST SP 800-38D (<a class="el" href="classGCM.html" title="Implementation of the Galois Counter Mode (GCM). ">GCM</a>). The one exception is <a class="el" href="classGF128.html#a56000a4cd7d436de42360e9d43eecde4" title="Doubles a value in the GF(2^128) field using EAX conventions. ">dblEAX()</a> which uses the conventions of <a class="el" href="classEAX.html" title="Implementation of the EAX authenticated cipher. ">EAX</a> mode instead.</p>
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<p>References: <a href="http://csrc.nist.gov/publications/nistpubs/800-38D/SP-800-38D.pdf">NIST SP 800-38D</a></p>
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<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classGCM.html" title="Implementation of the Galois Counter Mode (GCM). ">GCM</a>, <a class="el" href="classGHASH.html" title="Implementation of the GHASH message authenticator. ">GHASH</a> </dd></dl>
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<p>Definition at line <a class="el" href="GF128_8h_source.html#l00028">28</a> of file <a class="el" href="GF128_8h_source.html">GF128.h</a>.</p>
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</div><h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">void GF128::dbl </td>
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<td>(</td>
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<td class="paramtype">uint32_t </td>
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<td class="paramname"><em>V</em>[4]</td><td>)</td>
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<p>Doubles a value in the GF(2^128) field. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">V</td><td>The value to double, and the result. This array is assumed to be in big-endian order on entry and exit.</td></tr>
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<p>Block cipher modes such as <a href="https://en.wikipedia.org/wiki/Disk_encryption_theory#Xor-encrypt-xor_.28XEX.29">XEX</a> are similar to <a class="el" href="classCTR.html" title="Implementation of the Counter (CTR) mode for 128-bit block ciphers. ">CTR</a> mode but instead of incrementing the nonce every block, the modes multiply the nonce by 2 in the GF(2^128) field every block. This function is provided to help with implementing such modes.</p>
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<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classGF128.html#a56000a4cd7d436de42360e9d43eecde4" title="Doubles a value in the GF(2^128) field using EAX conventions. ">dblEAX()</a>, <a class="el" href="classGF128.html#a3732c9471771c36ac1b518e974d46b3e" title="Doubles a value in the GF(2^128) field using XTS conventions. ">dblXTS()</a>, <a class="el" href="classGF128.html#a7d9a341a1715d37d25feba21627bc3ab" title="Perform a multiplication in the GF(2^128) field. ">mul()</a> </dd></dl>
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<p>Definition at line <a class="el" href="GF128_8cpp_source.html#l00314">314</a> of file <a class="el" href="GF128_8cpp_source.html">GF128.cpp</a>.</p>
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<td class="memname">void GF128::dblEAX </td>
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<td>(</td>
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<td class="paramtype">uint32_t </td>
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<td class="paramname"><em>V</em>[4]</td><td>)</td>
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<p>Doubles a value in the GF(2^128) field using <a class="el" href="classEAX.html" title="Implementation of the EAX authenticated cipher. ">EAX</a> conventions. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">V</td><td>The value to double, and the result. This array is assumed to be in big-endian order on entry and exit.</td></tr>
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<p>This function differs from <a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d" title="Doubles a value in the GF(2^128) field. ">dbl()</a> that it uses the conventions of <a class="el" href="classEAX.html" title="Implementation of the EAX authenticated cipher. ">EAX</a> mode instead of those of NIST SP 800-38D (<a class="el" href="classGCM.html" title="Implementation of the Galois Counter Mode (GCM). ">GCM</a>). The two operations have equivalent security but the bits are ordered differently with the value shifted left instead of right.</p>
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<p>References: <a href="https://en.wikipedia.org/wiki/EAX_mode,">https://en.wikipedia.org/wiki/EAX_mode,</a> <a href="http://web.cs.ucdavis.edu/~rogaway/papers/eax.html">http://web.cs.ucdavis.edu/~rogaway/papers/eax.html</a></p>
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<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d" title="Doubles a value in the GF(2^128) field. ">dbl()</a>, <a class="el" href="classGF128.html#a3732c9471771c36ac1b518e974d46b3e" title="Doubles a value in the GF(2^128) field using XTS conventions. ">dblXTS()</a>, <a class="el" href="classGF128.html#a7d9a341a1715d37d25feba21627bc3ab" title="Perform a multiplication in the GF(2^128) field. ">mul()</a> </dd></dl>
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<p>Definition at line <a class="el" href="GF128_8cpp_source.html#l00406">406</a> of file <a class="el" href="GF128_8cpp_source.html">GF128.cpp</a>.</p>
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<td class="memname">void GF128::dblXTS </td>
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<td>(</td>
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<td class="paramname"><em>V</em>[4]</td><td>)</td>
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<p>Doubles a value in the GF(2^128) field using <a class="el" href="classXTS.html" title="Implementation of the XTS mode for 128-bit block ciphers. ">XTS</a> conventions. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">V</td><td>The value to double, and the result. This array is assumed to be in littlen-endian order on entry and exit.</td></tr>
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<p>This function differs from <a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d" title="Doubles a value in the GF(2^128) field. ">dbl()</a> that it uses the conventions of <a class="el" href="classXTS.html" title="Implementation of the XTS mode for 128-bit block ciphers. ">XTS</a> mode instead of those of NIST SP 800-38D (<a class="el" href="classGCM.html" title="Implementation of the Galois Counter Mode (GCM). ">GCM</a>). The two operations have equivalent security but the bits are ordered differently with the value shifted left instead of right.</p>
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<p>References: <a href="http://libeccio.di.unisa.it/Crypto14/Lab/p1619.pdf">IEEE Std. 1619-2007, XTS-AES</a></p>
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<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d" title="Doubles a value in the GF(2^128) field. ">dbl()</a>, <a class="el" href="classGF128.html#a56000a4cd7d436de42360e9d43eecde4" title="Doubles a value in the GF(2^128) field using EAX conventions. ">dblEAX()</a>, <a class="el" href="classGF128.html#a7d9a341a1715d37d25feba21627bc3ab" title="Perform a multiplication in the GF(2^128) field. ">mul()</a> </dd></dl>
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<p>Definition at line <a class="el" href="GF128_8cpp_source.html#l00497">497</a> of file <a class="el" href="GF128_8cpp_source.html">GF128.cpp</a>.</p>
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<td class="memname">void GF128::mul </td>
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<td>(</td>
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<td class="paramname"><em>Y</em>[4], </td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Perform a multiplication in the GF(2^128) field. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">Y</td><td>The first value to multiply, and the result. This array is assumed to be in big-endian order on entry and exit. </td></tr>
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<tr><td class="paramname">H</td><td>The second value to multiply, which must have been initialized by the <a class="el" href="classGF128.html#a43adbd72619e4f97ce427a60e7c0a248" title="Initialize multiplication in the GF(2^128) field. ">mulInit()</a> function.</td></tr>
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<p>This function and the companion <a class="el" href="classGF128.html#a43adbd72619e4f97ce427a60e7c0a248" title="Initialize multiplication in the GF(2^128) field. ">mulInit()</a> are intended for use by other classes that need access to the raw GF(2^128) field multiplication of <a class="el" href="classGHASH.html" title="Implementation of the GHASH message authenticator. ">GHASH</a> without the overhead of <a class="el" href="classGHASH.html" title="Implementation of the GHASH message authenticator. ">GHASH</a> itself.</p>
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<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classGF128.html#a43adbd72619e4f97ce427a60e7c0a248" title="Initialize multiplication in the GF(2^128) field. ">mulInit()</a>, <a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d" title="Doubles a value in the GF(2^128) field. ">dbl()</a> </dd></dl>
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<p>Definition at line <a class="el" href="GF128_8cpp_source.html#l00090">90</a> of file <a class="el" href="GF128_8cpp_source.html">GF128.cpp</a>.</p>
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<td class="memname">void GF128::mulInit </td>
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<td>(</td>
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<td class="paramtype">uint32_t </td>
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<td class="paramname"><em>H</em>[4], </td>
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<td class="paramname"><em>key</em> </td>
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<td>)</td>
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<td></td><td></td>
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<td class="mlabels-right">
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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</div><div class="memdoc">
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<p>Initialize multiplication in the GF(2^128) field. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">H</td><td>The hash state to be initialized. </td></tr>
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<tr><td class="paramname">key</td><td>Points to the 16 byte authentication key which is assumed to be in big-endian byte order.</td></tr>
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<p>This function and the companion <a class="el" href="classGF128.html#a7d9a341a1715d37d25feba21627bc3ab" title="Perform a multiplication in the GF(2^128) field. ">mul()</a> are intended for use by other classes that need access to the raw GF(2^128) field multiplication of <a class="el" href="classGHASH.html" title="Implementation of the GHASH message authenticator. ">GHASH</a> without the overhead of <a class="el" href="classGHASH.html" title="Implementation of the GHASH message authenticator. ">GHASH</a> itself.</p>
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<dl class="section see"><dt>See Also</dt><dd><a class="el" href="classGF128.html#a7d9a341a1715d37d25feba21627bc3ab" title="Perform a multiplication in the GF(2^128) field. ">mul()</a>, <a class="el" href="classGF128.html#aef22f6b7be5937f60ed2b7bcf831e52d" title="Doubles a value in the GF(2^128) field. ">dbl()</a> </dd></dl>
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<p>Definition at line <a class="el" href="GF128_8cpp_source.html#l00058">58</a> of file <a class="el" href="GF128_8cpp_source.html">GF128.cpp</a>.</p>
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<hr/>The documentation for this class was generated from the following files:<ul>
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<li><a class="el" href="GF128_8h_source.html">GF128.h</a></li>
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<li><a class="el" href="GF128_8cpp_source.html">GF128.cpp</a></li>
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</ul>
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