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Crypto++是一个非常强大的密码学库,主要是功能全

<a name="l00087"></a><a class="code" href="class_polynomial_over.html#_polynomial_over_fixed_ringz59_0">00087</a> <span class="comment"></span>                <span class="keywordtype">int</span> <a class="code" href="class_polynomial_over.html#_polynomial_over_fixed_ringz59_0">Degree</a>(<span class="keyword">const</span> Ring &amp;ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> int(CoefficientCount(ring))-1;}<span class="comment"></span>
00088 <span class="comment">                //!</span>
00089 <span class="comment"></span>                <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> CoefficientCount(<span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;<span class="comment"></span>
00090 <span class="comment">                //! return coefficient for x^i</span>
00091 <span class="comment"></span>                CoefficientType <a class="code" href="class_polynomial_over.html#_polynomial_over_fixed_ringz59_2">GetCoefficient</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;<span class="comment"></span>
00092 <span class="comment">        //@}</span>
00093 <span class="comment"></span><span class="comment"></span>
00094 <span class="comment">        //! \name MANIPULATORS</span>
00095 <span class="comment"></span><span class="comment">        //@{</span>
00096 <span class="comment"></span><span class="comment">                //!</span>
00097 <span class="comment"></span>                <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp;  operator=(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t);
00098 <span class="comment"></span>
00099 <span class="comment">                //!</span>
00100 <span class="comment"></span>                <span class="keywordtype">void</span> Randomize(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &amp;rng, <span class="keyword">const</span> RandomizationParameter &amp;parameter, <span class="keyword">const</span> Ring &amp;ring);
00101 <span class="comment"></span>
00102 <span class="comment">                //! set the coefficient for x^i to value</span>
00103 <span class="comment"></span>                <span class="keywordtype">void</span> <a class="code" href="class_polynomial_over.html#_polynomial_over_fixed_ringz61_1">SetCoefficient</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, <span class="keyword">const</span> CoefficientType &amp;value, <span class="keyword">const</span> Ring &amp;ring);
00104 <span class="comment"></span>
00105 <span class="comment">                //!</span>
00106 <span class="comment"></span>                <span class="keywordtype">void</span> Negate(<span class="keyword">const</span> Ring &amp;ring);
00107 <span class="comment"></span>
00108 <span class="comment">                //!</span>
00109 <span class="comment"></span>                <span class="keywordtype">void</span> swap(<a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> &amp;t);<span class="comment"></span>
00110 <span class="comment">        //@}</span>
00111 <span class="comment"></span>
00112 <span class="comment"></span>
00113 <span class="comment">        //! \name BASIC ARITHMETIC ON POLYNOMIALS</span>
00114 <span class="comment"></span><span class="comment">        //@{</span>
00115 <span class="comment"></span>                <span class="keywordtype">bool</span> Equals(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> &amp;t, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00116                 <span class="keywordtype">bool</span> IsZero(<span class="keyword">const</span> Ring &amp;ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> CoefficientCount(ring)==0;}
00117 
00118                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Plus(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00119                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Minus(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00120                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Inverse(<span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00121 
00122                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Times(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00123                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> DividedBy(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00124                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Modulo(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00125                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> MultiplicativeInverse(<span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00126                 <span class="keywordtype">bool</span> IsUnit(<span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00127 
00128                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; Accumulate(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring);
00129                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; Reduce(<span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; t, <span class="keyword">const</span> Ring &amp;ring);
00130 <span class="comment"></span>
00131 <span class="comment">                //!</span>
00132 <span class="comment"></span>                <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Doubled(<span class="keyword">const</span> Ring &amp;ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> Plus(*<span class="keyword">this</span>, ring);}<span class="comment"></span>
00133 <span class="comment">                //!</span>
00134 <span class="comment"></span>                <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> Squared(<span class="keyword">const</span> Ring &amp;ring)<span class="keyword"> const </span>{<span class="keywordflow">return</span> Times(*<span class="keyword">this</span>, ring);}
00135 
00136                 CoefficientType EvaluateAt(<span class="keyword">const</span> CoefficientType &amp;x, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;
00137 
00138                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; ShiftLeft(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> Ring &amp;ring);
00139                 <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a>&amp; ShiftRight(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> Ring &amp;ring);
00140 <span class="comment"></span>
00141 <span class="comment">                //! calculate r and q such that (a == d*q + r) &amp;&amp; (0 &lt;= degree of r &lt; degree of d)</span>
00142 <span class="comment"></span>                <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_over.html#_polynomial_over_fixed_ringz63_17">Divide</a>(<a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> &amp;r, <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> &amp;q, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;Ring&gt;</a> &amp;d, <span class="keyword">const</span> Ring &amp;ring);<span class="comment"></span>
00143 <span class="comment">        //@}</span>
00144 <span class="comment"></span><span class="comment"></span>
00145 <span class="comment">        //! \name INPUT/OUTPUT</span>
00146 <span class="comment"></span><span class="comment">        //@{</span>
00147 <span class="comment"></span>                std::istream&amp; Input(std::istream &amp;in, <span class="keyword">const</span> Ring &amp;ring);
00148                 std::ostream&amp; Output(std::ostream &amp;out, <span class="keyword">const</span> Ring &amp;ring) <span class="keyword">const</span>;<span class="comment"></span>
00149 <span class="comment">        //@}</span>
00150 <span class="comment"></span>
00151 <span class="keyword">private</span>:
00152         <span class="keywordtype">void</span> FromStr(<span class="keyword">const</span> <span class="keywordtype">char</span> *str, <span class="keyword">const</span> Ring &amp;ring);
00153 
00154         std::vector&lt;CoefficientType&gt; m_coefficients;
00155 };
00156 <span class="comment"></span>
00157 <span class="comment">//! Polynomials over a fixed ring</span>
00158 <span class="comment"></span><span class="comment">/*! Having a fixed ring allows overloaded operators */</span>
<a name="l00159"></a><a class="code" href="class_polynomial_over_fixed_ring.html">00159</a> <span class="keyword">template</span> &lt;<span class="keyword">class</span> T, <span class="keywordtype">int</span> instance&gt; <span class="keyword">class </span><a class="code" href="class_polynomial_over_fixed_ring.html">PolynomialOverFixedRing</a> : <span class="keyword">private</span> <a class="code" href="class_polynomial_over.html">PolynomialOver</a>&lt;T&gt;
00160 {
00161         <span class="keyword">typedef</span> <a class="code" href="class_polynomial_over.html">PolynomialOver&lt;T&gt;</a> <a class="code" href="class_polynomial_over.html">B</a>;
00162         <span class="keyword">typedef</span> <a class="code" href="class_polynomial_over_fixed_ring.html">PolynomialOverFixedRing&lt;T, instance&gt;</a> <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a>;
00163 
00164 <span class="keyword">public</span>:
00165         <span class="keyword">typedef</span> T Ring;
00166         <span class="keyword">typedef</span> <span class="keyword">typename</span> T::Element CoefficientType;
00167         <span class="keyword">typedef</span> B::DivideByZero DivideByZero;
00168         <span class="keyword">typedef</span> B::RandomizationParameter RandomizationParameter;
00169 <span class="comment"></span>
00170 <span class="comment">        //! \name CREATORS</span>
00171 <span class="comment"></span><span class="comment">        //@{</span>
00172 <span class="comment"></span><span class="comment">                //! creates the zero polynomial</span>
<a name="l00173"></a><a class="code" href="class_polynomial_over_fixed_ring.html#_polynomial_over_fixed_ringz67_0">00173</a> <span class="comment"></span>                <a class="code" href="class_polynomial_over_fixed_ring.html#_polynomial_over_fixed_ringz67_0">PolynomialOverFixedRing</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> count = 0) : <a class="code" href="class_polynomial_over.html">B</a>(fixedRing, count) {}
00174 <span class="comment"></span>
00175 <span class="comment">                //! copy constructor</span>
<a name="l00176"></a><a class="code" href="class_polynomial_over_fixed_ring.html#_polynomial_over_fixed_ringz67_1">00176</a> <span class="comment"></span>                <a class="code" href="class_polynomial_over_fixed_ring.html#_polynomial_over_fixed_ringz67_0">PolynomialOverFixedRing</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_over_fixed_ring.html">ThisType</a> &amp;t) : <a class="code" href="class_polynomial_over.html">B</a>(t) {}
00177 
00178                 <span class="keyword">explicit</span> <a class="code" href="class_polynomial_over_fixed_ring.html#_polynomial_over_fixed_ringz67_0">PolynomialOverFixedRing</a>(<span class="keyword">const</span> B &amp;t) : B(t) {}
00179 <span class="comment"></span>