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<title>Crypto++: GFP2_ONB< F > Class Template Reference</title>
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<div id="projectname">Crypto++
 <span id="projectnumber">7.0</span>
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<div id="projectbrief">Free C++ class library of cryptographic schemes</div>
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<a href="#pub-types">Public Types</a> |
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<div class="title">GFP2_ONB< F > Class Template Reference</div> </div>
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<p>GF(p^2), optimal normal basis.
<a href="class_g_f_p2___o_n_b.html#details">More...</a></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for GFP2_ONB< F >:</div>
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<img src="class_g_f_p2___o_n_b.png" usemap="#GFP2_5FONB_3C_20F_20_3E_map" alt=""/>
<map id="GFP2_5FONB_3C_20F_20_3E_map" name="GFP2_5FONB_3C_20F_20_3E_map">
<area href="class_abstract_ring.html" alt="AbstractRing< GFP2Element >" shape="rect" coords="0,56,194,80"/>
<area href="class_abstract_group.html" alt="AbstractGroup< GFP2Element >" shape="rect" coords="0,0,194,24"/>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:ad3bffbe1a6c331daf56bb6ec51cbc294"><td class="memItemLeft" align="right" valign="top"><a id="ad3bffbe1a6c331daf56bb6ec51cbc294"></a>
typedef F </td><td class="memItemRight" valign="bottom"><b>BaseField</b></td></tr>
<tr class="separator:ad3bffbe1a6c331daf56bb6ec51cbc294"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_types_class_abstract_ring"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_abstract_ring')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_abstract_ring.html">AbstractRing< GFP2Element ></a></td></tr>
<tr class="memitem:acd93e8ce4e2897173310c68fcb60f3e9 inherit pub_types_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"><a id="acd93e8ce4e2897173310c68fcb60f3e9"></a>
typedef <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:acd93e8ce4e2897173310c68fcb60f3e9 inherit pub_types_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_types_class_abstract_group"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_abstract_group')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_abstract_group.html">AbstractGroup< GFP2Element ></a></td></tr>
<tr class="memitem:a4a2b3308fb5c13f70fcc5746be52ba7b inherit pub_types_class_abstract_group"><td class="memItemLeft" align="right" valign="top"><a id="a4a2b3308fb5c13f70fcc5746be52ba7b"></a>
typedef <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:a4a2b3308fb5c13f70fcc5746be52ba7b inherit pub_types_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
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Public Member Functions</h2></td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>GFP2_ONB</b> (const <a class="el" href="class_integer.html">Integer</a> &p)</td></tr>
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const <a class="el" href="class_integer.html">Integer</a> & </td><td class="memItemRight" valign="bottom"><b>GetModulus</b> () const</td></tr>
<tr class="separator:a3a84528c019f87e690b2ee5c3e1516c1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5c1e9463122f48d9db8a0c3bd284bad1"><td class="memItemLeft" align="right" valign="top"><a id="a5c1e9463122f48d9db8a0c3bd284bad1"></a>
<a class="el" href="class_g_f_p2_element.html">GFP2Element</a> </td><td class="memItemRight" valign="bottom"><b>ConvertIn</b> (const <a class="el" href="class_integer.html">Integer</a> &a) const</td></tr>
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<a class="el" href="class_g_f_p2_element.html">GFP2Element</a> </td><td class="memItemRight" valign="bottom"><b>ConvertIn</b> (const <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> &a) const</td></tr>
<tr class="separator:a0a7633cc44f9b36efb1ace5cdd41579c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad5ec9517132671ca1fd5825c811e565d"><td class="memItemLeft" align="right" valign="top"><a id="ad5ec9517132671ca1fd5825c811e565d"></a>
<a class="el" href="class_g_f_p2_element.html">GFP2Element</a> </td><td class="memItemRight" valign="bottom"><b>ConvertOut</b> (const <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> &a) const</td></tr>
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<tr class="memitem:aab4d8f8eec60122c1f3e3ba2c9ad2673"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#aab4d8f8eec60122c1f3e3ba2c9ad2673">Equal</a> (const <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> &b) const</td></tr>
<tr class="memdesc:aab4d8f8eec60122c1f3e3ba2c9ad2673"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="#aab4d8f8eec60122c1f3e3ba2c9ad2673">More...</a><br /></td></tr>
<tr class="separator:aab4d8f8eec60122c1f3e3ba2c9ad2673"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a386495ffc3d413f461a9001fe6f30642"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#a386495ffc3d413f461a9001fe6f30642">Identity</a> () const</td></tr>
<tr class="memdesc:a386495ffc3d413f461a9001fe6f30642"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="#a386495ffc3d413f461a9001fe6f30642">More...</a><br /></td></tr>
<tr class="separator:a386495ffc3d413f461a9001fe6f30642"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abd707cb221dd44914e8cde2839ad90c7"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#abd707cb221dd44914e8cde2839ad90c7">Add</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">Element</a> &b) const</td></tr>
<tr class="memdesc:abd707cb221dd44914e8cde2839ad90c7"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="#abd707cb221dd44914e8cde2839ad90c7">More...</a><br /></td></tr>
<tr class="separator:abd707cb221dd44914e8cde2839ad90c7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac9fa7ce33239b3d7f88c9cac9c2d74d3"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#ac9fa7ce33239b3d7f88c9cac9c2d74d3">Inverse</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
<tr class="memdesc:ac9fa7ce33239b3d7f88c9cac9c2d74d3"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="#ac9fa7ce33239b3d7f88c9cac9c2d74d3">More...</a><br /></td></tr>
<tr class="separator:ac9fa7ce33239b3d7f88c9cac9c2d74d3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a39cef4f74a7bd5588a7293b1d364334e"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#a39cef4f74a7bd5588a7293b1d364334e">Double</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a39cef4f74a7bd5588a7293b1d364334e"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="#a39cef4f74a7bd5588a7293b1d364334e">More...</a><br /></td></tr>
<tr class="separator:a39cef4f74a7bd5588a7293b1d364334e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aedbcc151eca01f823b6d8c34f792fad9"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#aedbcc151eca01f823b6d8c34f792fad9">Subtract</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">Element</a> &b) const</td></tr>
<tr class="memdesc:aedbcc151eca01f823b6d8c34f792fad9"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="#aedbcc151eca01f823b6d8c34f792fad9">More...</a><br /></td></tr>
<tr class="separator:aedbcc151eca01f823b6d8c34f792fad9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9ea72a20954c87db4467e14fdaa67037"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#a9ea72a20954c87db4467e14fdaa67037">Accumulate</a> (<a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">Element</a> &b) const</td></tr>
<tr class="memdesc:a9ea72a20954c87db4467e14fdaa67037"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="#a9ea72a20954c87db4467e14fdaa67037">More...</a><br /></td></tr>
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<tr class="memitem:ac6d39d886f9ddc047fcc4c5adcc23db9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#ac6d39d886f9ddc047fcc4c5adcc23db9">Reduce</a> (<a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">Element</a> &b) const</td></tr>
<tr class="memdesc:ac6d39d886f9ddc047fcc4c5adcc23db9"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="#ac6d39d886f9ddc047fcc4c5adcc23db9">More...</a><br /></td></tr>
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<tr class="memitem:ac0e339d3509a26757486bbc78e339910"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#ac0e339d3509a26757486bbc78e339910">IsUnit</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
<tr class="memdesc:ac0e339d3509a26757486bbc78e339910"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="#ac0e339d3509a26757486bbc78e339910">More...</a><br /></td></tr>
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<tr class="memitem:aa1d3c030219de3c1635a72fbdf0c7228"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#aa1d3c030219de3c1635a72fbdf0c7228">MultiplicativeIdentity</a> () const</td></tr>
<tr class="memdesc:aa1d3c030219de3c1635a72fbdf0c7228"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="#aa1d3c030219de3c1635a72fbdf0c7228">More...</a><br /></td></tr>
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<tr class="memitem:abe477db3d5bf5fdb72b9fcc832ff8bac"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#abe477db3d5bf5fdb72b9fcc832ff8bac">Multiply</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">Element</a> &b) const</td></tr>
<tr class="memdesc:abe477db3d5bf5fdb72b9fcc832ff8bac"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="#abe477db3d5bf5fdb72b9fcc832ff8bac">More...</a><br /></td></tr>
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<tr class="memitem:a42f1dfe03023fb5502843e326892850c"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#a42f1dfe03023fb5502843e326892850c">MultiplicativeInverse</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a42f1dfe03023fb5502843e326892850c"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="#a42f1dfe03023fb5502843e326892850c">More...</a><br /></td></tr>
<tr class="separator:a42f1dfe03023fb5502843e326892850c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a41cd047c0fc625ecde993d839d8d86b7"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#a41cd047c0fc625ecde993d839d8d86b7">Square</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
<tr class="memdesc:a41cd047c0fc625ecde993d839d8d86b7"><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="class_square.html" title="Square block cipher. ">Square</a> an element in the group. <a href="#a41cd047c0fc625ecde993d839d8d86b7">More...</a><br /></td></tr>
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<tr class="memitem:ad71eeac946b5f17fcb6645bd2f281d23"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_g_f_p2_element.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f_p2___o_n_b.html#ad71eeac946b5f17fcb6645bd2f281d23">Exponentiate</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_integer.html">Integer</a> &e) const</td></tr>
<tr class="memdesc:ad71eeac946b5f17fcb6645bd2f281d23"><td class="mdescLeft"> </td><td class="mdescRight">Raises a base to an exponent in the group. <a href="#ad71eeac946b5f17fcb6645bd2f281d23">More...</a><br /></td></tr>
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const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><b>PthPower</b> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
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void </td><td class="memItemRight" valign="bottom"><b>RaiseToPthPower</b> (<a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
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const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><b>SpecialOperation1</b> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a) const</td></tr>
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<tr class="memitem:ad09d21b2ea1ddf904ee596de07e58d94"><td class="memItemLeft" align="right" valign="top"><a id="ad09d21b2ea1ddf904ee596de07e58d94"></a>
const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><b>SpecialOperation2</b> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &x, const <a class="el" href="class_g_f_p2_element.html">Element</a> &y, const <a class="el" href="class_g_f_p2_element.html">Element</a> &z) const</td></tr>
<tr class="separator:ad09d21b2ea1ddf904ee596de07e58d94"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_abstract_ring"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_abstract_ring')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_abstract_ring.html">AbstractRing< GFP2Element ></a></td></tr>
<tr class="memitem:ae55c525c1aa75bf898907bd6949e2b64 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"><a id="ae55c525c1aa75bf898907bd6949e2b64"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#ae55c525c1aa75bf898907bd6949e2b64">AbstractRing</a> ()</td></tr>
<tr class="memdesc:ae55c525c1aa75bf898907bd6949e2b64 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Construct an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <br /></td></tr>
<tr class="separator:ae55c525c1aa75bf898907bd6949e2b64 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acc8afd5ce95e32e45d3c30a710bf36dc inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#acc8afd5ce95e32e45d3c30a710bf36dc">AbstractRing</a> (const <a class="el" href="class_abstract_ring.html">AbstractRing</a> &source)</td></tr>
<tr class="memdesc:acc8afd5ce95e32e45d3c30a710bf36dc inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Copy construct an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <a href="class_abstract_ring.html#acc8afd5ce95e32e45d3c30a710bf36dc">More...</a><br /></td></tr>
<tr class="separator:acc8afd5ce95e32e45d3c30a710bf36dc inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a26709c02c869d09d756653ae1129f8a9 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top"><a class="el" href="class_abstract_ring.html">AbstractRing</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a26709c02c869d09d756653ae1129f8a9">operator=</a> (const <a class="el" href="class_abstract_ring.html">AbstractRing</a> &source)</td></tr>
<tr class="memdesc:a26709c02c869d09d756653ae1129f8a9 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Assign an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <a href="class_abstract_ring.html#a26709c02c869d09d756653ae1129f8a9">More...</a><br /></td></tr>
<tr class="separator:a26709c02c869d09d756653ae1129f8a9 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa7ce20a30d89a8257088930d1d06d0b7 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#aa7ce20a30d89a8257088930d1d06d0b7">Divide</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_g_f_p2_element.html">Element</a> &b) const</td></tr>
<tr class="memdesc:aa7ce20a30d89a8257088930d1d06d0b7 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Divides elements in the group. <a href="class_abstract_ring.html#aa7ce20a30d89a8257088930d1d06d0b7">More...</a><br /></td></tr>
<tr class="separator:aa7ce20a30d89a8257088930d1d06d0b7 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:adb4d33ac59a8f8bff1752b75809136e6 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_g_f_p2_element.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">CascadeExponentiate</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const <a class="el" href="class_g_f_p2_element.html">Element</a> &y, const <a class="el" href="class_integer.html">Integer</a> &e2) const</td></tr>
<tr class="memdesc:adb4d33ac59a8f8bff1752b75809136e6 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">More...</a><br /></td></tr>
<tr class="separator:adb4d33ac59a8f8bff1752b75809136e6 inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a63530b69e7bfa78e5ee7b072cc798f0a inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">SimultaneousExponentiate</a> (<a class="el" href="class_g_f_p2_element.html">Element</a> *results, const <a class="el" href="class_g_f_p2_element.html">Element</a> &base, const <a class="el" href="class_integer.html">Integer</a> *exponents, unsigned int exponentsCount) const</td></tr>
<tr class="memdesc:a63530b69e7bfa78e5ee7b072cc798f0a inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Exponentiates a base to multiple exponents in the Ring. <a href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">More...</a><br /></td></tr>
<tr class="separator:a63530b69e7bfa78e5ee7b072cc798f0a inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae19ef788f5ce5192e5867666ef38717f inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual const <a class="el" href="class_abstract_group.html">AbstractGroup</a>< <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> > & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#ae19ef788f5ce5192e5867666ef38717f">MultiplicativeGroup</a> () const</td></tr>
<tr class="memdesc:ae19ef788f5ce5192e5867666ef38717f inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative group. <a href="class_abstract_ring.html#ae19ef788f5ce5192e5867666ef38717f">More...</a><br /></td></tr>
<tr class="separator:ae19ef788f5ce5192e5867666ef38717f inherit pub_methods_class_abstract_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_abstract_group"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_abstract_group')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_abstract_group.html">AbstractGroup< GFP2Element ></a></td></tr>
<tr class="memitem:a257836994abefe25b80293f4c6b10f60 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a257836994abefe25b80293f4c6b10f60">InversionIsFast</a> () const</td></tr>
<tr class="memdesc:a257836994abefe25b80293f4c6b10f60 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Determine if inversion is fast. <a href="class_abstract_group.html#a257836994abefe25b80293f4c6b10f60">More...</a><br /></td></tr>
<tr class="separator:a257836994abefe25b80293f4c6b10f60 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac01536b91c4fa3d0e0f929917143595b inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_g_f_p2_element.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ac01536b91c4fa3d0e0f929917143595b">ScalarMultiply</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &a, const <a class="el" href="class_integer.html">Integer</a> &e) const</td></tr>
<tr class="memdesc:ac01536b91c4fa3d0e0f929917143595b inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Performs a scalar multiplication. <a href="class_abstract_group.html#ac01536b91c4fa3d0e0f929917143595b">More...</a><br /></td></tr>
<tr class="separator:ac01536b91c4fa3d0e0f929917143595b inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a89bd24f1a83e62ac8cc5ad014cb5883e inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual <a class="el" href="class_g_f_p2_element.html">Element</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a89bd24f1a83e62ac8cc5ad014cb5883e">CascadeScalarMultiply</a> (const <a class="el" href="class_g_f_p2_element.html">Element</a> &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const <a class="el" href="class_g_f_p2_element.html">Element</a> &y, const <a class="el" href="class_integer.html">Integer</a> &e2) const</td></tr>
<tr class="memdesc:a89bd24f1a83e62ac8cc5ad014cb5883e inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_abstract_group.html#a89bd24f1a83e62ac8cc5ad014cb5883e">More...</a><br /></td></tr>
<tr class="separator:a89bd24f1a83e62ac8cc5ad014cb5883e inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9c73ab688612e76786f43e311376eb8d inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a9c73ab688612e76786f43e311376eb8d">SimultaneousMultiply</a> (<a class="el" href="class_g_f_p2_element.html">Element</a> *results, const <a class="el" href="class_g_f_p2_element.html">Element</a> &base, const <a class="el" href="class_integer.html">Integer</a> *exponents, unsigned int exponentsCount) const</td></tr>
<tr class="memdesc:a9c73ab688612e76786f43e311376eb8d inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies a base to multiple exponents in a group. <a href="class_abstract_group.html#a9c73ab688612e76786f43e311376eb8d">More...</a><br /></td></tr>
<tr class="separator:a9c73ab688612e76786f43e311376eb8d inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<class F><br />
class GFP2_ONB< F ></h3>
<p>GF(p^2), optimal normal basis. </p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00046">46</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="aab4d8f8eec60122c1f3e3ba2c9ad2673"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aab4d8f8eec60122c1f3e3ba2c9ad2673">◆ </a></span>Equal()</h2>
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<td class="memname">bool <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Equal </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">GFP2Element</a> & </td>
<td class="paramname"><em>b</em> </td>
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<td>)</td>
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<p>Compare two elements for equality. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>true if the elements are equal, false otherwise</dd></dl>
<p><a class="el" href="class_g_f_p2___o_n_b.html#aab4d8f8eec60122c1f3e3ba2c9ad2673" title="Compare two elements for equality. ">Equal()</a> tests the elements for equality using <code>a==b</code> </p>
<p>Implements <a class="el" href="class_abstract_group.html#a0d72cb663566b7c056f846a561547bec">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00071">71</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
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<a id="a386495ffc3d413f461a9001fe6f30642"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a386495ffc3d413f461a9001fe6f30642">◆ </a></span>Identity()</h2>
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<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Identity </td>
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<p>Provides the Identity element. </p>
<dl class="section return"><dt>Returns</dt><dd>the Identity element </dd></dl>
<p>Implements <a class="el" href="class_abstract_group.html#a929ba4e6a7d7d80344946efad0456d5b">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00076">76</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#abd707cb221dd44914e8cde2839ad90c7">◆ </a></span>Add()</h2>
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<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Add </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
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<td></td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
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<td>)</td>
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<p>Adds elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>the sum of <code>a</code> and <code>b</code> </dd></dl>
<p>Implements <a class="el" href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00081">81</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
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<a id="ac9fa7ce33239b3d7f88c9cac9c2d74d3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac9fa7ce33239b3d7f88c9cac9c2d74d3">◆ </a></span>Inverse()</h2>
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<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Inverse </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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<p>Inverts the element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>the inverse of the element </dd></dl>
<p>Implements <a class="el" href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00088">88</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
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<a id="a39cef4f74a7bd5588a7293b1d364334e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a39cef4f74a7bd5588a7293b1d364334e">◆ </a></span>Double()</h2>
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<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Double </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
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<p>Doubles an element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>the element doubled </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#afaceaf9c9c24606efc38d30fd8aff5ee">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00095">95</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
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<a id="aedbcc151eca01f823b6d8c34f792fad9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aedbcc151eca01f823b6d8c34f792fad9">◆ </a></span>Subtract()</h2>
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<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Subtract </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
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<p>Subtracts elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the difference of <code>a</code> and <code>b</code>. The element <code>a</code> must provide a Subtract member function. </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00102">102</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="a9ea72a20954c87db4467e14fdaa67037"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9ea72a20954c87db4467e14fdaa67037">◆ </a></span>Accumulate()</h2>
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<div class="memproto">
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template<class F> </div>
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<td class="memname"><a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Accumulate </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
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<p>TODO. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>first element </td></tr>
<tr><td class="paramname">b</td><td>second element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>TODO </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00109">109</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="ac6d39d886f9ddc047fcc4c5adcc23db9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac6d39d886f9ddc047fcc4c5adcc23db9">◆ </a></span>Reduce()</h2>
<div class="memitem">
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<div class="memtemplate">
template<class F> </div>
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<td class="mlabels-left">
<table class="memname">
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<td class="memname"><a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Reduce </td>
<td>(</td>
<td class="paramtype"><a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Reduces an element in the congruence class. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>element to reduce </td></tr>
<tr><td class="paramname">b</td><td>the congruence class </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the reduced element </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">AbstractGroup< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00116">116</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="ac0e339d3509a26757486bbc78e339910"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac0e339d3509a26757486bbc78e339910">◆ </a></span>IsUnit()</h2>
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<div class="memtemplate">
template<class F> </div>
<table class="mlabels">
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<td class="mlabels-left">
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<td class="memname">bool <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::IsUnit </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
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</div><div class="memdoc">
<p>Determines whether an element is a unit in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>true if the element is a unit after reduction, false otherwise. </dd></dl>
<p>Implements <a class="el" href="class_abstract_ring.html#acc7079c244d980c670c329e483c4f107">AbstractRing< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00123">123</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="aa1d3c030219de3c1635a72fbdf0c7228"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa1d3c030219de3c1635a72fbdf0c7228">◆ </a></span>MultiplicativeIdentity()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class F> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::MultiplicativeIdentity </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Retrieves the multiplicative identity. </p>
<dl class="section return"><dt>Returns</dt><dd>the multiplicative identity </dd></dl>
<p>Implements <a class="el" href="class_abstract_ring.html#a390832165268e39e2a1f3263e5b44627">AbstractRing< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00128">128</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="abe477db3d5bf5fdb72b9fcc832ff8bac"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abe477db3d5bf5fdb72b9fcc832ff8bac">◆ </a></span>Multiply()</h2>
<div class="memitem">
<div class="memproto">
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template<class F> </div>
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<td class="mlabels-left">
<table class="memname">
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<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Multiply </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>b</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Multiplies elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the multiplicand </td></tr>
<tr><td class="paramname">b</td><td>the multiplier </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the product of a and b </dd></dl>
<p>Implements <a class="el" href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">AbstractRing< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00134">134</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="a42f1dfe03023fb5502843e326892850c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a42f1dfe03023fb5502843e326892850c">◆ </a></span>MultiplicativeInverse()</h2>
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<div class="memproto">
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template<class F> </div>
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<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::MultiplicativeInverse </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Calculate the multiplicative inverse of an element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<p>Implements <a class="el" href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">AbstractRing< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00148">148</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="a41cd047c0fc625ecde993d839d8d86b7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a41cd047c0fc625ecde993d839d8d86b7">◆ </a></span>Square()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class F> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">const <a class="el" href="class_g_f_p2_element.html">Element</a>& <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::<a class="el" href="class_square.html">Square</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p><a class="el" href="class_square.html" title="Square block cipher. ">Square</a> an element in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the element squared </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_ring.html#a54b38c3a067b893e0c87495bee7adcef">AbstractRing< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00153">153</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<a id="ad71eeac946b5f17fcb6645bd2f281d23"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad71eeac946b5f17fcb6645bd2f281d23">◆ </a></span>Exponentiate()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<class F> </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="class_g_f_p2_element.html">Element</a> <a class="el" href="class_g_f_p2___o_n_b.html">GFP2_ONB</a>< F >::Exponentiate </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_g_f_p2_element.html">Element</a> & </td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_integer.html">Integer</a> & </td>
<td class="paramname"><em>e</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">virtual</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Raises a base to an exponent in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the base </td></tr>
<tr><td class="paramname">e</td><td>the exponent </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the exponentiation </dd></dl>
<p>Reimplemented from <a class="el" href="class_abstract_ring.html#a0f011366054a4edb80be92f968083538">AbstractRing< GFP2Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="xtr_8h_source.html#l00161">161</a> of file <a class="el" href="xtr_8h_source.html">xtr.h</a>.</p>
</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="xtr_8h_source.html">xtr.h</a></li>
</ul>
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