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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"><html><head><meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"><title>Crypto++: algebra.h Source File</title><link href="doxygen.css" rel="stylesheet" type="text/css"></head><body><!-- Generated by Doxygen 1.3.2 --><div class="qindex"><a class="qindex" href="index.html">Main Page</a> | <a class="qindex" href="namespaces.html">Namespace List</a> | <a class="qindex" href="hierarchy.html">Class Hierarchy</a> | <a class="qindex" href="classes.html">Alphabetical List</a> | <a class="qindex" href="annotated.html">Compound List</a> | <a class="qindex" href="files.html">File List</a> | <a class="qindex" href="namespacemembers.html">Namespace Members</a> | <a class="qindex" href="functions.html">Compound Members</a> | <a class="qindex" href="globals.html">File Members</a></div><h1>algebra.h</h1><div class="fragment"><pre>00001 <span class="preprocessor">#ifndef CRYPTOPP_ALGEBRA_H</span>00002 <span class="preprocessor"></span><span class="preprocessor">#define CRYPTOPP_ALGEBRA_H</span>00003 <span class="preprocessor"></span>00004 <span class="preprocessor">#include "config.h"</span>00005 00006 NAMESPACE_BEGIN(CryptoPP)00007 00008 <span class="keyword">class </span><a class="code" href="class_integer.html">Integer</a>;00009 00010 <span class="comment">// "const Element&" returned by member functions are references</span>00011 <span class="comment">// to internal data members. Since each object may have only</span>00012 <span class="comment">// one such data member for holding results, the following code</span>00013 <span class="comment">// will produce incorrect results:</span>00014 <span class="comment">// abcd = group.Add(group.Add(a,b), group.Add(c,d));</span>00015 <span class="comment">// But this should be fine:</span>00016 <span class="comment">// abcd = group.Add(a, group.Add(b, group.Add(c,d));</span>00017 <span class="comment"></span>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><span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">class </span><a class="code" href="class_abstract_group.html">AbstractGroup</a>00020 {00021 <span class="keyword">public</span>:00022 <span class="keyword">typedef</span> T Element;00023 00024 <span class="keyword">virtual</span> ~<a class="code" href="class_abstract_group.html">AbstractGroup</a>() {}00025 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;00027 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& Identity() <span class="keyword">const</span> =0;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;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;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>;}00031 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>;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>;00034 <span class="keyword">virtual</span> Element& Accumulate(Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;00035 <span class="keyword">virtual</span> Element& Reduce(Element &a, <span class="keyword">const</span> Element &b) <span class="keyword">const</span>;00036 00037 <span class="keyword">virtual</span> Element ScalarMultiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e) <span class="keyword">const</span>;00038 <span class="keyword">virtual</span> Element CascadeScalarMultiply(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e2) <span class="keyword">const</span>;00039 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> <a class="code" href="class_integer.html">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount) <span class="keyword">const</span>;00041 };00042 <span class="comment"></span>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><a class="code" href="class_abstract_ring.html">AbstractRing</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_group.html">AbstractGroup</a><T>00045 {00046 <span class="keyword">public</span>:00047 <span class="keyword">typedef</span> T Element;00048 00049 <a class="code" href="class_abstract_ring.html">AbstractRing</a>() {m_mg.m_pRing = <span class="keyword">this</span>;}00050 <a class="code" href="class_abstract_ring.html">AbstractRing</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html">AbstractRing</a> &source) {m_mg.m_pRing = <span class="keyword">this</span>;}00051 <a class="code" href="class_abstract_ring.html">AbstractRing</a>& operator=(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html">AbstractRing</a> &source) {<span class="keywordflow">return</span> *<span class="keyword">this</span>;}00052 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;00054 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& MultiplicativeIdentity() <span class="keyword">const</span> =0;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;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;00057 00058 <span class="keyword">virtual</span> <span class="keyword">const</span> Element& <a class="code" href="class_square.html">Square</a>(<span class="keyword">const</span> Element &a) <span class="keyword">const</span>;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>;00060 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">Integer</a> &e) <span class="keyword">const</span>;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">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e2) <span class="keyword">const</span>;00063 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">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount) <span class="keyword">const</span>;00065 00066 <span class="keyword">virtual</span> <span class="keyword">const</span> <a class="code" href="class_abstract_group.html">AbstractGroup<T></a>& MultiplicativeGroup()<span class="keyword"> const</span>00067 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_mg;}00068 00069 <span class="keyword">private</span>:00070 <span class="keyword">class </span>MultiplicativeGroupT : <span class="keyword">public</span> <a class="code" href="class_abstract_group.html">AbstractGroup</a><T>00071 {00072 <span class="keyword">public</span>:00073 <span class="keyword">const</span> <a class="code" href="class_abstract_ring.html">AbstractRing<T></a>& GetRing()<span class="keyword"> const</span>00074 <span class="keyword"> </span>{<span class="keywordflow">return</span> *m_pRing;}00075 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>00077 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_group.html#_abstract_ringa13">Equal</a>(a, b);}00078 00079 <span class="keyword">const</span> Element& Identity()<span class="keyword"> const</span>00080 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa4">MultiplicativeIdentity</a>();}00081 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>00083 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa5">Multiply</a>(a, b);}00084 00085 Element& Accumulate(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>00086 <span class="keyword"> </span>{<span class="keywordflow">return</span> a = GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa5">Multiply</a>(a, b);}00087 00088 <span class="keyword">const</span> Element& Inverse(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>00089 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa6">MultiplicativeInverse</a>(a);}00090 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>00092 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa8">Divide</a>(a, b);}00093 00094 Element& Reduce(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>00095 <span class="keyword"> </span>{<span class="keywordflow">return</span> a = GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa8">Divide</a>(a, b);}00096 00097 <span class="keyword">const</span> Element& Double(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>00098 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_abstract_ringa7">Square</a>(a);}00099 00100 Element ScalarMultiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e)<span class="keyword"> const</span>00101 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_euclidean_domain_ofa18">Exponentiate</a>(a, e);}00102 00103 Element CascadeScalarMultiply(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e2)<span class="keyword"> const</span>00104 <span class="keyword"> </span>{<span class="keywordflow">return</span> GetRing().<a class="code" href="class_abstract_ring.html#_euclidean_domain_ofa19">CascadeExponentiate</a>(x, e1, y, e2);}00105 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">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount)<span class="keyword"> const</span>00107 <span class="keyword"> </span>{GetRing().<a class="code" href="class_abstract_ring.html#_euclidean_domain_ofa20">SimultaneousExponentiate</a>(results, base, exponents, exponentsCount);}00108 00109 <span class="keyword">const</span> <a class="code" href="class_abstract_ring.html">AbstractRing<T></a> *m_pRing;00110 };00111 00112 MultiplicativeGroupT m_mg;00113 };00114 00115 <span class="comment">// ********************************************************</span>00116 <span class="comment"></span>00117 <span class="comment">//! Base and Exponent</span>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">BaseAndExponent</a>00120 {00121 <span class="keyword">public</span>:00122 <a class="code" href="struct_base_and_exponent.html">BaseAndExponent</a>() {}00123 <a class="code" href="struct_base_and_exponent.html">BaseAndExponent</a>(<span class="keyword">const</span> T &base, <span class="keyword">const</span> E &exponent) : base(base), exponent(exponent) {}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;}00125 T base;00126 E exponent;00127 };00128 00129 <span class="comment">// VC60 workaround: incomplete member template support</span>00130 <span class="keyword">template</span> <<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator>00131 Element GeneralCascadeMultiplication(<span class="keyword">const</span> <a class="code" href="class_abstract_group.html">AbstractGroup<Element></a> &group, Iterator begin, Iterator end);00132 <span class="keyword">template</span> <<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator>00133 Element GeneralCascadeExponentiation(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html">AbstractRing<Element></a> &ring, Iterator begin, Iterator end);00134 00135 <span class="comment">// ********************************************************</span>00136 <span class="comment"></span>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><a class="code" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_ring.html">AbstractRing</a><T>00139 {⌨️ 快捷键说明
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