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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="l00178"></a>00178 <span class="comment"></span><span class="comment">        //@{</span>
<a name="l00179"></a>00179 <span class="comment"></span><span class="comment">                //!</span>
<a name="l00180"></a>00180 <span class="comment"></span>                PolynomialMod2 And(<span class="keyword">const</span> PolynomialMod2 &amp;b) <span class="keyword">const</span>;<span class="comment"></span>
<a name="l00181"></a>00181 <span class="comment">                //!</span>
<a name="l00182"></a>00182 <span class="comment"></span>                PolynomialMod2 Xor(<span class="keyword">const</span> PolynomialMod2 &amp;b) <span class="keyword">const</span>;<span class="comment"></span>
<a name="l00183"></a>00183 <span class="comment">                //!</span>
<a name="l00184"></a><a class="code" href="class_polynomial_mod2.html#cd4130ad85985d2d1a4318b77563c030">00184</a> <span class="comment"></span>                PolynomialMod2 Plus(<span class="keyword">const</span> PolynomialMod2 &amp;b)<span class="keyword"> const </span>{<span class="keywordflow">return</span> Xor(b);}<span class="comment"></span>
<a name="l00185"></a>00185 <span class="comment">                //!</span>
<a name="l00186"></a><a class="code" href="class_polynomial_mod2.html#a10aa6c97fa37f201fcb477e0aabe209">00186</a> <span class="comment"></span>                PolynomialMod2 Minus(<span class="keyword">const</span> PolynomialMod2 &amp;b)<span class="keyword"> const </span>{<span class="keywordflow">return</span> Xor(b);}<span class="comment"></span>
<a name="l00187"></a>00187 <span class="comment">                //!</span>
<a name="l00188"></a>00188 <span class="comment"></span>                PolynomialMod2 Times(<span class="keyword">const</span> PolynomialMod2 &amp;b) <span class="keyword">const</span>;<span class="comment"></span>
<a name="l00189"></a>00189 <span class="comment">                //!</span>
<a name="l00190"></a>00190 <span class="comment"></span>                PolynomialMod2 DividedBy(<span class="keyword">const</span> PolynomialMod2 &amp;b) <span class="keyword">const</span>;<span class="comment"></span>
<a name="l00191"></a>00191 <span class="comment">                //!</span>
<a name="l00192"></a>00192 <span class="comment"></span>                PolynomialMod2 Modulo(<span class="keyword">const</span> PolynomialMod2 &amp;b) <span class="keyword">const</span>;
<a name="l00193"></a>00193 <span class="comment"></span>
<a name="l00194"></a>00194 <span class="comment">                //!</span>
<a name="l00195"></a>00195 <span class="comment"></span>                PolynomialMod2 operator&gt;&gt;(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) <span class="keyword">const</span>;<span class="comment"></span>
<a name="l00196"></a>00196 <span class="comment">                //!</span>
<a name="l00197"></a>00197 <span class="comment"></span>                PolynomialMod2 operator&lt;&lt;(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n) <span class="keyword">const</span>;<span class="comment"></span>
<a name="l00198"></a>00198 <span class="comment">        //@}</span>
<a name="l00199"></a>00199 <span class="comment"></span><span class="comment"></span>
<a name="l00200"></a>00200 <span class="comment">        //! \name OTHER ARITHMETIC FUNCTIONS</span>
<a name="l00201"></a>00201 <span class="comment"></span><span class="comment">        //@{</span>
<a name="l00202"></a>00202 <span class="comment"></span><span class="comment">                //! sum modulo 2 of all coefficients</span>
<a name="l00203"></a>00203 <span class="comment"></span>                <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Parity() <span class="keyword">const</span>;
<a name="l00204"></a>00204 <span class="comment"></span>
<a name="l00205"></a>00205 <span class="comment">                //! check for irreducibility</span>
<a name="l00206"></a>00206 <span class="comment"></span>                <span class="keywordtype">bool</span> IsIrreducible() <span class="keyword">const</span>;
<a name="l00207"></a>00207 <span class="comment"></span>
<a name="l00208"></a>00208 <span class="comment">                //! is always zero since we're working modulo 2</span>
<a name="l00209"></a><a class="code" href="class_polynomial_mod2.html#5f6006abf328c20f32a5858e96b91c8d">00209</a> <span class="comment"></span>                PolynomialMod2 Doubled()<span class="keyword"> const </span>{<span class="keywordflow">return</span> Zero();}<span class="comment"></span>
<a name="l00210"></a>00210 <span class="comment">                //!</span>
<a name="l00211"></a>00211 <span class="comment"></span>                PolynomialMod2 Squared() <span class="keyword">const</span>;
<a name="l00212"></a>00212 <span class="comment"></span>
<a name="l00213"></a>00213 <span class="comment">                //! only 1 is a unit</span>
<a name="l00214"></a><a class="code" href="class_polynomial_mod2.html#4cdb6f0136198255766326388ddd4d42">00214</a> <span class="comment"></span>                <span class="keywordtype">bool</span> IsUnit()<span class="keyword"> const </span>{<span class="keywordflow">return</span> Equals(One());}<span class="comment"></span>
<a name="l00215"></a>00215 <span class="comment">                //! return inverse if *this is a unit, otherwise return 0</span>
<a name="l00216"></a><a class="code" href="class_polynomial_mod2.html#1a79c76a8039c159d0e3cfba93ad8184">00216</a> <span class="comment"></span>                PolynomialMod2 MultiplicativeInverse()<span class="keyword"> const </span>{<span class="keywordflow">return</span> IsUnit() ? One() : Zero();}
<a name="l00217"></a>00217 <span class="comment"></span>
<a name="l00218"></a>00218 <span class="comment">                //! greatest common divisor</span>
<a name="l00219"></a>00219 <span class="comment"></span>                <span class="keyword">static</span> PolynomialMod2 CRYPTOPP_API Gcd(<span class="keyword">const</span> PolynomialMod2 &amp;a, <span class="keyword">const</span> PolynomialMod2 &amp;n);<span class="comment"></span>
<a name="l00220"></a>00220 <span class="comment">                //! calculate multiplicative inverse of *this mod n</span>
<a name="l00221"></a>00221 <span class="comment"></span>                PolynomialMod2 InverseMod(<span class="keyword">const</span> PolynomialMod2 &amp;) <span class="keyword">const</span>;
<a name="l00222"></a>00222 <span class="comment"></span>
<a name="l00223"></a>00223 <span class="comment">                //! calculate r and q such that (a == d*q + r) &amp;&amp; (deg(r) &lt; deg(d))</span>
<a name="l00224"></a>00224 <span class="comment"></span>                <span class="keyword">static</span> <span class="keywordtype">void</span> CRYPTOPP_API Divide(PolynomialMod2 &amp;r, PolynomialMod2 &amp;q, <span class="keyword">const</span> PolynomialMod2 &amp;a, <span class="keyword">const</span> PolynomialMod2 &amp;d);<span class="comment"></span>
<a name="l00225"></a>00225 <span class="comment">        //@}</span>
<a name="l00226"></a>00226 <span class="comment"></span><span class="comment"></span>
<a name="l00227"></a>00227 <span class="comment">        //! \name INPUT/OUTPUT</span>
<a name="l00228"></a>00228 <span class="comment"></span><span class="comment">        //@{</span>
<a name="l00229"></a>00229 <span class="comment"></span><span class="comment">                //!</span>
<a name="l00230"></a>00230 <span class="comment"></span>                <span class="keyword">friend</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; out, <span class="keyword">const</span> PolynomialMod2 &amp;a);<span class="comment"></span>
<a name="l00231"></a>00231 <span class="comment">        //@}</span>
<a name="l00232"></a>00232 <span class="comment"></span>
<a name="l00233"></a>00233 <span class="keyword">private</span>:
<a name="l00234"></a><a class="code" href="class_polynomial_mod2.html#2e0505b1597d5b697c52bfc7420f4f73">00234</a>         <span class="keyword">friend</span> <span class="keyword">class </span><a class="code" href="class_g_f2_n_t.html" title="GF(2^n) with Trinomial Basis.">GF2NT</a>;
<a name="l00235"></a>00235 
<a name="l00236"></a>00236         <a class="code" href="class_sec_block.html" title="a block of memory allocated using A">SecWordBlock</a> reg;
<a name="l00237"></a>00237 };
<a name="l00238"></a>00238 <span class="comment"></span>
<a name="l00239"></a>00239 <span class="comment">//!</span>
<a name="l00240"></a><a class="code" href="gf2n_8h.html#22c25c181c409600aa2e4bf1067ac47a">00240</a> <span class="comment"></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#22c25c181c409600aa2e4bf1067ac47a">operator==</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b)
<a name="l00241"></a>00241 {<span class="keywordflow">return</span> a.Equals(b);}<span class="comment"></span>
<a name="l00242"></a>00242 <span class="comment">//!</span>
<a name="l00243"></a><a class="code" href="gf2n_8h.html#98d9036c415975aa2f0fc09fab285459">00243</a> <span class="comment"></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#98d9036c415975aa2f0fc09fab285459">operator!=</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b)
<a name="l00244"></a>00244 {<span class="keywordflow">return</span> !(a==b);}<span class="comment"></span>
<a name="l00245"></a>00245 <span class="comment">//! compares degree</span>
<a name="l00246"></a><a class="code" href="gf2n_8h.html#6afcb350d6723d75727472e6599c97c9">00246</a> <span class="comment"></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#6afcb350d6723d75727472e6599c97c9" title="compares degree">operator&gt; </a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b)
<a name="l00247"></a>00247 {<span class="keywordflow">return</span> a.Degree() &gt; b.Degree();}<span class="comment"></span>
<a name="l00248"></a>00248 <span class="comment">//! compares degree</span>
<a name="l00249"></a><a class="code" href="gf2n_8h.html#1798ff5aa4df5af5c3ac8c918d4c26fb">00249</a> <span class="comment"></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#1798ff5aa4df5af5c3ac8c918d4c26fb" title="compares degree">operator&gt;=</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b)
<a name="l00250"></a>00250 {<span class="keywordflow">return</span> a.Degree() &gt;= b.Degree();}<span class="comment"></span>
<a name="l00251"></a>00251 <span class="comment">//! compares degree</span>
<a name="l00252"></a><a class="code" href="gf2n_8h.html#f81f67e93bfb8bbb776cab689c83c7e9">00252</a> <span class="comment"></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#f81f67e93bfb8bbb776cab689c83c7e9" title="compares degree">operator&lt; </a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b)
<a name="l00253"></a>00253 {<span class="keywordflow">return</span> a.Degree() &lt; b.Degree();}<span class="comment"></span>
<a name="l00254"></a>00254 <span class="comment">//! compares degree</span>
<a name="l00255"></a><a class="code" href="gf2n_8h.html#0591ec795b46a111e7e3aebde19ae39a">00255</a> <span class="comment"></span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="gf2n_8h.html#0591ec795b46a111e7e3aebde19ae39a" title="compares degree">operator&lt;=</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b)
<a name="l00256"></a>00256 {<span class="keywordflow">return</span> a.Degree() &lt;= b.Degree();}<span class="comment"></span>
<a name="l00257"></a>00257 <span class="comment">//!</span>
<a name="l00258"></a><a class="code" href="gf2n_8h.html#ea147cb3653a657814e75f948361421d">00258</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#ea147cb3653a657814e75f948361421d">operator&amp;</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.And(b);}<span class="comment"></span>
<a name="l00259"></a>00259 <span class="comment">//!</span>
<a name="l00260"></a><a class="code" href="gf2n_8h.html#c33a27275adc171df7bab70eea3cc60b">00260</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#c33a27275adc171df7bab70eea3cc60b">operator^</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.Xor(b);}<span class="comment"></span>
<a name="l00261"></a>00261 <span class="comment">//!</span>
<a name="l00262"></a><a class="code" href="gf2n_8h.html#f90f6d4d1dec04baadfc546843f8da4c">00262</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#f90f6d4d1dec04baadfc546843f8da4c">operator+</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.Plus(b);}<span class="comment"></span>
<a name="l00263"></a>00263 <span class="comment">//!</span>
<a name="l00264"></a><a class="code" href="gf2n_8h.html#af85a1c53439d93124cf51fdefb0a717">00264</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#af85a1c53439d93124cf51fdefb0a717">operator-</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.Minus(b);}<span class="comment"></span>
<a name="l00265"></a>00265 <span class="comment">//!</span>
<a name="l00266"></a><a class="code" href="gf2n_8h.html#44ec4ea79676be4a167d23284f48e563">00266</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#44ec4ea79676be4a167d23284f48e563">operator*</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.Times(b);}<span class="comment"></span>
<a name="l00267"></a>00267 <span class="comment">//!</span>
<a name="l00268"></a><a class="code" href="gf2n_8h.html#7d22ea1158ee28e35a5d693e3f140301">00268</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#7d22ea1158ee28e35a5d693e3f140301">operator/</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.DividedBy(b);}<span class="comment"></span>
<a name="l00269"></a>00269 <span class="comment">//!</span>
<a name="l00270"></a><a class="code" href="gf2n_8h.html#8ca19aaa6cbfdcaca6402c6dfde6727e">00270</a> <span class="comment"></span><span class="keyword">inline</span> CryptoPP::PolynomialMod2 <a class="code" href="gf2n_8h.html#8ca19aaa6cbfdcaca6402c6dfde6727e">operator%</a>(<span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;a, <span class="keyword">const</span> CryptoPP::PolynomialMod2 &amp;b) {<span class="keywordflow">return</span> a.Modulo(b);}
<a name="l00271"></a>00271 
<a name="l00272"></a>00272 <span class="comment">// CodeWarrior 8 workaround: put these template instantiations after overloaded operator declarations,</span>
<a name="l00273"></a>00273 <span class="comment">// but before the use of QuotientRing&lt;EuclideanDomainOf&lt;PolynomialMod2&gt; &gt; for VC .NET 2003</span>
<a name="l00274"></a>00274 CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup&lt;PolynomialMod2&gt;</a>;
<a name="l00275"></a>00275 CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing&lt;PolynomialMod2&gt;</a>;
<a name="l00276"></a>00276 CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_euclidean_domain.html" title="Abstract Euclidean Domain.">AbstractEuclideanDomain&lt;PolynomialMod2&gt;</a>;