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著名的密码库Crypto++的文档 C++语言的杰作。程序员必备。

<a name="l00058"></a>00058         <span class="keyword">virtual</span> <span class="keyword">const</span> Element&amp; <a class="code" href="class_square.html" title="Square">Square</a>(<span class="keyword">const</span> Element &amp;a) <span class="keyword">const</span>;
<a name="l00059"></a>00059         <span class="keyword">virtual</span> <span class="keyword">const</span> Element&amp; Divide(<span class="keyword">const</span> Element &amp;a, <span class="keyword">const</span> Element &amp;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 &amp;a, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &amp;e) <span class="keyword">const</span>;
<a name="l00062"></a>00062         <span class="keyword">virtual</span> Element CascadeExponentiate(<span class="keyword">const</span> Element &amp;x, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &amp;e1, <span class="keyword">const</span> Element &amp;y, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &amp;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 &amp;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><a class="code" href="class_abstract_ring.html#e19ef788f5ce5192e5867666ef38717f">00066</a>         <span class="keyword">virtual</span> <span class="keyword">const</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup&lt;T&gt;</a>&amp; 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>&lt;T&gt;
<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&lt;T&gt;</a>&amp; 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 &amp;a, <span class="keyword">const</span> Element &amp;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&amp; 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&amp; Add(<span class="keyword">const</span> Element &amp;a, <span class="keyword">const</span> Element &amp;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&amp; Accumulate(Element &amp;a, <span class="keyword">const</span> Element &amp;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&amp; Inverse(<span class="keyword">const</span> Element &amp;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&amp; Subtract(<span class="keyword">const</span> Element &amp;a, <span class="keyword">const</span> Element &amp;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&amp; Reduce(Element &amp;a, <span class="keyword">const</span> Element &amp;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&amp; Double(<span class="keyword">const</span> Element &amp;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 &amp;a, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &amp;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 &amp;x, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &amp;e1, <span class="keyword">const</span> Element &amp;y, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &amp;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 &amp;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&lt;T&gt;</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> &lt;<span class="keyword">class</span> T, <span class="keyword">class</span> E = Integer&gt;
<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><a class="code" href="struct_base_and_exponent.html#f76a40c50c5bf9a4d337e104463015e3">00122</a>         <a class="code" href="struct_base_and_exponent.html#f76a40c50c5bf9a4d337e104463015e3">BaseAndExponent</a>() {}
<a name="l00123"></a><a class="code" href="struct_base_and_exponent.html#f76c5f14b01374be99107eb11c42741b">00123</a>         <a class="code" href="struct_base_and_exponent.html#f76a40c50c5bf9a4d337e104463015e3">BaseAndExponent</a>(<span class="keyword">const</span> T &amp;<a class="code" href="struct_base_and_exponent.html#2755b0083cf789f5dc529c3fb3688a5f">base</a>, <span class="keyword">const</span> E &amp;<a class="code" href="struct_base_and_exponent.html#301129e6c74f822ba4bd31a19ccabe82">exponent</a>) : base(base), exponent(exponent) {}
<a name="l00124"></a><a class="code" href="struct_base_and_exponent.html#bd3f6616decdd0d4606e82bb7b294264">00124</a>         <span class="keywordtype">bool</span> operator&lt;(const BaseAndExponent&lt;T, E&gt; &amp;rhs) <span class="keyword">const</span> {<span class="keywordflow">return</span> <a class="code" href="struct_base_and_exponent.html#301129e6c74f822ba4bd31a19ccabe82">exponent</a> &lt; rhs.exponent;}
<a name="l00125"></a><a class="code" href="struct_base_and_exponent.html#2755b0083cf789f5dc529c3fb3688a5f">00125</a>         T <a class="code" href="struct_base_and_exponent.html#2755b0083cf789f5dc529c3fb3688a5f">base</a>;
<a name="l00126"></a><a class="code" href="struct_base_and_exponent.html#301129e6c74f822ba4bd31a19ccabe82">00126</a>         E <a class="code" href="struct_base_and_exponent.html#301129e6c74f822ba4bd31a19ccabe82">exponent</a>;
<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> &lt;<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator&gt;
<a name="l00131"></a>00131         Element GeneralCascadeMultiplication(<span class="keyword">const</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup&lt;Element&gt;</a> &amp;group, Iterator begin, Iterator end);
<a name="l00132"></a>00132 <span class="keyword">template</span> &lt;<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator&gt;
<a name="l00133"></a>00133         Element GeneralCascadeExponentiation(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing&lt;Element&gt;</a> &amp;ring, Iterator begin, Iterator end);
<a name="l00134"></a>00134 
<a name="l00135"></a>00135 <span class="comment">// ********************************************************</span>