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<title>Crypto++: AbstractRing< 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="#nested-classes">Classes</a> |
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<div class="title">AbstractRing< T > Class Template Reference<span class="mlabels"><span class="mlabel">abstract</span></span></div> </div>
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<p>Abstract ring.
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for AbstractRing< T >:</div>
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<area href="class_abstract_group.html" title="Abstract group. " alt="AbstractGroup< T >" shape="rect" coords="0,0,188,24"/>
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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:acd93e8ce4e2897173310c68fcb60f3e9"><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"><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>
</table><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:ae55c525c1aa75bf898907bd6949e2b64"><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"><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"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acc8afd5ce95e32e45d3c30a710bf36dc"><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"><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="#acc8afd5ce95e32e45d3c30a710bf36dc">More...</a><br /></td></tr>
<tr class="separator:acc8afd5ce95e32e45d3c30a710bf36dc"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a26709c02c869d09d756653ae1129f8a9"><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"><td class="mdescLeft"> </td><td class="mdescRight">Assign an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. <a href="#a26709c02c869d09d756653ae1129f8a9">More...</a><br /></td></tr>
<tr class="separator:a26709c02c869d09d756653ae1129f8a9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acc7079c244d980c670c329e483c4f107"><td class="memItemLeft" align="right" valign="top">virtual bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#acc7079c244d980c670c329e483c4f107">IsUnit</a> (const Element &a) const =0</td></tr>
<tr class="memdesc:acc7079c244d980c670c329e483c4f107"><td class="mdescLeft"> </td><td class="mdescRight">Determines whether an element is a unit in the group. <a href="#acc7079c244d980c670c329e483c4f107">More...</a><br /></td></tr>
<tr class="separator:acc7079c244d980c670c329e483c4f107"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a390832165268e39e2a1f3263e5b44627"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a390832165268e39e2a1f3263e5b44627">MultiplicativeIdentity</a> () const =0</td></tr>
<tr class="memdesc:a390832165268e39e2a1f3263e5b44627"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative identity. <a href="#a390832165268e39e2a1f3263e5b44627">More...</a><br /></td></tr>
<tr class="separator:a390832165268e39e2a1f3263e5b44627"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4ba8818fc72fa298cd52fd483bdd6ad4"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">Multiply</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:a4ba8818fc72fa298cd52fd483bdd6ad4"><td class="mdescLeft"> </td><td class="mdescRight">Multiplies elements in the group. <a href="#a4ba8818fc72fa298cd52fd483bdd6ad4">More...</a><br /></td></tr>
<tr class="separator:a4ba8818fc72fa298cd52fd483bdd6ad4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aba109f4e7932d77a8251c1ec20627571"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">MultiplicativeInverse</a> (const Element &a) const =0</td></tr>
<tr class="memdesc:aba109f4e7932d77a8251c1ec20627571"><td class="mdescLeft"> </td><td class="mdescRight">Calculate the multiplicative inverse of an element in the group. <a href="#aba109f4e7932d77a8251c1ec20627571">More...</a><br /></td></tr>
<tr class="separator:aba109f4e7932d77a8251c1ec20627571"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a54b38c3a067b893e0c87495bee7adcef"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_ring.html#a54b38c3a067b893e0c87495bee7adcef">Square</a> (const Element &a) const</td></tr>
<tr class="memdesc:a54b38c3a067b893e0c87495bee7adcef"><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="#a54b38c3a067b893e0c87495bee7adcef">More...</a><br /></td></tr>
<tr class="separator:a54b38c3a067b893e0c87495bee7adcef"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa7ce20a30d89a8257088930d1d06d0b7"><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"><td class="mdescLeft"> </td><td class="mdescRight">Divides elements in the group. <a href="#aa7ce20a30d89a8257088930d1d06d0b7">More...</a><br /></td></tr>
<tr class="separator:aa7ce20a30d89a8257088930d1d06d0b7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0f011366054a4edb80be92f968083538"><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"><td class="mdescLeft"> </td><td class="mdescRight">Raises a base to an exponent in the group. <a href="#a0f011366054a4edb80be92f968083538">More...</a><br /></td></tr>
<tr class="separator:a0f011366054a4edb80be92f968083538"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:adb4d33ac59a8f8bff1752b75809136e6"><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"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="#adb4d33ac59a8f8bff1752b75809136e6">More...</a><br /></td></tr>
<tr class="separator:adb4d33ac59a8f8bff1752b75809136e6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a63530b69e7bfa78e5ee7b072cc798f0a"><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"><td class="mdescLeft"> </td><td class="mdescRight">Exponentiates a base to multiple exponents in the Ring. <a href="#a63530b69e7bfa78e5ee7b072cc798f0a">More...</a><br /></td></tr>
<tr class="separator:a63530b69e7bfa78e5ee7b072cc798f0a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae19ef788f5ce5192e5867666ef38717f"><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"><td class="mdescLeft"> </td><td class="mdescRight">Retrieves the multiplicative group. <a href="#ae19ef788f5ce5192e5867666ef38717f">More...</a><br /></td></tr>
<tr class="separator:ae19ef788f5ce5192e5867666ef38717f"><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:a0d72cb663566b7c056f846a561547bec 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#a0d72cb663566b7c056f846a561547bec">Equal</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:a0d72cb663566b7c056f846a561547bec inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Compare two elements for equality. <a href="class_abstract_group.html#a0d72cb663566b7c056f846a561547bec">More...</a><br /></td></tr>
<tr class="separator:a0d72cb663566b7c056f846a561547bec inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a929ba4e6a7d7d80344946efad0456d5b inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#a929ba4e6a7d7d80344946efad0456d5b">Identity</a> () const =0</td></tr>
<tr class="memdesc:a929ba4e6a7d7d80344946efad0456d5b inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Provides the Identity element. <a href="class_abstract_group.html#a929ba4e6a7d7d80344946efad0456d5b">More...</a><br /></td></tr>
<tr class="separator:a929ba4e6a7d7d80344946efad0456d5b inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa813430d9e4244de24c487d090eb5797 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">Add</a> (const Element &a, const Element &b) const =0</td></tr>
<tr class="memdesc:aa813430d9e4244de24c487d090eb5797 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Adds elements in the group. <a href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">More...</a><br /></td></tr>
<tr class="separator:aa813430d9e4244de24c487d090eb5797 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab22563bc0dcb544399d7e22b3589e165 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">Inverse</a> (const Element &a) const =0</td></tr>
<tr class="memdesc:ab22563bc0dcb544399d7e22b3589e165 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Inverts the element in the group. <a href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">More...</a><br /></td></tr>
<tr class="separator:ab22563bc0dcb544399d7e22b3589e165 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </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:afaceaf9c9c24606efc38d30fd8aff5ee inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#afaceaf9c9c24606efc38d30fd8aff5ee">Double</a> (const Element &a) const</td></tr>
<tr class="memdesc:afaceaf9c9c24606efc38d30fd8aff5ee inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Doubles an element in the group. <a href="class_abstract_group.html#afaceaf9c9c24606efc38d30fd8aff5ee">More...</a><br /></td></tr>
<tr class="separator:afaceaf9c9c24606efc38d30fd8aff5ee inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa19e1bef00198fb30eb01df3f7076717 inherit pub_methods_class_abstract_group"><td class="memItemLeft" align="right" valign="top">virtual const Element & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">Subtract</a> (const Element &a, const Element &b) const</td></tr>
<tr class="memdesc:aa19e1bef00198fb30eb01df3f7076717 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Subtracts elements in the group. <a href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">More...</a><br /></td></tr>
<tr class="separator:aa19e1bef00198fb30eb01df3f7076717 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab03cc0a23f23c6aa1c003e11f9abb8c5 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#ab03cc0a23f23c6aa1c003e11f9abb8c5">Accumulate</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:ab03cc0a23f23c6aa1c003e11f9abb8c5 inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">TODO. <a href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">More...</a><br /></td></tr>
<tr class="separator:ab03cc0a23f23c6aa1c003e11f9abb8c5 inherit pub_methods_class_abstract_group"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a40f7de55eddc193e07a7c3b5acad781a 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#a40f7de55eddc193e07a7c3b5acad781a">Reduce</a> (Element &a, const Element &b) const</td></tr>
<tr class="memdesc:a40f7de55eddc193e07a7c3b5acad781a inherit pub_methods_class_abstract_group"><td class="mdescLeft"> </td><td class="mdescRight">Reduces an element in the congruence class. <a href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">More...</a><br /></td></tr>
<tr class="separator:a40f7de55eddc193e07a7c3b5acad781a 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>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<class T><br />
class AbstractRing< T ></h3>
<p>Abstract 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>
</table>
</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#l00118">118</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
<a id="acc8afd5ce95e32e45d3c30a710bf36dc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acc8afd5ce95e32e45d3c30a710bf36dc">◆ </a></span>AbstractRing()</h2>
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<td class="memname"><a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::<a class="el" href="class_abstract_ring.html">AbstractRing</a> </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T > & </td>
<td class="paramname"><em>source</em></td><td>)</td>
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<p>Copy construct an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">source</td><td>other <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a> </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00128">128</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a26709c02c869d09d756653ae1129f8a9">◆ </a></span>operator=()</h2>
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<td class="memname"><a class="el" href="class_abstract_ring.html">AbstractRing</a>& <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::operator= </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T > & </td>
<td class="paramname"><em>source</em></td><td>)</td>
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<p>Assign an <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">source</td><td>other <a class="el" href="class_abstract_ring.html" title="Abstract ring. ">AbstractRing</a> </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00133">133</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="#acc7079c244d980c670c329e483c4f107">◆ </a></span>IsUnit()</h2>
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<td class="memname">virtual bool <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::IsUnit </td>
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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>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>Implemented in <a class="el" href="class_quotient_ring.html#aa88de7f173b84432a46ba6511ed777cd">QuotientRing< T ></a>, <a class="el" href="class_quotient_ring.html#aa88de7f173b84432a46ba6511ed777cd">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a>, <a class="el" href="class_ring_of_polynomials_over.html#a902a6f8e12158a1b2a8f18565463e5ce">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#ad17003ea655d6638d40b1dcd17534186">EuclideanDomainOf< T ></a>, <a class="el" href="class_euclidean_domain_of.html#ad17003ea655d6638d40b1dcd17534186">EuclideanDomainOf< PolynomialMod2 ></a>, <a class="el" href="class_g_f2_n_p.html#aa87c0ef74a17bc31c29156bd34cb3e4b">GF2NP</a>, <a class="el" href="class_modular_arithmetic.html#a0d8edd3e4ff60627b92e93ebd00cdfb3">ModularArithmetic</a>, and <a class="el" href="class_g_f_p2___o_n_b.html#ac0e339d3509a26757486bbc78e339910">GFP2_ONB< F ></a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a390832165268e39e2a1f3263e5b44627">◆ </a></span>MultiplicativeIdentity()</h2>
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<td class="memname">virtual const Element& <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::MultiplicativeIdentity </td>
<td>(</td>
<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>Implemented in <a class="el" href="class_quotient_ring.html#a2b5ab1827c7e73fba29f23f5a6e0e6d4">QuotientRing< T ></a>, <a class="el" href="class_quotient_ring.html#a2b5ab1827c7e73fba29f23f5a6e0e6d4">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a>, <a class="el" href="class_ring_of_polynomials_over.html#ab9713800e8ff192ab7f4c232b44cf31c">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a8112935a4dd4996e011fef24b4d2564a">EuclideanDomainOf< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a8112935a4dd4996e011fef24b4d2564a">EuclideanDomainOf< PolynomialMod2 ></a>, <a class="el" href="class_montgomery_representation.html#aebab2112b22e0af65d4d0048166ca432">MontgomeryRepresentation</a>, <a class="el" href="class_modular_arithmetic.html#af942a7ca057b363cb7a4c74f15a9530e">ModularArithmetic</a>, and <a class="el" href="class_g_f_p2___o_n_b.html#aa1d3c030219de3c1635a72fbdf0c7228">GFP2_ONB< F ></a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4ba8818fc72fa298cd52fd483bdd6ad4">◆ </a></span>Multiply()</h2>
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<td class="memname">virtual const Element& <a class="el" href="class_abstract_ring.html">AbstractRing</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="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
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<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>Implemented in <a class="el" href="class_quotient_ring.html#ae4dc3dd42c8bc2bd37eff95e8a001f1a">QuotientRing< T ></a>, <a class="el" href="class_quotient_ring.html#ae4dc3dd42c8bc2bd37eff95e8a001f1a">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a>, <a class="el" href="class_ring_of_polynomials_over.html#a37731e8b8eecc4dac0b782443387dc95">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a570d89c94098cfd66ac5e5e2faa81d1b">EuclideanDomainOf< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a570d89c94098cfd66ac5e5e2faa81d1b">EuclideanDomainOf< PolynomialMod2 ></a>, <a class="el" href="class_montgomery_representation.html#a793d265b8165135e2e972bf333ac5a49">MontgomeryRepresentation</a>, <a class="el" href="class_modular_arithmetic.html#a3b88a85b11eb1a826d26d01bdaafbf0a">ModularArithmetic</a>, and <a class="el" href="class_g_f_p2___o_n_b.html#abe477db3d5bf5fdb72b9fcc832ff8bac">GFP2_ONB< F ></a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aba109f4e7932d77a8251c1ec20627571">◆ </a></span>MultiplicativeInverse()</h2>
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<td class="memname">virtual const Element& <a class="el" href="class_abstract_ring.html">AbstractRing</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>Implemented in <a class="el" href="class_quotient_ring.html#ac78f2284a7bdd06c39fd849ea7d23d48">QuotientRing< T ></a>, <a class="el" href="class_quotient_ring.html#ac78f2284a7bdd06c39fd849ea7d23d48">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a>, <a class="el" href="class_ring_of_polynomials_over.html#a75a3ae02cf9e1690dbc87be7e97f0248">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a317c5a5b15b53b0087fc2c1acc2738c0">EuclideanDomainOf< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a317c5a5b15b53b0087fc2c1acc2738c0">EuclideanDomainOf< PolynomialMod2 ></a>, <a class="el" href="class_montgomery_representation.html#ae1c2c1f3144d88ee4cdb2bd5b5a376b8">MontgomeryRepresentation</a>, <a class="el" href="class_modular_arithmetic.html#a149c6c7abe3e1729880658db5650e48a">ModularArithmetic</a>, and <a class="el" href="class_g_f_p2___o_n_b.html#a42f1dfe03023fb5502843e326892850c">GFP2_ONB< F ></a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a54b38c3a067b893e0c87495bee7adcef">◆ </a></span>Square()</h2>
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<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><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 in <a class="el" href="class_quotient_ring.html#a4cf651be2789bdd9d9db9b156ebd1d33">QuotientRing< T ></a>, <a class="el" href="class_quotient_ring.html#a4cf651be2789bdd9d9db9b156ebd1d33">QuotientRing< EuclideanDomainOf< PolynomialMod2 > ></a>, <a class="el" href="class_ring_of_polynomials_over.html#a81b2df6ff2a50c000a9cc7dccd37ba5e">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#acb21bd68efa18945d012b6a879d661e8">EuclideanDomainOf< T ></a>, <a class="el" href="class_euclidean_domain_of.html#acb21bd68efa18945d012b6a879d661e8">EuclideanDomainOf< PolynomialMod2 ></a>, <a class="el" href="class_g_f2_n_t.html#a519600850f1585fbf0682b347b9e6d37">GF2NT</a>, <a class="el" href="class_montgomery_representation.html#a2f24e4fb6d9b9fc9c6b363d41e7ee449">MontgomeryRepresentation</a>, <a class="el" href="class_modular_arithmetic.html#a7f74883ad789f0db51ed9b45385c14db">ModularArithmetic</a>, and <a class="el" href="class_g_f_p2___o_n_b.html#a41cd047c0fc625ecde993d839d8d86b7">GFP2_ONB< F ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00037">37</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa7ce20a30d89a8257088930d1d06d0b7">◆ </a></span>Divide()</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>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>b</em> </td>
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<p>Divides elements in the group. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the dividend </td></tr>
<tr><td class="paramname">b</td><td>the divisor </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the quotient </dd></dl>
<p>Reimplemented in <a class="el" href="class_ring_of_polynomials_over.html#a689e7df1b7183b782d8c78dba07760b7">RingOfPolynomialsOver< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a52cd96d2233db782eb7c74d3645be28d">EuclideanDomainOf< T ></a>, <a class="el" href="class_euclidean_domain_of.html#a52cd96d2233db782eb7c74d3645be28d">EuclideanDomainOf< PolynomialMod2 ></a>, and <a class="el" href="class_modular_arithmetic.html#a584d214676856d1463e14c6407d1cd31">ModularArithmetic</a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00042">42</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a0f011366054a4edb80be92f968083538">◆ </a></span>Exponentiate()</h2>
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<td class="memname">T <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::Exponentiate </td>
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<td>)</td>
<td></td><td> const</td>
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<span class="mlabels"><span class="mlabel">virtual</span></span> </td>
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<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 in <a class="el" href="class_g_f_p2___o_n_b.html#ad71eeac946b5f17fcb6645bd2f281d23">GFP2_ONB< F ></a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00316">316</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#adb4d33ac59a8f8bff1752b75809136e6">◆ </a></span>CascadeExponentiate()</h2>
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template<class T > </div>
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<td class="memname">T <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::CascadeExponentiate </td>
<td>(</td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>x</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>e1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>y</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>e2</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
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<span class="mlabels"><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">x</td><td>first element </td></tr>
<tr><td class="paramname">e1</td><td>first exponent </td></tr>
<tr><td class="paramname">y</td><td>second element </td></tr>
<tr><td class="paramname">e2</td><td>second exponent </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>TODO </dd></dl>
<p>Reimplemented in <a class="el" href="class_montgomery_representation.html#a63d9f4e3b09f34349fcc87059d86a77a">MontgomeryRepresentation</a>, and <a class="el" href="class_modular_arithmetic.html#abc45ee154d39d39e45e0d0f7a053a8c1">ModularArithmetic</a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00323">323</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
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<a id="a63530b69e7bfa78e5ee7b072cc798f0a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a63530b69e7bfa78e5ee7b072cc798f0a">◆ </a></span>SimultaneousExponentiate()</h2>
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<td class="memname">void <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::SimultaneousExponentiate </td>
<td>(</td>
<td class="paramtype">Element * </td>
<td class="paramname"><em>results</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const Element & </td>
<td class="paramname"><em>base</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>exponents</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned int </td>
<td class="paramname"><em>exponentsCount</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const</td>
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<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">virtual</span></span> </td>
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<p>Exponentiates a base to multiple exponents in the Ring. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">results</td><td>an array of Elements </td></tr>
<tr><td class="paramname">base</td><td>the base to raise to the exponents </td></tr>
<tr><td class="paramname">exponents</td><td>an array of exponents </td></tr>
<tr><td class="paramname">exponentsCount</td><td>the number of exponents in the array</td></tr>
</table>
</dd>
</dl>
<p><a class="el" href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a" title="Exponentiates a base to multiple exponents in the Ring. ">SimultaneousExponentiate()</a> raises the base to each exponent in the exponents array and stores the result at the respective position in the results array.</p>
<p><a class="el" href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a" title="Exponentiates a base to multiple exponents in the Ring. ">SimultaneousExponentiate()</a> must be implemented in a derived class. </p><dl class="section pre"><dt>Precondition</dt><dd><code><a class="el" href="misc_8h.html#a2d7e4464ea73d6393ebe78f952253426" title="Counts elements in an array. ">COUNTOF(results)</a> == exponentsCount</code> </dd>
<dd>
<code><a class="el" href="misc_8h.html#a2d7e4464ea73d6393ebe78f952253426" title="Counts elements in an array. ">COUNTOF(exponents)</a> == exponentsCount</code> </dd></dl>
<p>Reimplemented in <a class="el" href="class_montgomery_representation.html#a1b03500e21a63d27be5c137877b69d43">MontgomeryRepresentation</a>, and <a class="el" href="class_modular_arithmetic.html#aaf8e51fdf899092a19520f3e0a367608">ModularArithmetic</a>.</p>
<p class="definition">Definition at line <a class="el" href="algebra_8cpp_source.html#l00334">334</a> of file <a class="el" href="algebra_8cpp_source.html">algebra.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae19ef788f5ce5192e5867666ef38717f">◆ </a></span>MultiplicativeGroup()</h2>
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template<class T> </div>
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<td class="memname">virtual const <a class="el" href="class_abstract_group.html">AbstractGroup</a><T>& <a class="el" href="class_abstract_ring.html">AbstractRing</a>< T >::MultiplicativeGroup </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>
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<p>Retrieves the multiplicative group. </p>
<dl class="section return"><dt>Returns</dt><dd>the multiplicative group </dd></dl>
<p class="definition">Definition at line <a class="el" href="algebra_8h_source.html#l00194">194</a> of file <a class="el" href="algebra_8h_source.html">algebra.h</a>.</p>
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</div>
<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>
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