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<title>Crypto++: QuotientRing< T > 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">QuotientRing< T > Class Template Reference</div> </div>
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<p>Quotient ring.
<a href="class_quotient_ring.html#details">More...</a></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for QuotientRing< T >:</div>
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<map id="QuotientRing_3C_20T_20_3E_map" name="QuotientRing_3C_20T_20_3E_map">
<area href="class_abstract_ring.html" alt="AbstractRing< T::Element >" shape="rect" coords="0,56,165,80"/>
<area href="class_abstract_group.html" title="Abstract group. " alt="AbstractGroup< T >" shape="rect" coords="0,0,165,24"/>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
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typedef T </td><td class="memItemRight" valign="bottom"><b>EuclideanDomain</b></td></tr>
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<tr class="memitem:aa5fc43636ce1b8ab3c8aa4ec309242e0"><td class="memItemLeft" align="right" valign="top"><a id="aa5fc43636ce1b8ab3c8aa4ec309242e0"></a>
typedef T::Element </td><td class="memItemRight" valign="bottom"><b>Element</b></td></tr>
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<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< T::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 T </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< T ></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 T </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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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ad75b4078b485d09683b5c9eec944a714"><td class="memItemLeft" align="right" valign="top"><a id="ad75b4078b485d09683b5c9eec944a714"></a>
 </td><td class="memItemRight" valign="bottom"><b>QuotientRing</b> (const EuclideanDomain &domain, const Element &modulus)</td></tr>
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<tr class="memitem:a7351765fe7217917c25b40bfd29cb7ce"><td class="memItemLeft" align="right" valign="top"><a id="a7351765fe7217917c25b40bfd29cb7ce"></a>
const EuclideanDomain & </td><td class="memItemRight" valign="bottom"><b>GetDomain</b> () const</td></tr>
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<tr class="memitem:a251c7b3cdd89ceddd25fb92df81b07c4"><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"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a95a675aaca290e8cc05a56361c7d56f3"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a95a675aaca290e8cc05a56361c7d56f3">Equal</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a95a675aaca290e8cc05a56361c7d56f3"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="#a95a675aaca290e8cc05a56361c7d56f3">More...</a><br /></td></tr>
<tr class="separator:a95a675aaca290e8cc05a56361c7d56f3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a80815f5757c80106ae7dc2db2799b835"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a80815f5757c80106ae7dc2db2799b835">Identity</a> () const</td></tr>
<tr class="memdesc:a80815f5757c80106ae7dc2db2799b835"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="#a80815f5757c80106ae7dc2db2799b835">More...</a><br /></td></tr>
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<tr class="memitem:ae373c31fe91c497e9eabd2c33b70ed98"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#ae373c31fe91c497e9eabd2c33b70ed98">Add</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ae373c31fe91c497e9eabd2c33b70ed98"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="#ae373c31fe91c497e9eabd2c33b70ed98">More...</a><br /></td></tr>
<tr class="separator:ae373c31fe91c497e9eabd2c33b70ed98"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6bc3a34f0a3f04741005d6d5722b480b"><td class="memItemLeft" align="right" valign="top">Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a6bc3a34f0a3f04741005d6d5722b480b">Accumulate</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a6bc3a34f0a3f04741005d6d5722b480b"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="#a6bc3a34f0a3f04741005d6d5722b480b">More...</a><br /></td></tr>
<tr class="separator:a6bc3a34f0a3f04741005d6d5722b480b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa94188206e0504c0a5afae6a7af8e827"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#aa94188206e0504c0a5afae6a7af8e827">Inverse</a> (const Element &a) const</td></tr>
<tr class="memdesc:aa94188206e0504c0a5afae6a7af8e827"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="#aa94188206e0504c0a5afae6a7af8e827">More...</a><br /></td></tr>
<tr class="separator:aa94188206e0504c0a5afae6a7af8e827"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a08834bbb0829ab02b7f33fd1fd6ef65a"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a08834bbb0829ab02b7f33fd1fd6ef65a">Subtract</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a08834bbb0829ab02b7f33fd1fd6ef65a"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="#a08834bbb0829ab02b7f33fd1fd6ef65a">More...</a><br /></td></tr>
<tr class="separator:a08834bbb0829ab02b7f33fd1fd6ef65a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aaa33bb2ffbdf18997c825d5fdfb68ed4"><td class="memItemLeft" align="right" valign="top">Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#aaa33bb2ffbdf18997c825d5fdfb68ed4">Reduce</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:aaa33bb2ffbdf18997c825d5fdfb68ed4"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="#aaa33bb2ffbdf18997c825d5fdfb68ed4">More...</a><br /></td></tr>
<tr class="separator:aaa33bb2ffbdf18997c825d5fdfb68ed4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a2eb5b91a5e873fb022a3bb479bb81801"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a2eb5b91a5e873fb022a3bb479bb81801">Double</a> (const Element &a) const</td></tr>
<tr class="memdesc:a2eb5b91a5e873fb022a3bb479bb81801"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="#a2eb5b91a5e873fb022a3bb479bb81801">More...</a><br /></td></tr>
<tr class="separator:a2eb5b91a5e873fb022a3bb479bb81801"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa88de7f173b84432a46ba6511ed777cd"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#aa88de7f173b84432a46ba6511ed777cd">IsUnit</a> (const Element &a) const</td></tr>
<tr class="memdesc:aa88de7f173b84432a46ba6511ed777cd"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="#aa88de7f173b84432a46ba6511ed777cd">More...</a><br /></td></tr>
<tr class="separator:aa88de7f173b84432a46ba6511ed777cd"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a2b5ab1827c7e73fba29f23f5a6e0e6d4"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a2b5ab1827c7e73fba29f23f5a6e0e6d4">MultiplicativeIdentity</a> () const</td></tr>
<tr class="memdesc:a2b5ab1827c7e73fba29f23f5a6e0e6d4"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="#a2b5ab1827c7e73fba29f23f5a6e0e6d4">More...</a><br /></td></tr>
<tr class="separator:a2b5ab1827c7e73fba29f23f5a6e0e6d4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae4dc3dd42c8bc2bd37eff95e8a001f1a"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#ae4dc3dd42c8bc2bd37eff95e8a001f1a">Multiply</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ae4dc3dd42c8bc2bd37eff95e8a001f1a"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="#ae4dc3dd42c8bc2bd37eff95e8a001f1a">More...</a><br /></td></tr>
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<tr class="memitem:a4cf651be2789bdd9d9db9b156ebd1d33"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#a4cf651be2789bdd9d9db9b156ebd1d33">Square</a> (const Element &a) const</td></tr>
<tr class="memdesc:a4cf651be2789bdd9d9db9b156ebd1d33"><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="#a4cf651be2789bdd9d9db9b156ebd1d33">More...</a><br /></td></tr>
<tr class="separator:a4cf651be2789bdd9d9db9b156ebd1d33"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac78f2284a7bdd06c39fd849ea7d23d48"><td class="memItemLeft" align="right" valign="top">const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quotient_ring.html#ac78f2284a7bdd06c39fd849ea7d23d48">MultiplicativeInverse</a> (const Element &a) const</td></tr>
<tr class="memdesc:ac78f2284a7bdd06c39fd849ea7d23d48"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="#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>< T > &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< T::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>
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<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>< T > & </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< T ></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>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<class T><br />
class QuotientRing< T ></h3>
<p>Quotient ring. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>element class or type</td></tr>
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</dd>
</dl>
<p><code>const Element&</code> returned by member functions are references to internal data members. Since each object may have only one such data member for holding results, the following code will produce incorrect results: </p><pre> abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre><p> But this should be fine: </p><pre> abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00386">386</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="a95a675aaca290e8cc05a56361c7d56f3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a95a675aaca290e8cc05a56361c7d56f3">◆ </a></span>Equal()</h2>
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<td class="memname">bool <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::Equal </td>
<td>(</td>
<td class="paramtype">const Element & </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>
</table>
</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_quotient_ring.html#a95a675aaca290e8cc05a56361c7d56f3" 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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00401">401</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a80815f5757c80106ae7dc2db2799b835">◆ </a></span>Identity()</h2>
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<td class="memname">const Element& <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00404">404</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<a id="ae373c31fe91c497e9eabd2c33b70ed98"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae373c31fe91c497e9eabd2c33b70ed98">◆ </a></span>Add()</h2>
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<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>
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<td></td><td> const</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>
</table>
</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00407">407</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6bc3a34f0a3f04741005d6d5722b480b">◆ </a></span>Accumulate()</h2>
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<td class="paramtype">Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00410">410</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa94188206e0504c0a5afae6a7af8e827">◆ </a></span>Inverse()</h2>
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<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</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>
</table>
</dd>
</dl>
<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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00413">413</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a08834bbb0829ab02b7f33fd1fd6ef65a">◆ </a></span>Subtract()</h2>
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<td>(</td>
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<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
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<td class="paramname"><em>b</em> </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>
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</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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00416">416</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aaa33bb2ffbdf18997c825d5fdfb68ed4">◆ </a></span>Reduce()</h2>
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<td class="memname">Element& <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::Reduce </td>
<td>(</td>
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<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>
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</dd>
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<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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00419">419</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2eb5b91a5e873fb022a3bb479bb81801">◆ </a></span>Double()</h2>
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<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>
</table>
</dd>
</dl>
<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< T ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00422">422</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa88de7f173b84432a46ba6511ed777cd">◆ </a></span>IsUnit()</h2>
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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>
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<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< T::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00425">425</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2b5ab1827c7e73fba29f23f5a6e0e6d4">◆ </a></span>MultiplicativeIdentity()</h2>
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<td class="memname">const Element& <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::MultiplicativeIdentity </td>
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<td class="paramname"></td><td>)</td>
<td> const</td>
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<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< T::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00428">428</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae4dc3dd42c8bc2bd37eff95e8a001f1a">◆ </a></span>Multiply()</h2>
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<td class="memname">const Element& <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::Multiply </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<td></td><td> const</td>
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<p>Multiplies elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">a</td><td>the multiplicand </td></tr>
<tr><td class="paramname">b</td><td>the multiplier </td></tr>
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</dd>
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<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< T::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00431">431</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4cf651be2789bdd9d9db9b156ebd1d33">◆ </a></span>Square()</h2>
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<td class="paramtype">const Element & </td>
<td class="paramname"><em>a</em></td><td>)</td>
<td> const</td>
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<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>
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</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< T::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00434">434</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ac78f2284a7bdd06c39fd849ea7d23d48">◆ </a></span>MultiplicativeInverse()</h2>
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<td class="memname">const <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::Element & <a class="el" href="class_quotient_ring.html">QuotientRing</a>< T >::MultiplicativeInverse </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>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< T::Element ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00070">70</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
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<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="algebra_8h_source.html">algebra.h</a></li>
<li><a class="el" href="algebra_8cpp_source.html">algebra.cpp</a></li>
</ul>
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