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<title>Crypto++: GF2NP Class 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-methods">Public Member Functions</a> |
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<div class="title">GF2NP Class Reference</div> </div>
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<p>GF(2^n) with Polynomial Basis.
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for GF2NP:</div>
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<img src="class_g_f2_n_p.png" usemap="#GF2NP_map" alt=""/>
<map id="GF2NP_map" name="GF2NP_map">
<area href="class_quotient_ring.html" alt="QuotientRing< EuclideanDomainOf< PolynomialMod2 > >" shape="rect" coords="206,112,608,136"/>
<area href="class_abstract_ring.html" alt="AbstractRing< EuclideanDomainOf< PolynomialMod2 > ::Element >" shape="rect" coords="206,56,608,80"/>
<area href="class_abstract_group.html" alt="AbstractGroup< EuclideanDomainOf< PolynomialMod2 > ::Element >" shape="rect" coords="206,0,608,24"/>
<area href="class_g_f2_n_p_p.html" title="GF(2^n) with Pentanomial Basis. " alt="GF2NPP" shape="rect" coords="0,224,402,248"/>
<area href="class_g_f2_n_t.html" title="GF(2^n) with Trinomial Basis. " alt="GF2NT" shape="rect" coords="412,224,814,248"/>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a17c7806095a9fa5ed8da633cc166a3f2"><td class="memItemLeft" align="right" valign="top"><a id="a17c7806095a9fa5ed8da633cc166a3f2"></a>
 </td><td class="memItemRight" valign="bottom"><b>GF2NP</b> (const <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> &modulus)</td></tr>
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<tr class="memitem:aa882b0e903bc9a92ec35f81ef8c9e3ff"><td class="memItemLeft" align="right" valign="top"><a id="aa882b0e903bc9a92ec35f81ef8c9e3ff"></a>
virtual <a class="el" href="class_g_f2_n_p.html">GF2NP</a> * </td><td class="memItemRight" valign="bottom"><b>Clone</b> () const</td></tr>
<tr class="separator:aa882b0e903bc9a92ec35f81ef8c9e3ff"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1fa95c56391a3661f1171b2ce94b0f60"><td class="memItemLeft" align="right" valign="top"><a id="a1fa95c56391a3661f1171b2ce94b0f60"></a>
virtual void </td><td class="memItemRight" valign="bottom"><b>DEREncode</b> (<a class="el" href="class_buffered_transformation.html">BufferedTransformation</a> &bt) const</td></tr>
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<tr class="memitem:a24b96323321725716b2e5046c6ff6080"><td class="memItemLeft" align="right" valign="top"><a id="a24b96323321725716b2e5046c6ff6080"></a>
void </td><td class="memItemRight" valign="bottom"><b>DEREncodeElement</b> (<a class="el" href="class_buffered_transformation.html">BufferedTransformation</a> &out, const Element &a) const</td></tr>
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<tr class="memitem:aa46052b02995de9a8c2a12a1a7ad7533"><td class="memItemLeft" align="right" valign="top"><a id="aa46052b02995de9a8c2a12a1a7ad7533"></a>
void </td><td class="memItemRight" valign="bottom"><b>BERDecodeElement</b> (<a class="el" href="class_buffered_transformation.html">BufferedTransformation</a> &in, Element &a) const</td></tr>
<tr class="separator:aa46052b02995de9a8c2a12a1a7ad7533"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6e1d77aefacee1a620dee8f1299cee9b"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f2_n_p.html#a6e1d77aefacee1a620dee8f1299cee9b">Equal</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a6e1d77aefacee1a620dee8f1299cee9b"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="#a6e1d77aefacee1a620dee8f1299cee9b">More...</a><br /></td></tr>
<tr class="separator:a6e1d77aefacee1a620dee8f1299cee9b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa87c0ef74a17bc31c29156bd34cb3e4b"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_g_f2_n_p.html#aa87c0ef74a17bc31c29156bd34cb3e4b">IsUnit</a> (const Element &a) const</td></tr>
<tr class="memdesc:aa87c0ef74a17bc31c29156bd34cb3e4b"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="#aa87c0ef74a17bc31c29156bd34cb3e4b">More...</a><br /></td></tr>
<tr class="separator:aa87c0ef74a17bc31c29156bd34cb3e4b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae4a472d5d24354f4130428dece8aa726"><td class="memItemLeft" align="right" valign="top"><a id="ae4a472d5d24354f4130428dece8aa726"></a>
unsigned int </td><td class="memItemRight" valign="bottom"><b>MaxElementBitLength</b> () const</td></tr>
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<tr class="memitem:a9db342e042aa64b3528e877c8d7210de"><td class="memItemLeft" align="right" valign="top"><a id="a9db342e042aa64b3528e877c8d7210de"></a>
unsigned int </td><td class="memItemRight" valign="bottom"><b>MaxElementByteLength</b> () const</td></tr>
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<tr class="memitem:a862e6ba0f9c46d9de21e4432b954feea"><td class="memItemLeft" align="right" valign="top"><a id="a862e6ba0f9c46d9de21e4432b954feea"></a>
Element </td><td class="memItemRight" valign="bottom"><b>SquareRoot</b> (const Element &a) const</td></tr>
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<tr class="memitem:ae9efbaac206669b2373e3cc1d104bf82"><td class="memItemLeft" align="right" valign="top"><a id="ae9efbaac206669b2373e3cc1d104bf82"></a>
Element </td><td class="memItemRight" valign="bottom"><b>HalfTrace</b> (const Element &a) const</td></tr>
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<tr class="memitem:a6ea9f23178ca65cffa7e3ab097a9ade0"><td class="memItemLeft" align="right" valign="top"><a id="a6ea9f23178ca65cffa7e3ab097a9ade0"></a>
Element </td><td class="memItemRight" valign="bottom"><b>SolveQuadraticEquation</b> (const Element &a) const</td></tr>
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<tr class="inherit_header pub_methods_class_quotient_ring"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quotient_ring')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quotient_ring.html">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a></td></tr>
<tr class="memitem:ad75b4078b485d09683b5c9eec944a714 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top"><a id="ad75b4078b485d09683b5c9eec944a714"></a>
 </td><td class="memItemRight" valign="bottom"><b>QuotientRing</b> (const <a class="el" href="class_euclidean_domain_of.html">EuclideanDomain</a> &domain, const Element &modulus)</td></tr>
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<tr class="memitem:a7351765fe7217917c25b40bfd29cb7ce inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top"><a id="a7351765fe7217917c25b40bfd29cb7ce"></a>
const <a class="el" href="class_euclidean_domain_of.html">EuclideanDomain</a> & </td><td class="memItemRight" valign="bottom"><b>GetDomain</b> () const</td></tr>
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<tr class="memitem:a251c7b3cdd89ceddd25fb92df81b07c4 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top"><a id="a251c7b3cdd89ceddd25fb92df81b07c4"></a>
const Element & </td><td class="memItemRight" valign="bottom"><b>GetModulus</b> () const</td></tr>
<tr class="separator:a251c7b3cdd89ceddd25fb92df81b07c4 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a95a675aaca290e8cc05a56361c7d56f3 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><b>Equal</b> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a95a675aaca290e8cc05a56361c7d56f3 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="class_quotient_ring.html#a95a675aaca290e8cc05a56361c7d56f3">More...</a><br /></td></tr>
<tr class="separator:a95a675aaca290e8cc05a56361c7d56f3 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a80815f5757c80106ae7dc2db2799b835 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Identity</b> () const</td></tr>
<tr class="memdesc:a80815f5757c80106ae7dc2db2799b835 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="class_quotient_ring.html#a80815f5757c80106ae7dc2db2799b835">More...</a><br /></td></tr>
<tr class="separator:a80815f5757c80106ae7dc2db2799b835 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae373c31fe91c497e9eabd2c33b70ed98 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Add</b> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ae373c31fe91c497e9eabd2c33b70ed98 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="class_quotient_ring.html#ae373c31fe91c497e9eabd2c33b70ed98">More...</a><br /></td></tr>
<tr class="separator:ae373c31fe91c497e9eabd2c33b70ed98 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6bc3a34f0a3f04741005d6d5722b480b inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">Element & </td><td class="memItemRight" valign="bottom"><b>Accumulate</b> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a6bc3a34f0a3f04741005d6d5722b480b inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_quotient_ring.html#a6bc3a34f0a3f04741005d6d5722b480b">More...</a><br /></td></tr>
<tr class="separator:a6bc3a34f0a3f04741005d6d5722b480b inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa94188206e0504c0a5afae6a7af8e827 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Inverse</b> (const Element &a) const</td></tr>
<tr class="memdesc:aa94188206e0504c0a5afae6a7af8e827 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="class_quotient_ring.html#aa94188206e0504c0a5afae6a7af8e827">More...</a><br /></td></tr>
<tr class="separator:aa94188206e0504c0a5afae6a7af8e827 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a08834bbb0829ab02b7f33fd1fd6ef65a inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Subtract</b> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a08834bbb0829ab02b7f33fd1fd6ef65a inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="class_quotient_ring.html#a08834bbb0829ab02b7f33fd1fd6ef65a">More...</a><br /></td></tr>
<tr class="separator:a08834bbb0829ab02b7f33fd1fd6ef65a inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aaa33bb2ffbdf18997c825d5fdfb68ed4 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">Element & </td><td class="memItemRight" valign="bottom"><b>Reduce</b> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:aaa33bb2ffbdf18997c825d5fdfb68ed4 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="class_quotient_ring.html#aaa33bb2ffbdf18997c825d5fdfb68ed4">More...</a><br /></td></tr>
<tr class="separator:aaa33bb2ffbdf18997c825d5fdfb68ed4 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a2eb5b91a5e873fb022a3bb479bb81801 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Double</b> (const Element &a) const</td></tr>
<tr class="memdesc:a2eb5b91a5e873fb022a3bb479bb81801 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="class_quotient_ring.html#a2eb5b91a5e873fb022a3bb479bb81801">More...</a><br /></td></tr>
<tr class="separator:a2eb5b91a5e873fb022a3bb479bb81801 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa88de7f173b84432a46ba6511ed777cd inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><b>IsUnit</b> (const Element &a) const</td></tr>
<tr class="memdesc:aa88de7f173b84432a46ba6511ed777cd inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="class_quotient_ring.html#aa88de7f173b84432a46ba6511ed777cd">More...</a><br /></td></tr>
<tr class="separator:aa88de7f173b84432a46ba6511ed777cd inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a2b5ab1827c7e73fba29f23f5a6e0e6d4 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>MultiplicativeIdentity</b> () const</td></tr>
<tr class="memdesc:a2b5ab1827c7e73fba29f23f5a6e0e6d4 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="class_quotient_ring.html#a2b5ab1827c7e73fba29f23f5a6e0e6d4">More...</a><br /></td></tr>
<tr class="separator:a2b5ab1827c7e73fba29f23f5a6e0e6d4 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae4dc3dd42c8bc2bd37eff95e8a001f1a inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Multiply</b> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ae4dc3dd42c8bc2bd37eff95e8a001f1a inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="class_quotient_ring.html#ae4dc3dd42c8bc2bd37eff95e8a001f1a">More...</a><br /></td></tr>
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<tr class="memitem:a4cf651be2789bdd9d9db9b156ebd1d33 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>Square</b> (const Element &a) const</td></tr>
<tr class="memdesc:a4cf651be2789bdd9d9db9b156ebd1d33 inherit pub_methods_class_quotient_ring"><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="class_quotient_ring.html#a4cf651be2789bdd9d9db9b156ebd1d33">More...</a><br /></td></tr>
<tr class="separator:a4cf651be2789bdd9d9db9b156ebd1d33 inherit pub_methods_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac78f2284a7bdd06c39fd849ea7d23d48 inherit pub_methods_class_quotient_ring"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><b>MultiplicativeInverse</b> (const Element &a) const</td></tr>
<tr class="memdesc:ac78f2284a7bdd06c39fd849ea7d23d48 inherit pub_methods_class_quotient_ring"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="class_quotient_ring.html#ac78f2284a7bdd06c39fd849ea7d23d48">More...</a><br /></td></tr>
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bool </td><td class="memItemRight" valign="bottom"><b>operator==</b> (const <a class="el" href="class_quotient_ring.html">QuotientRing</a>< <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> > > &rhs) const</td></tr>
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<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< EuclideanDomainOf< PolynomialMod2 > ::Element ></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 Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#aa7ce20a30d89a8257088930d1d06d0b7">Divide</a> (const Element &a, const Element &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:a0f011366054a4edb80be92f968083538 inherit pub_methods_class_abstract_ring"><td class="memItemLeft" align="right" valign="top">virtual Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a0f011366054a4edb80be92f968083538">Exponentiate</a> (const Element &a, const <a class="el" href="class_integer.html">Integer</a> &e) const</td></tr>
<tr class="memdesc:a0f011366054a4edb80be92f968083538 inherit pub_methods_class_abstract_ring"><td class="mdescLeft"> </td><td class="mdescRight">Raises a base to an exponent in the group. <a href="class_abstract_ring.html#a0f011366054a4edb80be92f968083538">More...</a><br /></td></tr>
<tr class="separator:a0f011366054a4edb80be92f968083538 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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">CascadeExponentiate</a> (const Element &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const Element &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> (Element *results, const Element &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_euclidean_domain_of.html">EuclideanDomainOf</a>< <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> > ::Element > & </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< EuclideanDomainOf< PolynomialMod2 > ::Element ></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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ac01536b91c4fa3d0e0f929917143595b">ScalarMultiply</a> (const Element &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 Element </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a89bd24f1a83e62ac8cc5ad014cb5883e">CascadeScalarMultiply</a> (const Element &x, const <a class="el" href="class_integer.html">Integer</a> &e1, const Element &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> (Element *results, const Element &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>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_class_quotient_ring"><td colspan="2" onclick="javascript:toggleInherit('pub_types_class_quotient_ring')"><img src="closed.png" alt="-"/> Public Types inherited from <a class="el" href="class_quotient_ring.html">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a></td></tr>
<tr class="memitem:aeba485b8efc03cb16525c389519833e1 inherit pub_types_class_quotient_ring"><td class="memItemLeft" align="right" valign="top"><a id="aeba485b8efc03cb16525c389519833e1"></a>
typedef <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> > </td><td class="memItemRight" valign="bottom"><b>EuclideanDomain</b></td></tr>
<tr class="separator:aeba485b8efc03cb16525c389519833e1 inherit pub_types_class_quotient_ring"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa5fc43636ce1b8ab3c8aa4ec309242e0 inherit pub_types_class_quotient_ring"><td class="memItemLeft" align="right" valign="top"><a id="aa5fc43636ce1b8ab3c8aa4ec309242e0"></a>
typedef <a class="el" href="class_euclidean_domain_of.html">EuclideanDomainOf</a>< <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> > ::Element </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
<tr class="separator:aa5fc43636ce1b8ab3c8aa4ec309242e0 inherit pub_types_class_quotient_ring"><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< EuclideanDomainOf< PolynomialMod2 > ::Element ></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_euclidean_domain_of.html">EuclideanDomainOf</a>< <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> > ::Element </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< EuclideanDomainOf< PolynomialMod2 > ::Element ></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_euclidean_domain_of.html">EuclideanDomainOf</a>< <a class="el" href="class_polynomial_mod2.html">PolynomialMod2</a> > ::Element </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>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>GF(2^n) with Polynomial Basis. </p>
<p class="definition">Definition at line <a class="el" href="gf2n_8h_source.html#l00295">295</a> of file <a class="el" href="gf2n_8h_source.html">gf2n.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="a6e1d77aefacee1a620dee8f1299cee9b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a6e1d77aefacee1a620dee8f1299cee9b">◆ </a></span>Equal()</h2>
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<td class="memname">bool GF2NP::Equal </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<td>)</td>
<td></td><td> const</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>
</dl>
<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_f2_n_p.html#a6e1d77aefacee1a620dee8f1299cee9b" 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< EuclideanDomainOf< PolynomialMod2 > ::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="gf2n_8h_source.html#l00307">307</a> of file <a class="el" href="gf2n_8h_source.html">gf2n.h</a>.</p>
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<a id="aa87c0ef74a17bc31c29156bd34cb3e4b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa87c0ef74a17bc31c29156bd34cb3e4b">◆ </a></span>IsUnit()</h2>
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<td class="memname">bool GF2NP::IsUnit </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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<p>Determines whether an element is a unit in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">a</td><td>the element </td></tr>
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</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< EuclideanDomainOf< PolynomialMod2 > ::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="gf2n_8h_source.html#l00310">310</a> of file <a class="el" href="gf2n_8h_source.html">gf2n.h</a>.</p>
</div>
</div>
<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="gf2n_8h_source.html">gf2n.h</a></li>
<li><a class="el" href="gf2n_8cpp_source.html">gf2n.cpp</a></li>
</ul>
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