<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<title>Crypto++: algebra.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<link href="doxygen.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<!-- Generated by Doxygen 1.6.1 -->
<div class="navigation" id="top">
<div class="tabs">
<ul>
<li><a href="index.html"><span>Main Page</span></a></li>
<li><a href="namespaces.html"><span>Namespaces</span></a></li>
<li><a href="annotated.html"><span>Classes</span></a></li>
<li class="current"><a href="files.html"><span>Files</span></a></li>
</ul>
</div>
<div class="tabs">
<ul>
<li><a href="files.html"><span>File List</span></a></li>
<li><a href="globals.html"><span>File Members</span></a></li>
</ul>
</div>
<h1>algebra.h</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="preprocessor">#ifndef CRYPTOPP_ALGEBRA_H</span>
<a name="l00002"></a>00002 <span class="preprocessor"></span><span class="preprocessor">#define CRYPTOPP_ALGEBRA_H</span>
<a name="l00003"></a>00003 <span class="preprocessor"></span>
<a name="l00004"></a>00004 <span class="preprocessor">#include "config.h"</span>
<a name="l00005"></a>00005
<a name="l00006"></a>00006 NAMESPACE_BEGIN(CryptoPP)
<a name="l00007"></a>00007
<a name="l00008"></a>00008 class <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>;
<a name="l00009"></a>00009
<a name="l00010"></a>00010 <span class="comment">// "const Element&" returned by member functions are references</span>
<a name="l00011"></a>00011 <span class="comment">// to internal data members. Since each object may have only</span>
<a name="l00012"></a>00012 <span class="comment">// one such data member for holding results, the following code</span>
<a name="l00013"></a>00013 <span class="comment">// will produce incorrect results:</span>
<a name="l00014"></a>00014 <span class="comment">// abcd = group.Add(group.Add(a,b), group.Add(c,d));</span>
<a name="l00015"></a>00015 <span class="comment">// But this should be fine:</span>
<a name="l00016"></a>00016 <span class="comment">// abcd = group.Add(a, group.Add(b, group.Add(c,d));</span>
<a name="l00017"></a>00017 <span class="comment"></span>
<a name="l00018"></a>00018 <span class="comment">//! Abstract Group</span>
<a name="l00019"></a><a class="code" href="class_abstract_group.html">00019</a> <span class="comment"></span>template <class T> class CRYPTOPP_NO_VTABLE <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup</a>
<a name="l00020"></a>00020 {
<a name="l00021"></a>00021 <span class="keyword">public</span>:
<a name="l00022"></a>00022 <span class="keyword">typedef</span> T Element;
<a name="l00023"></a>00023
<a name="l00024"></a>00024 <span class="keyword">virtual</span> ~AbstractGroup() {}
<a name="l00025"></a>00025
<a name="l00026"></a>00026 <span class="keyword">virtual</span> <span class="keywordtype">bool</span> Equal(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span> =0;
<a name="l00027"></a>00027 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Identity() <span class="keyword">const</span> =0;
<a name="l00028"></a>00028 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Add(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span> =0;
<a name="l00029"></a>00029 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Inverse(<span class="keyword">const</span> Element &a) <span class="keyword">const</span> =0;
<a name="l00030"></a>00030 <span class="keyword">virtual</span> <span class="keywordtype">bool</span> InversionIsFast()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">false</span>;}
<a name="l00031"></a>00031
<a name="l00032"></a>00032 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Double(<span class="keyword">const</span> Element &a) <span class="keyword">const</span>;
<a name="l00033"></a>00033 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Subtract(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;
<a name="l00034"></a>00034 <span class="keyword">virtual</span> Element& Accumulate(Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;
<a name="l00035"></a>00035 <span class="keyword">virtual</span> Element& Reduce(Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;
<a name="l00036"></a>00036
<a name="l00037"></a>00037 <span class="keyword">virtual</span> Element ScalarMultiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Integer &e) <span class="keyword">const</span>;
<a name="l00038"></a>00038 <span class="keyword">virtual</span> Element CascadeScalarMultiply(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> Integer &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> Integer &e2) <span class="keyword">const</span>;
<a name="l00039"></a>00039
<a name="l00040"></a>00040 <span class="keyword">virtual</span> <span class="keywordtype">void</span> SimultaneousMultiply(Element *results, <span class="keyword">const</span> Element &base, <span class="keyword">const</span> Integer *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount) <span class="keyword">const</span>;
<a name="l00041"></a>00041 };
<a name="l00042"></a>00042 <span class="comment"></span>
<a name="l00043"></a>00043 <span class="comment">//! Abstract Ring</span>
<a name="l00044"></a><a class="code" href="class_abstract_ring.html">00044</a> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">class </span>CRYPTOPP_NO_VTABLE <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup</a><T>
<a name="l00045"></a>00045 {
<a name="l00046"></a>00046 <span class="keyword">public</span>:
<a name="l00047"></a>00047 <span class="keyword">typedef</span> T Element;
<a name="l00048"></a>00048
<a name="l00049"></a>00049 <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a>() {m_mg.m_pRing = <span class="keyword">this</span>;}
<a name="l00050"></a>00050 <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a> &source) {m_mg.m_pRing = <span class="keyword">this</span>;}
<a name="l00051"></a>00051 <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a>& operator=(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a> &source) {<span class="keywordflow">return</span> *<span class="keyword">this</span>;}
<a name="l00052"></a>00052
<a name="l00053"></a>00053 <span class="keyword">virtual</span> <span class="keywordtype">bool</span> IsUnit(<span class="keyword">const</span> Element &a) <span class="keyword">const</span> =0;
<a name="l00054"></a>00054 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& MultiplicativeIdentity() <span class="keyword">const</span> =0;
<a name="l00055"></a>00055 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Multiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span> =0;
<a name="l00056"></a>00056 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& MultiplicativeInverse(<span class="keyword">const</span> Element &a) <span class="keyword">const</span> =0;
<a name="l00057"></a>00057
<a name="l00058"></a>00058 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& <a class="code" href="class_square.html" title="Square">Square</a>(<span class="keyword">const</span> Element &a) <span class="keyword">const</span>;
<a name="l00059"></a>00059 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Divide(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;
<a name="l00060"></a>00060
<a name="l00061"></a>00061 <span class="keyword">virtual</span> Element Exponentiate(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e) <span class="keyword">const</span>;
<a name="l00062"></a>00062 <span class="keyword">virtual</span> Element CascadeExponentiate(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e2) <span class="keyword">const</span>;
<a name="l00063"></a>00063
<a name="l00064"></a>00064 <span class="keyword">virtual</span> <span class="keywordtype">void</span> SimultaneousExponentiate(Element *results, <span class="keyword">const</span> Element &base, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount) <span class="keyword">const</span>;
<a name="l00065"></a>00065
<a name="l00066"></a>00066 <span class="keyword">virtual</span> <span class="keyword">const</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T></a>& MultiplicativeGroup()<span class="keyword"> const</span>
<a name="l00067"></a>00067 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_mg;}
<a name="l00068"></a>00068
<a name="l00069"></a>00069 <span class="keyword">private</span>:
<a name="l00070"></a>00070 <span class="keyword">class </span>MultiplicativeGroupT : <span class="keyword">public</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup</a><T>
<a name="l00071"></a>00071 {
<a name="l00072"></a>00072 <span class="keyword">public</span>:
<a name="l00073"></a>00073 <span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T></a>& GetRing()<span class="keyword"> const</span>
<a name="l00074"></a>00074 <span class="keyword"> </span>{<span class="keywordflow">return</span> *m_pRing;}
<a name="l00075"></a>00075
<a name="l00076"></a>00076 <span class="keywordtype">bool</span> Equal(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00077"></a>00077 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().Equal(a, b);}
<a name="l00078"></a>00078
<a name="l00079"></a>00079 <span class="keyword">const</span> Element& Identity()<span class="keyword"> const</span>
<a name="l00080"></a>00080 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().MultiplicativeIdentity();}
<a name="l00081"></a>00081
<a name="l00082"></a>00082 <span class="keyword">const</span> Element& Add(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00083"></a>00083 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().Multiply(a, b);}
<a name="l00084"></a>00084
<a name="l00085"></a>00085 Element& Accumulate(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00086"></a>00086 <span class="keyword"> </span>{<span class="keywordflow">return</span> a = GetRing().Multiply(a, b);}
<a name="l00087"></a>00087
<a name="l00088"></a>00088 <span class="keyword">const</span> Element& Inverse(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00089"></a>00089 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().MultiplicativeInverse(a);}
<a name="l00090"></a>00090
<a name="l00091"></a>00091 <span class="keyword">const</span> Element& Subtract(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00092"></a>00092 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().Divide(a, b);}
<a name="l00093"></a>00093
<a name="l00094"></a>00094 Element& Reduce(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00095"></a>00095 <span class="keyword"> </span>{<span class="keywordflow">return</span> a = GetRing().Divide(a, b);}
<a name="l00096"></a>00096
<a name="l00097"></a>00097 <span class="keyword">const</span> Element& Double(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00098"></a>00098 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().Square(a);}
<a name="l00099"></a>00099
<a name="l00100"></a>00100 Element ScalarMultiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e)<span class="keyword"> const</span>
<a name="l00101"></a>00101 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().Exponentiate(a, e);}
<a name="l00102"></a>00102
<a name="l00103"></a>00103 Element CascadeScalarMultiply(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e2)<span class="keyword"> const</span>
<a name="l00104"></a>00104 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().CascadeExponentiate(x, e1, y, e2);}
<a name="l00105"></a>00105
<a name="l00106"></a>00106 <span class="keywordtype">void</span> SimultaneousMultiply(Element *results, <span class="keyword">const</span> Element &base, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount)<span class="keyword"> const</span>
<a name="l00107"></a>00107 <span class="keyword"> </span>{GetRing().SimultaneousExponentiate(results, base, exponents, exponentsCount);}
<a name="l00108"></a>00108
<a name="l00109"></a>00109 <span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T></a> *m_pRing;
<a name="l00110"></a>00110 };
<a name="l00111"></a>00111
<a name="l00112"></a>00112 MultiplicativeGroupT m_mg;
<a name="l00113"></a>00113 };
<a name="l00114"></a>00114
<a name="l00115"></a>00115 <span class="comment">// ********************************************************</span>
<a name="l00116"></a>00116 <span class="comment"></span>
<a name="l00117"></a>00117 <span class="comment">//! Base and Exponent</span>
<a name="l00118"></a>00118 <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keyword">class</span> E = Integer>
<a name="l00119"></a><a class="code" href="struct_base_and_exponent.html">00119</a> <span class="keyword">struct </span><a class="code" href="struct_base_and_exponent.html" title="Base and Exponent.">BaseAndExponent</a>
<a name="l00120"></a>00120 {
<a name="l00121"></a>00121 <span class="keyword">public</span>:
<a name="l00122"></a>00122 <a class="code" href="struct_base_and_exponent.html" title="Base and Exponent.">BaseAndExponent</a>() {}
<a name="l00123"></a>00123 <a class="code" href="struct_base_and_exponent.html" title="Base and Exponent.">BaseAndExponent</a>(<span class="keyword">const</span> T &base, <span class="keyword">const</span> E &exponent) : base(base), exponent(exponent) {}
<a name="l00124"></a>00124 <span class="keywordtype">bool</span> operator<(const BaseAndExponent<T, E> &rhs) <span class="keyword">const</span> {<span class="keywordflow">return</span> exponent < rhs.exponent;}
<a name="l00125"></a>00125 T base;
<a name="l00126"></a>00126 E exponent;
<a name="l00127"></a>00127 };
<a name="l00128"></a>00128
<a name="l00129"></a>00129 <span class="comment">// VC60 workaround: incomplete member template support</span>
<a name="l00130"></a>00130 <span class="keyword">template</span> <<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator>
<a name="l00131"></a>00131 Element GeneralCascadeMultiplication(<span class="keyword">const</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<Element></a> &group, Iterator begin, Iterator end);
<a name="l00132"></a>00132 <span class="keyword">template</span> <<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator>
<a name="l00133"></a>00133 Element GeneralCascadeExponentiation(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<Element></a> &ring, Iterator begin, Iterator end);
<a name="l00134"></a>00134
<a name="l00135"></a>00135 <span class="comment">// ********************************************************</span>
<a name="l00136"></a>00136 <span class="comment"></span>
<a name="l00137"></a>00137 <span class="comment">//! Abstract Euclidean Domain</span>
<a name="l00138"></a><a class="code" href="class_abstract_euclidean_domain.html">00138</a> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">class </span>CRYPTOPP_NO_VTABLE <a class="code" href="class_abstract_euclidean_domain.html" title="Abstract Euclidean Domain.">AbstractEuclideanDomain</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a><T>
<a name="l00139"></a>00139 {
<a name="l00140"></a>00140 <span class="keyword">public</span>:
<a name="l00141"></a>00141 <span class="keyword">typedef</span> T Element;
<a name="l00142"></a>00142
<a name="l00143"></a>00143 <span class="keyword">virtual</span> <span class="keywordtype">void</span> DivisionAlgorithm(Element &r, Element &q, <span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &d) <span class="keyword">const</span> =0;
<a name="l00144"></a>00144
<a name="l00145"></a>00145 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Mod(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span> =0;
<a name="l00146"></a>00146 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Gcd(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;
<a name="l00147"></a>00147
<a name="l00148"></a>00148 <span class="keyword">protected</span>:
<a name="l00149"></a>00149 <span class="keyword">mutable</span> Element result;
<a name="l00150"></a>00150 };
<a name="l00151"></a>00151
<a name="l00152"></a>00152 <span class="comment">// ********************************************************</span>
<a name="l00153"></a>00153 <span class="comment"></span>
<a name="l00154"></a>00154 <span class="comment">//! EuclideanDomainOf</span>
<a name="l00155"></a><a class="code" href="class_euclidean_domain_of.html">00155</a> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">class </span><a class="code" href="class_euclidean_domain_of.html" title="EuclideanDomainOf.">EuclideanDomainOf</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_euclidean_domain.html" title="Abstract Euclidean Domain.">AbstractEuclideanDomain</a><T>
<a name="l00156"></a>00156 {
<a name="l00157"></a>00157 <span class="keyword">public</span>:
<a name="l00158"></a>00158 <span class="keyword">typedef</span> T Element;
<a name="l00159"></a>00159
<a name="l00160"></a>00160 <a class="code" href="class_euclidean_domain_of.html" title="EuclideanDomainOf.">EuclideanDomainOf</a>() {}
<a name="l00161"></a>00161
<a name="l00162"></a>00162 <span class="keywordtype">bool</span> Equal(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00163"></a>00163 <span class="keyword"> </span>{<span class="keywordflow">return</span> a==b;}
<a name="l00164"></a>00164
<a name="l00165"></a>00165 <span class="keyword">const</span> Element& Identity()<span class="keyword"> const</span>
<a name="l00166"></a>00166 <span class="keyword"> </span>{<span class="keywordflow">return</span> Element::Zero();}
<a name="l00167"></a>00167
<a name="l00168"></a>00168 <span class="keyword">const</span> Element& Add(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00169"></a>00169 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a+b;}
<a name="l00170"></a>00170
<a name="l00171"></a>00171 Element& Accumulate(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00172"></a>00172 <span class="keyword"> </span>{<span class="keywordflow">return</span> a+=b;}
<a name="l00173"></a>00173
<a name="l00174"></a>00174 <span class="keyword">const</span> Element& Inverse(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00175"></a>00175 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = -a;}
<a name="l00176"></a>00176
<a name="l00177"></a>00177 <span class="keyword">const</span> Element& Subtract(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00178"></a>00178 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a-b;}
<a name="l00179"></a>00179
<a name="l00180"></a>00180 Element& Reduce(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00181"></a>00181 <span class="keyword"> </span>{<span class="keywordflow">return</span> a-=b;}
<a name="l00182"></a>00182
<a name="l00183"></a>00183 <span class="keyword">const</span> Element& Double(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00184"></a>00184 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a.Doubled();}
<a name="l00185"></a>00185
<a name="l00186"></a>00186 <span class="keyword">const</span> Element& MultiplicativeIdentity()<span class="keyword"> const</span>
<a name="l00187"></a>00187 <span class="keyword"> </span>{<span class="keywordflow">return</span> Element::One();}
<a name="l00188"></a>00188
<a name="l00189"></a>00189 <span class="keyword">const</span> Element& Multiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00190"></a>00190 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a*b;}
<a name="l00191"></a>00191
<a name="l00192"></a>00192 <span class="keyword">const</span> Element& <a class="code" href="class_square.html" title="Square">Square</a>(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00193"></a>00193 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a.Squared();}
<a name="l00194"></a>00194
<a name="l00195"></a>00195 <span class="keywordtype">bool</span> IsUnit(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00196"></a>00196 <span class="keyword"> </span>{<span class="keywordflow">return</span> a.IsUnit();}
<a name="l00197"></a>00197
<a name="l00198"></a>00198 <span class="keyword">const</span> Element& MultiplicativeInverse(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00199"></a>00199 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a.MultiplicativeInverse();}
<a name="l00200"></a>00200
<a name="l00201"></a>00201 <span class="keyword">const</span> Element& Divide(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00202"></a>00202 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a/b;}
<a name="l00203"></a>00203
<a name="l00204"></a>00204 <span class="keyword">const</span> Element& Mod(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00205"></a>00205 <span class="keyword"> </span>{<span class="keywordflow">return</span> result = a%b;}
<a name="l00206"></a>00206
<a name="l00207"></a>00207 <span class="keywordtype">void</span> DivisionAlgorithm(Element &r, Element &q, <span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &d)<span class="keyword"> const</span>
<a name="l00208"></a>00208 <span class="keyword"> </span>{Element::Divide(r, q, a, d);}
<a name="l00209"></a>00209
<a name="l00210"></a>00210 <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> <a class="code" href="class_euclidean_domain_of.html" title="EuclideanDomainOf.">EuclideanDomainOf<T></a> &rhs)<span class="keyword"> const</span>
<a name="l00211"></a>00211 <span class="keyword"> </span>{<span class="keywordflow">return</span> <span class="keyword">true</span>;}
<a name="l00212"></a>00212
<a name="l00213"></a>00213 <span class="keyword">private</span>:
<a name="l00214"></a>00214 <span class="keyword">mutable</span> Element result;
<a name="l00215"></a>00215 };
<a name="l00216"></a>00216 <span class="comment"></span>
<a name="l00217"></a>00217 <span class="comment">//! Quotient Ring</span>
<a name="l00218"></a><a class="code" href="class_quotient_ring.html">00218</a> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">class </span><a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a><typename T::Element>
<a name="l00219"></a>00219 {
<a name="l00220"></a>00220 <span class="keyword">public</span>:
<a name="l00221"></a>00221 <span class="keyword">typedef</span> T EuclideanDomain;
<a name="l00222"></a>00222 <span class="keyword">typedef</span> <span class="keyword">typename</span> T::Element Element;
<a name="l00223"></a>00223
<a name="l00224"></a>00224 <a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing</a>(<span class="keyword">const</span> EuclideanDomain &domain, <span class="keyword">const</span> Element &modulus)
<a name="l00225"></a>00225 : m_domain(domain), m_modulus(modulus) {}
<a name="l00226"></a>00226
<a name="l00227"></a>00227 <span class="keyword">const</span> EuclideanDomain & GetDomain()<span class="keyword"> const</span>
<a name="l00228"></a>00228 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain;}
<a name="l00229"></a>00229
<a name="l00230"></a>00230 <span class="keyword">const</span> Element& GetModulus()<span class="keyword"> const</span>
<a name="l00231"></a>00231 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_modulus;}
<a name="l00232"></a>00232
<a name="l00233"></a>00233 <span class="keywordtype">bool</span> Equal(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00234"></a>00234 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Equal(m_domain.Mod(m_domain.Subtract(a, b), m_modulus), m_domain.Identity());}
<a name="l00235"></a>00235
<a name="l00236"></a>00236 <span class="keyword">const</span> Element& Identity()<span class="keyword"> const</span>
<a name="l00237"></a>00237 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Identity();}
<a name="l00238"></a>00238
<a name="l00239"></a>00239 <span class="keyword">const</span> Element& Add(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00240"></a>00240 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Add(a, b);}
<a name="l00241"></a>00241
<a name="l00242"></a>00242 Element& Accumulate(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00243"></a>00243 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Accumulate(a, b);}
<a name="l00244"></a>00244
<a name="l00245"></a>00245 <span class="keyword">const</span> Element& Inverse(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00246"></a>00246 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Inverse(a);}
<a name="l00247"></a>00247
<a name="l00248"></a>00248 <span class="keyword">const</span> Element& Subtract(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00249"></a>00249 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Subtract(a, b);}
<a name="l00250"></a>00250
<a name="l00251"></a>00251 Element& Reduce(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00252"></a>00252 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Reduce(a, b);}
<a name="l00253"></a>00253
<a name="l00254"></a>00254 <span class="keyword">const</span> Element& Double(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00255"></a>00255 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Double(a);}
<a name="l00256"></a>00256
<a name="l00257"></a>00257 <span class="keywordtype">bool</span> IsUnit(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00258"></a>00258 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.IsUnit(m_domain.Gcd(a, m_modulus));}
<a name="l00259"></a>00259
<a name="l00260"></a>00260 <span class="keyword">const</span> Element& MultiplicativeIdentity()<span class="keyword"> const</span>
<a name="l00261"></a>00261 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.MultiplicativeIdentity();}
<a name="l00262"></a>00262
<a name="l00263"></a>00263 <span class="keyword">const</span> Element& Multiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00264"></a>00264 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Mod(m_domain.Multiply(a, b), m_modulus);}
<a name="l00265"></a>00265
<a name="l00266"></a>00266 <span class="keyword">const</span> Element& <a class="code" href="class_square.html" title="Square">Square</a>(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00267"></a>00267 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain.Mod(m_domain.Square(a), m_modulus);}
<a name="l00268"></a>00268
<a name="l00269"></a>00269 <span class="keyword">const</span> Element& MultiplicativeInverse(<span class="keyword">const</span> Element &a) <span class="keyword">const</span>;
<a name="l00270"></a>00270
<a name="l00271"></a>00271 <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> <a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing<T></a> &rhs)<span class="keyword"> const</span>
<a name="l00272"></a>00272 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_domain == rhs.m_domain && m_modulus == rhs.m_modulus;}
<a name="l00273"></a>00273
<a name="l00274"></a>00274 <span class="keyword">protected</span>:
<a name="l00275"></a>00275 EuclideanDomain m_domain;
<a name="l00276"></a>00276 Element m_modulus;
<a name="l00277"></a>00277 };
<a name="l00278"></a>00278
<a name="l00279"></a>00279 NAMESPACE_END
<a name="l00280"></a>00280
<a name="l00281"></a>00281 <span class="preprocessor">#ifdef CRYPTOPP_MANUALLY_INSTANTIATE_TEMPLATES</span>
<a name="l00282"></a>00282 <span class="preprocessor"></span><span class="preprocessor">#include "algebra.cpp"</span>
<a name="l00283"></a>00283 <span class="preprocessor">#endif</span>
<a name="l00284"></a>00284 <span class="preprocessor"></span>
<a name="l00285"></a>00285 <span class="preprocessor">#endif</span>
</pre></div></div>
<hr size="1"/><address style="text-align: right;"><small>Generated on 9 Dec 2009 for Crypto++ by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.6.1 </small></address>
</body>
</html>
