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<div class="title">gf2n.cpp</div> </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">// gf2n.cpp - written and placed in the public domain by Wei Dai</span>
<a name="l00002"></a>00002
<a name="l00003"></a>00003 <span class="preprocessor">#include "pch.h"</span>
<a name="l00004"></a>00004
<a name="l00005"></a>00005 <span class="preprocessor">#ifndef CRYPTOPP_IMPORTS</span>
<a name="l00006"></a>00006 <span class="preprocessor"></span>
<a name="l00007"></a>00007 <span class="preprocessor">#include "<a class="code" href="gf2n_8h.html">gf2n.h</a>"</span>
<a name="l00008"></a>00008 <span class="preprocessor">#include "algebra.h"</span>
<a name="l00009"></a>00009 <span class="preprocessor">#include "words.h"</span>
<a name="l00010"></a>00010 <span class="preprocessor">#include "randpool.h"</span>
<a name="l00011"></a>00011 <span class="preprocessor">#include "asn.h"</span>
<a name="l00012"></a>00012 <span class="preprocessor">#include "oids.h"</span>
<a name="l00013"></a>00013
<a name="l00014"></a>00014 <span class="preprocessor">#include <iostream></span>
<a name="l00015"></a>00015
<a name="l00016"></a>00016 NAMESPACE_BEGIN(CryptoPP)
<a name="l00017"></a>00017
<a name="l00018"></a><a class="code" href="class_polynomial_mod2.html#ac67d4fb61b199c101f5de08d3aa2e782">00018</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>::<a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>()
<a name="l00019"></a>00019 {
<a name="l00020"></a>00020 }
<a name="l00021"></a>00021
<a name="l00022"></a><a class="code" href="class_polynomial_mod2.html#a51790dcfe87a449169e8cb5c0f20da7e">00022</a> <a class="code" href="class_polynomial_mod2.html#ac67d4fb61b199c101f5de08d3aa2e782" title="creates the zero polynomial">PolynomialMod2::PolynomialMod2</a>(word value, <span class="keywordtype">size_t</span> bitLength)
<a name="l00023"></a>00023 : reg(BitsToWords(bitLength))
<a name="l00024"></a>00024 {
<a name="l00025"></a>00025 assert(value==0 || reg.size()>0);
<a name="l00026"></a>00026
<a name="l00027"></a>00027 <span class="keywordflow">if</span> (reg.size() > 0)
<a name="l00028"></a>00028 {
<a name="l00029"></a>00029 reg[0] = value;
<a name="l00030"></a>00030 SetWords(reg+1, 0, reg.size()-1);
<a name="l00031"></a>00031 }
<a name="l00032"></a>00032 }
<a name="l00033"></a>00033
<a name="l00034"></a><a class="code" href="class_polynomial_mod2.html#a6866391c010ebef60c452df7961e809c">00034</a> <a class="code" href="class_polynomial_mod2.html#ac67d4fb61b199c101f5de08d3aa2e782" title="creates the zero polynomial">PolynomialMod2::PolynomialMod2</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& t)
<a name="l00035"></a>00035 : reg(t.reg.size())
<a name="l00036"></a>00036 {
<a name="l00037"></a>00037 CopyWords(reg, t.reg, reg.size());
<a name="l00038"></a>00038 }
<a name="l00039"></a>00039
<a name="l00040"></a>00040 <span class="keywordtype">void</span> PolynomialMod2::Randomize(<a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &rng, <span class="keywordtype">size_t</span> nbits)
<a name="l00041"></a>00041 {
<a name="l00042"></a>00042 <span class="keyword">const</span> <span class="keywordtype">size_t</span> nbytes = nbits/8 + 1;
<a name="l00043"></a>00043 <a class="code" href="class_sec_block.html" title="a block of memory allocated using A">SecByteBlock</a> buf(nbytes);
<a name="l00044"></a>00044 rng.<a class="code" href="class_random_number_generator.html#a497145546d24e6d4abaf10b7e0f1ba17" title="generate random array of bytes">GenerateBlock</a>(buf, nbytes);
<a name="l00045"></a>00045 buf[0] = (byte)Crop(buf[0], nbits % 8);
<a name="l00046"></a>00046 Decode(buf, nbytes);
<a name="l00047"></a>00047 }
<a name="l00048"></a>00048
<a name="l00049"></a><a class="code" href="class_polynomial_mod2.html#abf3ecc0dafe04c57dacea983a9a6690e">00049</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> <a class="code" href="class_polynomial_mod2.html#abf3ecc0dafe04c57dacea983a9a6690e" title="return x^(n-1) + ... + x + 1">PolynomialMod2::AllOnes</a>(<span class="keywordtype">size_t</span> bitLength)
<a name="l00050"></a>00050 {
<a name="l00051"></a>00051 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result((word)0, bitLength);
<a name="l00052"></a>00052 SetWords(result.reg, ~(word)0, result.reg.size());
<a name="l00053"></a>00053 <span class="keywordflow">if</span> (bitLength%WORD_BITS)
<a name="l00054"></a>00054 result.reg[result.reg.size()-1] = (word)Crop(result.reg[result.reg.size()-1], bitLength%WORD_BITS);
<a name="l00055"></a>00055 <span class="keywordflow">return</span> result;
<a name="l00056"></a>00056 }
<a name="l00057"></a>00057
<a name="l00058"></a>00058 <span class="keywordtype">void</span> PolynomialMod2::SetBit(<span class="keywordtype">size_t</span> n, <span class="keywordtype">int</span> value)
<a name="l00059"></a>00059 {
<a name="l00060"></a>00060 <span class="keywordflow">if</span> (value)
<a name="l00061"></a>00061 {
<a name="l00062"></a>00062 reg.<a class="code" href="class_sec_block.html#a4ef9516e973051e6afa38bba526da3e9" title="change size only if newSize > current size. contents are preserved and additional area is set to 0...">CleanGrow</a>(n/WORD_BITS + 1);
<a name="l00063"></a>00063 reg[n/WORD_BITS] |= (word(1) << (n%WORD_BITS));
<a name="l00064"></a>00064 }
<a name="l00065"></a>00065 <span class="keywordflow">else</span>
<a name="l00066"></a>00066 {
<a name="l00067"></a>00067 <span class="keywordflow">if</span> (n/WORD_BITS < reg.size())
<a name="l00068"></a>00068 reg[n/WORD_BITS] &= ~(word(1) << (n%WORD_BITS));
<a name="l00069"></a>00069 }
<a name="l00070"></a>00070 }
<a name="l00071"></a>00071
<a name="l00072"></a><a class="code" href="class_polynomial_mod2.html#ab98b4e2262584878ef7b12bc35301ee7">00072</a> byte <a class="code" href="class_polynomial_mod2.html#ab98b4e2262584878ef7b12bc35301ee7" title="return the n-th byte">PolynomialMod2::GetByte</a>(<span class="keywordtype">size_t</span> n)<span class="keyword"> const</span>
<a name="l00073"></a>00073 <span class="keyword"></span>{
<a name="l00074"></a>00074 <span class="keywordflow">if</span> (n/WORD_SIZE >= reg.size())
<a name="l00075"></a>00075 <span class="keywordflow">return</span> 0;
<a name="l00076"></a>00076 <span class="keywordflow">else</span>
<a name="l00077"></a>00077 <span class="keywordflow">return</span> byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
<a name="l00078"></a>00078 }
<a name="l00079"></a>00079
<a name="l00080"></a><a class="code" href="class_polynomial_mod2.html#af15c7ead361d1f7ea23d5e4bd5535989">00080</a> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_mod2.html#af15c7ead361d1f7ea23d5e4bd5535989" title="set the n-th byte to value">PolynomialMod2::SetByte</a>(<span class="keywordtype">size_t</span> n, byte value)
<a name="l00081"></a>00081 {
<a name="l00082"></a>00082 reg.<a class="code" href="class_sec_block.html#a4ef9516e973051e6afa38bba526da3e9" title="change size only if newSize > current size. contents are preserved and additional area is set to 0...">CleanGrow</a>(BytesToWords(n+1));
<a name="l00083"></a>00083 reg[n/WORD_SIZE] &= ~(word(0xff) << 8*(n%WORD_SIZE));
<a name="l00084"></a>00084 reg[n/WORD_SIZE] |= (word(value) << 8*(n%WORD_SIZE));
<a name="l00085"></a>00085 }
<a name="l00086"></a>00086
<a name="l00087"></a><a class="code" href="class_polynomial_mod2.html#a87949fb32436e1f2f96d7b813405c032">00087</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> <a class="code" href="class_polynomial_mod2.html#a87949fb32436e1f2f96d7b813405c032" title="return x^i">PolynomialMod2::Monomial</a>(<span class="keywordtype">size_t</span> i)
<a name="l00088"></a>00088 {
<a name="l00089"></a>00089 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> r((word)0, i+1);
<a name="l00090"></a>00090 r.SetBit(i);
<a name="l00091"></a>00091 <span class="keywordflow">return</span> r;
<a name="l00092"></a>00092 }
<a name="l00093"></a>00093
<a name="l00094"></a><a class="code" href="class_polynomial_mod2.html#a6d843c32a41885cb33d0aec19e40dda6">00094</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> <a class="code" href="class_polynomial_mod2.html#a6d843c32a41885cb33d0aec19e40dda6" title="return x^t0 + x^t1 + x^t2">PolynomialMod2::Trinomial</a>(<span class="keywordtype">size_t</span> t0, <span class="keywordtype">size_t</span> t1, <span class="keywordtype">size_t</span> t2)
<a name="l00095"></a>00095 {
<a name="l00096"></a>00096 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> r((word)0, t0+1);
<a name="l00097"></a>00097 r.SetBit(t0);
<a name="l00098"></a>00098 r.SetBit(t1);
<a name="l00099"></a>00099 r.SetBit(t2);
<a name="l00100"></a>00100 <span class="keywordflow">return</span> r;
<a name="l00101"></a>00101 }
<a name="l00102"></a>00102
<a name="l00103"></a><a class="code" href="class_polynomial_mod2.html#a507094d47020af3d23a9fd68cc4b527d">00103</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> <a class="code" href="class_polynomial_mod2.html#a507094d47020af3d23a9fd68cc4b527d" title="return x^t0 + x^t1 + x^t2 + x^t3 + x^t4">PolynomialMod2::Pentanomial</a>(<span class="keywordtype">size_t</span> t0, <span class="keywordtype">size_t</span> t1, <span class="keywordtype">size_t</span> t2, <span class="keywordtype">size_t</span> t3, <span class="keywordtype">size_t</span> t4)
<a name="l00104"></a>00104 {
<a name="l00105"></a>00105 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> r((word)0, t0+1);
<a name="l00106"></a>00106 r.SetBit(t0);
<a name="l00107"></a>00107 r.SetBit(t1);
<a name="l00108"></a>00108 r.SetBit(t2);
<a name="l00109"></a>00109 r.SetBit(t3);
<a name="l00110"></a>00110 r.SetBit(t4);
<a name="l00111"></a>00111 <span class="keywordflow">return</span> r;
<a name="l00112"></a>00112 }
<a name="l00113"></a>00113
<a name="l00114"></a>00114 <span class="keyword">template</span> <word i>
<a name="l00115"></a><a class="code" href="struct_new_polynomial_mod2.html">00115</a> <span class="keyword">struct </span><a class="code" href="struct_new_polynomial_mod2.html">NewPolynomialMod2</a>
<a name="l00116"></a>00116 {
<a name="l00117"></a>00117 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> * operator()()<span class="keyword"> const</span>
<a name="l00118"></a>00118 <span class="keyword"> </span>{
<a name="l00119"></a>00119 <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>(i);
<a name="l00120"></a>00120 }
<a name="l00121"></a>00121 };
<a name="l00122"></a>00122
<a name="l00123"></a>00123 <span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &PolynomialMod2::Zero()
<a name="l00124"></a>00124 {
<a name="l00125"></a>00125 <span class="keywordflow">return</span> <a class="code" href="class_singleton.html">Singleton<PolynomialMod2></a>().Ref();
<a name="l00126"></a>00126 }
<a name="l00127"></a>00127
<a name="l00128"></a>00128 <span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &PolynomialMod2::One()
<a name="l00129"></a>00129 {
<a name="l00130"></a>00130 <span class="keywordflow">return</span> <a class="code" href="class_singleton.html">Singleton<PolynomialMod2, NewPolynomialMod2<1></a> >().Ref();
<a name="l00131"></a>00131 }
<a name="l00132"></a>00132
<a name="l00133"></a>00133 <span class="keywordtype">void</span> PolynomialMod2::Decode(<span class="keyword">const</span> byte *input, <span class="keywordtype">size_t</span> inputLen)
<a name="l00134"></a>00134 {
<a name="l00135"></a>00135 <a class="code" href="class_string_store.html" title="string-based implementation of Store interface">StringStore</a> store(input, inputLen);
<a name="l00136"></a>00136 Decode(store, inputLen);
<a name="l00137"></a>00137 }
<a name="l00138"></a>00138
<a name="l00139"></a><a class="code" href="class_polynomial_mod2.html#a5e50bea6c06c2acb63e257c0ab568e72">00139</a> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_mod2.html#a5e50bea6c06c2acb63e257c0ab568e72" title="encode in big-endian format">PolynomialMod2::Encode</a>(byte *output, <span class="keywordtype">size_t</span> outputLen)<span class="keyword"> const</span>
<a name="l00140"></a>00140 <span class="keyword"></span>{
<a name="l00141"></a>00141 <a class="code" href="class_array_sink.html" title="Copy input to a memory buffer.">ArraySink</a> sink(output, outputLen);
<a name="l00142"></a>00142 <a class="code" href="class_polynomial_mod2.html#a5e50bea6c06c2acb63e257c0ab568e72" title="encode in big-endian format">Encode</a>(sink, outputLen);
<a name="l00143"></a>00143 }
<a name="l00144"></a>00144
<a name="l00145"></a>00145 <span class="keywordtype">void</span> PolynomialMod2::Decode(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt, <span class="keywordtype">size_t</span> inputLen)
<a name="l00146"></a>00146 {
<a name="l00147"></a>00147 reg.<a class="code" href="class_sec_block.html#a2d78e75002fd02e5b89bd72a9e65e769" title="change size and set contents to 0">CleanNew</a>(BytesToWords(inputLen));
<a name="l00148"></a>00148
<a name="l00149"></a>00149 <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i=inputLen; i > 0; i--)
<a name="l00150"></a>00150 {
<a name="l00151"></a>00151 byte b;
<a name="l00152"></a>00152 bt.<a class="code" href="class_buffered_transformation.html#a9e1ad913c8fe697d269f408a7d5928fc" title="try to retrieve a single byte">Get</a>(b);
<a name="l00153"></a>00153 reg[(i-1)/WORD_SIZE] |= word(b) << ((i-1)%WORD_SIZE)*8;
<a name="l00154"></a>00154 }
<a name="l00155"></a>00155 }
<a name="l00156"></a>00156
<a name="l00157"></a>00157 <span class="keywordtype">void</span> <a class="code" href="class_polynomial_mod2.html#a5e50bea6c06c2acb63e257c0ab568e72" title="encode in big-endian format">PolynomialMod2::Encode</a>(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt, <span class="keywordtype">size_t</span> outputLen)<span class="keyword"> const</span>
<a name="l00158"></a>00158 <span class="keyword"></span>{
<a name="l00159"></a>00159 <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i=outputLen; i > 0; i--)
<a name="l00160"></a>00160 bt.<a class="code" href="class_buffered_transformation.html#ae70658b0d271f8e114ac6c3cc9774ede" title="input a byte for processing">Put</a>(<a class="code" href="class_polynomial_mod2.html#ab98b4e2262584878ef7b12bc35301ee7" title="return the n-th byte">GetByte</a>(i-1));
<a name="l00161"></a>00161 }
<a name="l00162"></a>00162
<a name="l00163"></a><a class="code" href="class_polynomial_mod2.html#a700d15948c49f52c01d0ad1bd25c1a3d">00163</a> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_mod2.html#a700d15948c49f52c01d0ad1bd25c1a3d" title="encode value as big-endian octet string">PolynomialMod2::DEREncodeAsOctetString</a>(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt, <span class="keywordtype">size_t</span> length)<span class="keyword"> const</span>
<a name="l00164"></a>00164 <span class="keyword"></span>{
<a name="l00165"></a>00165 <a class="code" href="class_d_e_r_general_encoder.html" title="DER General Encoder.">DERGeneralEncoder</a> enc(bt, OCTET_STRING);
<a name="l00166"></a>00166 <a class="code" href="class_polynomial_mod2.html#a5e50bea6c06c2acb63e257c0ab568e72" title="encode in big-endian format">Encode</a>(enc, length);
<a name="l00167"></a>00167 enc.MessageEnd();
<a name="l00168"></a>00168 }
<a name="l00169"></a>00169
<a name="l00170"></a><a class="code" href="class_polynomial_mod2.html#a69c7853e0d24f1056be18112ee4f5a8e">00170</a> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_mod2.html#a69c7853e0d24f1056be18112ee4f5a8e" title="decode value as big-endian octet string">PolynomialMod2::BERDecodeAsOctetString</a>(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt, <span class="keywordtype">size_t</span> length)
<a name="l00171"></a>00171 {
<a name="l00172"></a>00172 <a class="code" href="class_b_e_r_general_decoder.html" title="BER General Decoder.">BERGeneralDecoder</a> dec(bt, OCTET_STRING);
<a name="l00173"></a>00173 <span class="keywordflow">if</span> (!dec.IsDefiniteLength() || dec.RemainingLength() != length)
<a name="l00174"></a>00174 BERDecodeError();
<a name="l00175"></a>00175 Decode(dec, length);
<a name="l00176"></a>00176 dec.MessageEnd();
<a name="l00177"></a>00177 }
<a name="l00178"></a>00178
<a name="l00179"></a><a class="code" href="class_polynomial_mod2.html#a11d3c636bf8dc72aacee1803b395e751">00179</a> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_mod2.html#a11d3c636bf8dc72aacee1803b395e751" title="number of significant words = ceiling(ByteCount()/sizeof(word))">PolynomialMod2::WordCount</a>()<span class="keyword"> const</span>
<a name="l00180"></a>00180 <span class="keyword"></span>{
<a name="l00181"></a>00181 <span class="keywordflow">return</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>)CountWords(reg, reg.size());
<a name="l00182"></a>00182 }
<a name="l00183"></a>00183
<a name="l00184"></a><a class="code" href="class_polynomial_mod2.html#a928dd8ce9f76230479eb3bb6edc750e8">00184</a> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_mod2.html#a928dd8ce9f76230479eb3bb6edc750e8" title="number of significant bytes = ceiling(BitCount()/8)">PolynomialMod2::ByteCount</a>()<span class="keyword"> const</span>
<a name="l00185"></a>00185 <span class="keyword"></span>{
<a name="l00186"></a>00186 <span class="keywordtype">unsigned</span> wordCount = <a class="code" href="class_polynomial_mod2.html#a11d3c636bf8dc72aacee1803b395e751" title="number of significant words = ceiling(ByteCount()/sizeof(word))">WordCount</a>();
<a name="l00187"></a>00187 <span class="keywordflow">if</span> (wordCount)
<a name="l00188"></a>00188 <span class="keywordflow">return</span> (wordCount-1)*WORD_SIZE + BytePrecision(reg[wordCount-1]);
<a name="l00189"></a>00189 <span class="keywordflow">else</span>
<a name="l00190"></a>00190 <span class="keywordflow">return</span> 0;
<a name="l00191"></a>00191 }
<a name="l00192"></a>00192
<a name="l00193"></a><a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207">00193</a> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">PolynomialMod2::BitCount</a>()<span class="keyword"> const</span>
<a name="l00194"></a>00194 <span class="keyword"></span>{
<a name="l00195"></a>00195 <span class="keywordtype">unsigned</span> wordCount = <a class="code" href="class_polynomial_mod2.html#a11d3c636bf8dc72aacee1803b395e751" title="number of significant words = ceiling(ByteCount()/sizeof(word))">WordCount</a>();
<a name="l00196"></a>00196 <span class="keywordflow">if</span> (wordCount)
<a name="l00197"></a>00197 <span class="keywordflow">return</span> (wordCount-1)*WORD_BITS + BitPrecision(reg[wordCount-1]);
<a name="l00198"></a>00198 <span class="keywordflow">else</span>
<a name="l00199"></a>00199 <span class="keywordflow">return</span> 0;
<a name="l00200"></a>00200 }
<a name="l00201"></a>00201
<a name="l00202"></a><a class="code" href="class_polynomial_mod2.html#ac126ac265f57eaa7d0557eb21b50e5e5">00202</a> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_polynomial_mod2.html#ac126ac265f57eaa7d0557eb21b50e5e5" title="sum modulo 2 of all coefficients">PolynomialMod2::Parity</a>()<span class="keyword"> const</span>
<a name="l00203"></a>00203 <span class="keyword"></span>{
<a name="l00204"></a>00204 <span class="keywordtype">unsigned</span> i;
<a name="l00205"></a>00205 word temp=0;
<a name="l00206"></a>00206 <span class="keywordflow">for</span> (i=0; i<reg.size(); i++)
<a name="l00207"></a>00207 temp ^= reg[i];
<a name="l00208"></a>00208 <span class="keywordflow">return</span> <a class="code" href="class_polynomial_mod2.html#ac126ac265f57eaa7d0557eb21b50e5e5" title="sum modulo 2 of all coefficients">CryptoPP::Parity</a>(temp);
<a name="l00209"></a>00209 }
<a name="l00210"></a>00210
<a name="l00211"></a>00211 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& PolynomialMod2::operator=(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& t)
<a name="l00212"></a>00212 {
<a name="l00213"></a>00213 reg.<a class="code" href="class_sec_block.html#a2cf5dc5e31c63eb927f935af6104f36a" title="set contents and size">Assign</a>(t.reg);
<a name="l00214"></a>00214 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00215"></a>00215 }
<a name="l00216"></a>00216
<a name="l00217"></a>00217 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& PolynomialMod2::operator^=(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& t)
<a name="l00218"></a>00218 {
<a name="l00219"></a>00219 reg.<a class="code" href="class_sec_block.html#a4ef9516e973051e6afa38bba526da3e9" title="change size only if newSize > current size. contents are preserved and additional area is set to 0...">CleanGrow</a>(t.reg.size());
<a name="l00220"></a>00220 XorWords(reg, t.reg, t.reg.size());
<a name="l00221"></a>00221 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00222"></a>00222 }
<a name="l00223"></a>00223
<a name="l00224"></a>00224 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::Xor(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &b)<span class="keyword"> const</span>
<a name="l00225"></a>00225 <span class="keyword"></span>{
<a name="l00226"></a>00226 <span class="keywordflow">if</span> (b.reg.size() >= reg.size())
<a name="l00227"></a>00227 {
<a name="l00228"></a>00228 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result((word)0, b.reg.size()*WORD_BITS);
<a name="l00229"></a>00229 XorWords(result.reg, reg, b.reg, reg.size());
<a name="l00230"></a>00230 CopyWords(result.reg+reg.size(), b.reg+reg.size(), b.reg.size()-reg.size());
<a name="l00231"></a>00231 <span class="keywordflow">return</span> result;
<a name="l00232"></a>00232 }
<a name="l00233"></a>00233 <span class="keywordflow">else</span>
<a name="l00234"></a>00234 {
<a name="l00235"></a>00235 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result((word)0, reg.size()*WORD_BITS);
<a name="l00236"></a>00236 XorWords(result.reg, reg, b.reg, b.reg.size());
<a name="l00237"></a>00237 CopyWords(result.reg+b.reg.size(), reg+b.reg.size(), reg.size()-b.reg.size());
<a name="l00238"></a>00238 <span class="keywordflow">return</span> result;
<a name="l00239"></a>00239 }
<a name="l00240"></a>00240 }
<a name="l00241"></a>00241
<a name="l00242"></a>00242 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::And(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &b)<span class="keyword"> const</span>
<a name="l00243"></a>00243 <span class="keyword"></span>{
<a name="l00244"></a>00244 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result((word)0, WORD_BITS*STDMIN(reg.size(), b.reg.size()));
<a name="l00245"></a>00245 AndWords(result.reg, reg, b.reg, result.reg.size());
<a name="l00246"></a>00246 <span class="keywordflow">return</span> result;
<a name="l00247"></a>00247 }
<a name="l00248"></a>00248
<a name="l00249"></a>00249 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::Times(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &b)<span class="keyword"> const</span>
<a name="l00250"></a>00250 <span class="keyword"></span>{
<a name="l00251"></a>00251 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result((word)0, <a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>() + b.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>());
<a name="l00252"></a>00252
<a name="l00253"></a>00253 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=b.<a class="code" href="class_polynomial_mod2.html#ae274b547e478a6cc0065089b7b915e47" title="the zero polynomial will return a degree of -1">Degree</a>(); i>=0; i--)
<a name="l00254"></a>00254 {
<a name="l00255"></a>00255 result <<= 1;
<a name="l00256"></a>00256 <span class="keywordflow">if</span> (b[i])
<a name="l00257"></a>00257 XorWords(result.reg, reg, reg.size());
<a name="l00258"></a>00258 }
<a name="l00259"></a>00259 <span class="keywordflow">return</span> result;
<a name="l00260"></a>00260 }
<a name="l00261"></a>00261
<a name="l00262"></a>00262 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::Squared()<span class="keyword"> const</span>
<a name="l00263"></a>00263 <span class="keyword"></span>{
<a name="l00264"></a>00264 <span class="keyword">static</span> <span class="keyword">const</span> word map[16] = {0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, 85};
<a name="l00265"></a>00265
<a name="l00266"></a>00266 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result((word)0, 2*reg.size()*WORD_BITS);
<a name="l00267"></a>00267
<a name="l00268"></a>00268 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i=0; i<reg.size(); i++)
<a name="l00269"></a>00269 {
<a name="l00270"></a>00270 <span class="keywordtype">unsigned</span> j;
<a name="l00271"></a>00271
<a name="l00272"></a>00272 <span class="keywordflow">for</span> (j=0; j<WORD_BITS; j+=8)
<a name="l00273"></a>00273 result.reg[2*i] |= map[(reg[i] >> (j/2)) % 16] << j;
<a name="l00274"></a>00274
<a name="l00275"></a>00275 <span class="keywordflow">for</span> (j=0; j<WORD_BITS; j+=8)
<a name="l00276"></a>00276 result.reg[2*i+1] |= map[(reg[i] >> (j/2 + WORD_BITS/2)) % 16] << j;
<a name="l00277"></a>00277 }
<a name="l00278"></a>00278
<a name="l00279"></a>00279 <span class="keywordflow">return</span> result;
<a name="l00280"></a>00280 }
<a name="l00281"></a>00281
<a name="l00282"></a><a class="code" href="class_polynomial_mod2.html#a73d92da2ee829619041eca82567b87bc">00282</a> <span class="keywordtype">void</span> <a class="code" href="class_polynomial_mod2.html#a73d92da2ee829619041eca82567b87bc" title="calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))">PolynomialMod2::Divide</a>(<a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &remainder, <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &quotient,
<a name="l00283"></a>00283 <span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &dividend, <span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &divisor)
<a name="l00284"></a>00284 {
<a name="l00285"></a>00285 <span class="keywordflow">if</span> (!divisor)
<a name="l00286"></a>00286 <span class="keywordflow">throw</span> <a class="code" href="class_polynomial_mod2_1_1_divide_by_zero.html" title="divide by zero exception">PolynomialMod2::DivideByZero</a>();
<a name="l00287"></a>00287
<a name="l00288"></a>00288 <span class="keywordtype">int</span> degree = divisor.<a class="code" href="class_polynomial_mod2.html#ae274b547e478a6cc0065089b7b915e47" title="the zero polynomial will return a degree of -1">Degree</a>();
<a name="l00289"></a>00289 remainder.reg.<a class="code" href="class_sec_block.html#a2d78e75002fd02e5b89bd72a9e65e769" title="change size and set contents to 0">CleanNew</a>(BitsToWords(degree+1));
<a name="l00290"></a>00290 <span class="keywordflow">if</span> (dividend.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>() >= divisor.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>())
<a name="l00291"></a>00291 quotient.reg.<a class="code" href="class_sec_block.html#a2d78e75002fd02e5b89bd72a9e65e769" title="change size and set contents to 0">CleanNew</a>(BitsToWords(dividend.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>() - divisor.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>() + 1));
<a name="l00292"></a>00292 <span class="keywordflow">else</span>
<a name="l00293"></a>00293 quotient.reg.<a class="code" href="class_sec_block.html#a2d78e75002fd02e5b89bd72a9e65e769" title="change size and set contents to 0">CleanNew</a>(0);
<a name="l00294"></a>00294
<a name="l00295"></a>00295 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=dividend.<a class="code" href="class_polynomial_mod2.html#ae274b547e478a6cc0065089b7b915e47" title="the zero polynomial will return a degree of -1">Degree</a>(); i>=0; i--)
<a name="l00296"></a>00296 {
<a name="l00297"></a>00297 remainder <<= 1;
<a name="l00298"></a>00298 remainder.reg[0] |= dividend[i];
<a name="l00299"></a>00299 <span class="keywordflow">if</span> (remainder[degree])
<a name="l00300"></a>00300 {
<a name="l00301"></a>00301 remainder -= divisor;
<a name="l00302"></a>00302 quotient.SetBit(i);
<a name="l00303"></a>00303 }
<a name="l00304"></a>00304 }
<a name="l00305"></a>00305 }
<a name="l00306"></a>00306
<a name="l00307"></a>00307 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::DividedBy(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &b)<span class="keyword"> const</span>
<a name="l00308"></a>00308 <span class="keyword"></span>{
<a name="l00309"></a>00309 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> remainder, quotient;
<a name="l00310"></a>00310 <a class="code" href="class_polynomial_mod2.html#a73d92da2ee829619041eca82567b87bc" title="calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))">PolynomialMod2::Divide</a>(remainder, quotient, *<span class="keyword">this</span>, b);
<a name="l00311"></a>00311 <span class="keywordflow">return</span> quotient;
<a name="l00312"></a>00312 }
<a name="l00313"></a>00313
<a name="l00314"></a>00314 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::Modulo(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &b)<span class="keyword"> const</span>
<a name="l00315"></a>00315 <span class="keyword"></span>{
<a name="l00316"></a>00316 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> remainder, quotient;
<a name="l00317"></a>00317 <a class="code" href="class_polynomial_mod2.html#a73d92da2ee829619041eca82567b87bc" title="calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))">PolynomialMod2::Divide</a>(remainder, quotient, *<span class="keyword">this</span>, b);
<a name="l00318"></a>00318 <span class="keywordflow">return</span> remainder;
<a name="l00319"></a>00319 }
<a name="l00320"></a>00320
<a name="l00321"></a>00321 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& PolynomialMod2::operator<<=(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n)
<a name="l00322"></a>00322 {
<a name="l00323"></a>00323 <span class="keywordflow">if</span> (!reg.size())
<a name="l00324"></a>00324 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00325"></a>00325
<a name="l00326"></a>00326 <span class="keywordtype">int</span> i;
<a name="l00327"></a>00327 word u;
<a name="l00328"></a>00328 word carry=0;
<a name="l00329"></a>00329 word *r=reg;
<a name="l00330"></a>00330
<a name="l00331"></a>00331 <span class="keywordflow">if</span> (n==1) <span class="comment">// special case code for most frequent case</span>
<a name="l00332"></a>00332 {
<a name="l00333"></a>00333 i = (int)reg.size();
<a name="l00334"></a>00334 <span class="keywordflow">while</span> (i--)
<a name="l00335"></a>00335 {
<a name="l00336"></a>00336 u = *r;
<a name="l00337"></a>00337 *r = (u << 1) | carry;
<a name="l00338"></a>00338 carry = u >> (WORD_BITS-1);
<a name="l00339"></a>00339 r++;
<a name="l00340"></a>00340 }
<a name="l00341"></a>00341
<a name="l00342"></a>00342 <span class="keywordflow">if</span> (carry)
<a name="l00343"></a>00343 {
<a name="l00344"></a>00344 reg.<a class="code" href="class_sec_block.html#a8dea287fba8236b0979b52beece0ec1b" title="change size only if newSize > current size. contents are preserved">Grow</a>(reg.size()+1);
<a name="l00345"></a>00345 reg[reg.size()-1] = carry;
<a name="l00346"></a>00346 }
<a name="l00347"></a>00347
<a name="l00348"></a>00348 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00349"></a>00349 }
<a name="l00350"></a>00350
<a name="l00351"></a>00351 <span class="keywordtype">int</span> shiftWords = n / WORD_BITS;
<a name="l00352"></a>00352 <span class="keywordtype">int</span> shiftBits = n % WORD_BITS;
<a name="l00353"></a>00353
<a name="l00354"></a>00354 <span class="keywordflow">if</span> (shiftBits)
<a name="l00355"></a>00355 {
<a name="l00356"></a>00356 i = (int)reg.size();
<a name="l00357"></a>00357 <span class="keywordflow">while</span> (i--)
<a name="l00358"></a>00358 {
<a name="l00359"></a>00359 u = *r;
<a name="l00360"></a>00360 *r = (u << shiftBits) | carry;
<a name="l00361"></a>00361 carry = u >> (WORD_BITS-shiftBits);
<a name="l00362"></a>00362 r++;
<a name="l00363"></a>00363 }
<a name="l00364"></a>00364 }
<a name="l00365"></a>00365
<a name="l00366"></a>00366 <span class="keywordflow">if</span> (carry)
<a name="l00367"></a>00367 {
<a name="l00368"></a>00368 reg.<a class="code" href="class_sec_block.html#a8dea287fba8236b0979b52beece0ec1b" title="change size only if newSize > current size. contents are preserved">Grow</a>(reg.size()+shiftWords+1);
<a name="l00369"></a>00369 reg[reg.size()-1] = carry;
<a name="l00370"></a>00370 }
<a name="l00371"></a>00371 <span class="keywordflow">else</span>
<a name="l00372"></a>00372 reg.<a class="code" href="class_sec_block.html#a8dea287fba8236b0979b52beece0ec1b" title="change size only if newSize > current size. contents are preserved">Grow</a>(reg.size()+shiftWords);
<a name="l00373"></a>00373
<a name="l00374"></a>00374 <span class="keywordflow">if</span> (shiftWords)
<a name="l00375"></a>00375 {
<a name="l00376"></a>00376 <span class="keywordflow">for</span> (i = (<span class="keywordtype">int</span>)reg.size()-1; i>=shiftWords; i--)
<a name="l00377"></a>00377 reg[i] = reg[i-shiftWords];
<a name="l00378"></a>00378 <span class="keywordflow">for</span> (; i>=0; i--)
<a name="l00379"></a>00379 reg[i] = 0;
<a name="l00380"></a>00380 }
<a name="l00381"></a>00381
<a name="l00382"></a>00382 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00383"></a>00383 }
<a name="l00384"></a>00384
<a name="l00385"></a>00385 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>& PolynomialMod2::operator>>=(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n)
<a name="l00386"></a>00386 {
<a name="l00387"></a>00387 <span class="keywordflow">if</span> (!reg.size())
<a name="l00388"></a>00388 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00389"></a>00389
<a name="l00390"></a>00390 <span class="keywordtype">int</span> shiftWords = n / WORD_BITS;
<a name="l00391"></a>00391 <span class="keywordtype">int</span> shiftBits = n % WORD_BITS;
<a name="l00392"></a>00392
<a name="l00393"></a>00393 <span class="keywordtype">size_t</span> i;
<a name="l00394"></a>00394 word u;
<a name="l00395"></a>00395 word carry=0;
<a name="l00396"></a>00396 word *r=reg+reg.size()-1;
<a name="l00397"></a>00397
<a name="l00398"></a>00398 <span class="keywordflow">if</span> (shiftBits)
<a name="l00399"></a>00399 {
<a name="l00400"></a>00400 i = reg.size();
<a name="l00401"></a>00401 <span class="keywordflow">while</span> (i--)
<a name="l00402"></a>00402 {
<a name="l00403"></a>00403 u = *r;
<a name="l00404"></a>00404 *r = (u >> shiftBits) | carry;
<a name="l00405"></a>00405 carry = u << (WORD_BITS-shiftBits);
<a name="l00406"></a>00406 r--;
<a name="l00407"></a>00407 }
<a name="l00408"></a>00408 }
<a name="l00409"></a>00409
<a name="l00410"></a>00410 <span class="keywordflow">if</span> (shiftWords)
<a name="l00411"></a>00411 {
<a name="l00412"></a>00412 <span class="keywordflow">for</span> (i=0; i<reg.size()-shiftWords; i++)
<a name="l00413"></a>00413 reg[i] = reg[i+shiftWords];
<a name="l00414"></a>00414 <span class="keywordflow">for</span> (; i<reg.size(); i++)
<a name="l00415"></a>00415 reg[i] = 0;
<a name="l00416"></a>00416 }
<a name="l00417"></a>00417
<a name="l00418"></a>00418 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00419"></a>00419 }
<a name="l00420"></a>00420
<a name="l00421"></a>00421 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::operator<<(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n)<span class="keyword"> const</span>
<a name="l00422"></a>00422 <span class="keyword"></span>{
<a name="l00423"></a>00423 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result(*<span class="keyword">this</span>);
<a name="l00424"></a>00424 <span class="keywordflow">return</span> result<<=n;
<a name="l00425"></a>00425 }
<a name="l00426"></a>00426
<a name="l00427"></a>00427 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> PolynomialMod2::operator>>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n)<span class="keyword"> const</span>
<a name="l00428"></a>00428 <span class="keyword"></span>{
<a name="l00429"></a>00429 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> result(*<span class="keyword">this</span>);
<a name="l00430"></a>00430 <span class="keywordflow">return</span> result>>=n;
<a name="l00431"></a>00431 }
<a name="l00432"></a>00432
<a name="l00433"></a>00433 <span class="keywordtype">bool</span> PolynomialMod2::operator!()<span class="keyword"> const</span>
<a name="l00434"></a>00434 <span class="keyword"></span>{
<a name="l00435"></a>00435 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i=0; i<reg.size(); i++)
<a name="l00436"></a>00436 <span class="keywordflow">if</span> (reg[i]) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00437"></a>00437 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00438"></a>00438 }
<a name="l00439"></a>00439
<a name="l00440"></a>00440 <span class="keywordtype">bool</span> PolynomialMod2::Equals(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &rhs)<span class="keyword"> const</span>
<a name="l00441"></a>00441 <span class="keyword"></span>{
<a name="l00442"></a>00442 <span class="keywordtype">size_t</span> i, smallerSize = STDMIN(reg.size(), rhs.reg.size());
<a name="l00443"></a>00443
<a name="l00444"></a>00444 <span class="keywordflow">for</span> (i=0; i<smallerSize; i++)
<a name="l00445"></a>00445 <span class="keywordflow">if</span> (reg[i] != rhs.reg[i]) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00446"></a>00446
<a name="l00447"></a>00447 <span class="keywordflow">for</span> (i=smallerSize; i<reg.size(); i++)
<a name="l00448"></a>00448 <span class="keywordflow">if</span> (reg[i] != 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00449"></a>00449
<a name="l00450"></a>00450 <span class="keywordflow">for</span> (i=smallerSize; i<rhs.reg.size(); i++)
<a name="l00451"></a>00451 <span class="keywordflow">if</span> (rhs.reg[i] != 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00452"></a>00452
<a name="l00453"></a>00453 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00454"></a>00454 }
<a name="l00455"></a>00455
<a name="l00456"></a>00456 std::ostream& operator<<(std::ostream& out, <span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &a)
<a name="l00457"></a>00457 {
<a name="l00458"></a>00458 <span class="comment">// Get relevant conversion specifications from ostream.</span>
<a name="l00459"></a>00459 <span class="keywordtype">long</span> f = out.flags() & std::ios::basefield; <span class="comment">// Get base digits.</span>
<a name="l00460"></a>00460 <span class="keywordtype">int</span> bits, block;
<a name="l00461"></a>00461 <span class="keywordtype">char</span> suffix;
<a name="l00462"></a>00462 <span class="keywordflow">switch</span>(f)
<a name="l00463"></a>00463 {
<a name="l00464"></a>00464 <span class="keywordflow">case</span> std::ios::oct :
<a name="l00465"></a>00465 bits = 3;
<a name="l00466"></a>00466 block = 4;
<a name="l00467"></a>00467 suffix = <span class="charliteral">'o'</span>;
<a name="l00468"></a>00468 <span class="keywordflow">break</span>;
<a name="l00469"></a>00469 <span class="keywordflow">case</span> std::ios::hex :
<a name="l00470"></a>00470 bits = 4;
<a name="l00471"></a>00471 block = 2;
<a name="l00472"></a>00472 suffix = <span class="charliteral">'h'</span>;
<a name="l00473"></a>00473 <span class="keywordflow">break</span>;
<a name="l00474"></a>00474 <span class="keywordflow">default</span> :
<a name="l00475"></a>00475 bits = 1;
<a name="l00476"></a>00476 block = 8;
<a name="l00477"></a>00477 suffix = <span class="charliteral">'b'</span>;
<a name="l00478"></a>00478 }
<a name="l00479"></a>00479
<a name="l00480"></a>00480 <span class="keywordflow">if</span> (!a)
<a name="l00481"></a>00481 <span class="keywordflow">return</span> out << <span class="charliteral">'0'</span> << suffix;
<a name="l00482"></a>00482
<a name="l00483"></a>00483 <a class="code" href="class_sec_block.html" title="a block of memory allocated using A">SecBlock<char></a> s(a.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>()/bits+1);
<a name="l00484"></a>00484 <span class="keywordtype">unsigned</span> i;
<a name="l00485"></a>00485
<a name="l00486"></a>00486 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">char</span> upper[]=<span class="stringliteral">"0123456789ABCDEF"</span>;
<a name="l00487"></a>00487 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">char</span> lower[]=<span class="stringliteral">"0123456789abcdef"</span>;
<a name="l00488"></a>00488 <span class="keyword">const</span> <span class="keywordtype">char</span>* vec = (out.flags() & std::ios::uppercase) ? upper : lower;
<a name="l00489"></a>00489
<a name="l00490"></a>00490 <span class="keywordflow">for</span> (i=0; i*bits < a.<a class="code" href="class_polynomial_mod2.html#a4c78f049759b0aacf8dcb687ed17a207" title="number of significant bits = Degree() + 1">BitCount</a>(); i++)
<a name="l00491"></a>00491 {
<a name="l00492"></a>00492 <span class="keywordtype">int</span> digit=0;
<a name="l00493"></a>00493 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=0; j<bits; j++)
<a name="l00494"></a>00494 digit |= a[i*bits+j] << j;
<a name="l00495"></a>00495 s[i]=vec[digit];
<a name="l00496"></a>00496 }
<a name="l00497"></a>00497
<a name="l00498"></a>00498 <span class="keywordflow">while</span> (i--)
<a name="l00499"></a>00499 {
<a name="l00500"></a>00500 out << s[i];
<a name="l00501"></a>00501 <span class="keywordflow">if</span> (i && (i%block)==0)
<a name="l00502"></a>00502 out << <span class="charliteral">','</span>;
<a name="l00503"></a>00503 }
<a name="l00504"></a>00504
<a name="l00505"></a>00505 <span class="keywordflow">return</span> out << suffix;
<a name="l00506"></a>00506 }
<a name="l00507"></a>00507
<a name="l00508"></a><a class="code" href="class_polynomial_mod2.html#a3940dec2ab787489ad4ce67013fe4611">00508</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> <a class="code" href="class_polynomial_mod2.html#a3940dec2ab787489ad4ce67013fe4611" title="greatest common divisor">PolynomialMod2::Gcd</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &a, <span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &b)
<a name="l00509"></a>00509 {
<a name="l00510"></a>00510 <span class="keywordflow">return</span> <a class="code" href="class_euclidean_domain_of.html">EuclideanDomainOf<PolynomialMod2></a>().<a class="code" href="class_polynomial_mod2.html#a3940dec2ab787489ad4ce67013fe4611" title="greatest common divisor">Gcd</a>(a, b);
<a name="l00511"></a>00511 }
<a name="l00512"></a>00512
<a name="l00513"></a><a class="code" href="class_polynomial_mod2.html#ae8005d38604e28556889ea89412fe33f">00513</a> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> <a class="code" href="class_polynomial_mod2.html#ae8005d38604e28556889ea89412fe33f" title="calculate multiplicative inverse of *this mod n">PolynomialMod2::InverseMod</a>(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &modulus)<span class="keyword"> const</span>
<a name="l00514"></a>00514 <span class="keyword"></span>{
<a name="l00515"></a>00515 <span class="keyword">typedef</span> <a class="code" href="class_euclidean_domain_of.html">EuclideanDomainOf<PolynomialMod2></a> Domain;
<a name="l00516"></a>00516 <span class="keywordflow">return</span> <a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing<Domain></a>(Domain(), modulus).<a class="code" href="class_polynomial_mod2.html#af93d5dd751be38de7a66413217f56f17" title="return inverse if *this is a unit, otherwise return 0">MultiplicativeInverse</a>(*<span class="keyword">this</span>);
<a name="l00517"></a>00517 }
<a name="l00518"></a>00518
<a name="l00519"></a><a class="code" href="class_polynomial_mod2.html#a769b126e4495f436e9eabe50c87b5077">00519</a> <span class="keywordtype">bool</span> <a class="code" href="class_polynomial_mod2.html#a769b126e4495f436e9eabe50c87b5077" title="check for irreducibility">PolynomialMod2::IsIrreducible</a>()<span class="keyword"> const</span>
<a name="l00520"></a>00520 <span class="keyword"></span>{
<a name="l00521"></a>00521 <span class="keywordtype">signed</span> <span class="keywordtype">int</span> d = <a class="code" href="class_polynomial_mod2.html#ae274b547e478a6cc0065089b7b915e47" title="the zero polynomial will return a degree of -1">Degree</a>();
<a name="l00522"></a>00522 <span class="keywordflow">if</span> (d <= 0)
<a name="l00523"></a>00523 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00524"></a>00524
<a name="l00525"></a>00525 <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> t(2), u(t);
<a name="l00526"></a>00526 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=1; i<=d/2; i++)
<a name="l00527"></a>00527 {
<a name="l00528"></a>00528 u = u.Squared()%(*this);
<a name="l00529"></a>00529 <span class="keywordflow">if</span> (!<a class="code" href="class_polynomial_mod2.html#a3940dec2ab787489ad4ce67013fe4611" title="greatest common divisor">Gcd</a>(u+t, *<span class="keyword">this</span>).<a class="code" href="class_polynomial_mod2.html#ae106fdd2fe4747f2f7fa677543070822" title="only 1 is a unit">IsUnit</a>())
<a name="l00530"></a>00530 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00531"></a>00531 }
<a name="l00532"></a>00532 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00533"></a>00533 }
<a name="l00534"></a>00534
<a name="l00535"></a>00535 <span class="comment">// ********************************************************</span>
<a name="l00536"></a>00536
<a name="l00537"></a>00537 GF2NP::GF2NP(<span class="keyword">const</span> <a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a> &modulus)
<a name="l00538"></a>00538 : <a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing</a><<a class="code" href="class_euclidean_domain_of.html" title="EuclideanDomainOf.">EuclideanDomainOf</a><<a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>> >(<a class="code" href="class_euclidean_domain_of.html" title="EuclideanDomainOf.">EuclideanDomainOf</a><<a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>>(), modulus), m(modulus.Degree())
<a name="l00539"></a>00539 {
<a name="l00540"></a>00540 }
<a name="l00541"></a>00541
<a name="l00542"></a>00542 GF2NP::Element GF2NP::SquareRoot(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00543"></a>00543 <span class="keyword"></span>{
<a name="l00544"></a>00544 Element r = a;
<a name="l00545"></a>00545 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=1; i<m; i++)
<a name="l00546"></a>00546 r = <a class="code" href="class_square.html" title="Square">Square</a>(r);
<a name="l00547"></a>00547 <span class="keywordflow">return</span> r;
<a name="l00548"></a>00548 }
<a name="l00549"></a>00549
<a name="l00550"></a>00550 GF2NP::Element GF2NP::HalfTrace(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00551"></a>00551 <span class="keyword"></span>{
<a name="l00552"></a>00552 assert(m%2 == 1);
<a name="l00553"></a>00553 Element h = a;
<a name="l00554"></a>00554 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=1; i<=(m-1)/2; i++)
<a name="l00555"></a>00555 h = Add(<a class="code" href="class_square.html" title="Square">Square</a>(<a class="code" href="class_square.html" title="Square">Square</a>(h)), a);
<a name="l00556"></a>00556 <span class="keywordflow">return</span> h;
<a name="l00557"></a>00557 }
<a name="l00558"></a>00558
<a name="l00559"></a>00559 GF2NP::Element GF2NP::SolveQuadraticEquation(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00560"></a>00560 <span class="keyword"></span>{
<a name="l00561"></a>00561 <span class="keywordflow">if</span> (m%2 == 0)
<a name="l00562"></a>00562 {
<a name="l00563"></a>00563 Element z, w;
<a name="l00564"></a>00564 <a class="code" href="class_random_pool.html" title="Randomness Pool.">RandomPool</a> rng;
<a name="l00565"></a>00565 <span class="keywordflow">do</span>
<a name="l00566"></a>00566 {
<a name="l00567"></a>00567 Element p((<a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &)rng, m);
<a name="l00568"></a>00568 z = PolynomialMod2::Zero();
<a name="l00569"></a>00569 w = p;
<a name="l00570"></a>00570 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=1; i<=m-1; i++)
<a name="l00571"></a>00571 {
<a name="l00572"></a>00572 w = <a class="code" href="class_square.html" title="Square">Square</a>(w);
<a name="l00573"></a>00573 z = <a class="code" href="class_square.html" title="Square">Square</a>(z);
<a name="l00574"></a>00574 Accumulate(z, Multiply(w, a));
<a name="l00575"></a>00575 Accumulate(w, p);
<a name="l00576"></a>00576 }
<a name="l00577"></a>00577 } <span class="keywordflow">while</span> (w.IsZero());
<a name="l00578"></a>00578 <span class="keywordflow">return</span> z;
<a name="l00579"></a>00579 }
<a name="l00580"></a>00580 <span class="keywordflow">else</span>
<a name="l00581"></a>00581 <span class="keywordflow">return</span> HalfTrace(a);
<a name="l00582"></a>00582 }
<a name="l00583"></a>00583
<a name="l00584"></a>00584 <span class="comment">// ********************************************************</span>
<a name="l00585"></a>00585
<a name="l00586"></a>00586 GF2NT::GF2NT(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t0, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t1, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t2)
<a name="l00587"></a>00587 : <a class="code" href="class_g_f2_n_p.html" title="GF(2^n) with Polynomial Basis.">GF2NP</a>(<a class="code" href="class_polynomial_mod2.html" title="Polynomial with Coefficients in GF(2)">PolynomialMod2</a>::Trinomial(t0, t1, t2))
<a name="l00588"></a>00588 , t0(t0), t1(t1)
<a name="l00589"></a>00589 , result((word)0, m)
<a name="l00590"></a>00590 {
<a name="l00591"></a>00591 assert(t0 > t1 && t1 > t2 && t2==0);
<a name="l00592"></a>00592 }
<a name="l00593"></a>00593
<a name="l00594"></a>00594 <span class="keyword">const</span> GF2NT::Element& GF2NT::MultiplicativeInverse(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00595"></a>00595 <span class="keyword"></span>{
<a name="l00596"></a>00596 <span class="keywordflow">if</span> (t0-t1 < WORD_BITS)
<a name="l00597"></a>00597 <span class="keywordflow">return</span> GF2NP::MultiplicativeInverse(a);
<a name="l00598"></a>00598
<a name="l00599"></a>00599 <a class="code" href="class_sec_block.html">SecWordBlock</a> T(m_modulus.reg.size() * 4);
<a name="l00600"></a>00600 word *b = T;
<a name="l00601"></a>00601 word *c = T+m_modulus.reg.size();
<a name="l00602"></a>00602 word *f = T+2*m_modulus.reg.size();
<a name="l00603"></a>00603 word *g = T+3*m_modulus.reg.size();
<a name="l00604"></a>00604 <span class="keywordtype">size_t</span> bcLen=1, fgLen=m_modulus.reg.size();
<a name="l00605"></a>00605 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0;
<a name="l00606"></a>00606
<a name="l00607"></a>00607 SetWords(T, 0, 3*m_modulus.reg.size());
<a name="l00608"></a>00608 b[0]=1;
<a name="l00609"></a>00609 assert(a.reg.size() <= m_modulus.reg.size());
<a name="l00610"></a>00610 CopyWords(f, a.reg, a.reg.size());
<a name="l00611"></a>00611 CopyWords(g, m_modulus.reg, m_modulus.reg.size());
<a name="l00612"></a>00612
<a name="l00613"></a>00613 <span class="keywordflow">while</span> (1)
<a name="l00614"></a>00614 {
<a name="l00615"></a>00615 word t=f[0];
<a name="l00616"></a>00616 <span class="keywordflow">while</span> (!t)
<a name="l00617"></a>00617 {
<a name="l00618"></a>00618 ShiftWordsRightByWords(f, fgLen, 1);
<a name="l00619"></a>00619 <span class="keywordflow">if</span> (c[bcLen-1])
<a name="l00620"></a>00620 bcLen++;
<a name="l00621"></a>00621 assert(bcLen <= m_modulus.reg.size());
<a name="l00622"></a>00622 ShiftWordsLeftByWords(c, bcLen, 1);
<a name="l00623"></a>00623 k+=WORD_BITS;
<a name="l00624"></a>00624 t=f[0];
<a name="l00625"></a>00625 }
<a name="l00626"></a>00626
<a name="l00627"></a>00627 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0;
<a name="l00628"></a>00628 <span class="keywordflow">while</span> (t%2 == 0)
<a name="l00629"></a>00629 {
<a name="l00630"></a>00630 t>>=1;
<a name="l00631"></a>00631 i++;
<a name="l00632"></a>00632 }
<a name="l00633"></a>00633 k+=i;
<a name="l00634"></a>00634
<a name="l00635"></a>00635 <span class="keywordflow">if</span> (t==1 && CountWords(f, fgLen)==1)
<a name="l00636"></a>00636 <span class="keywordflow">break</span>;
<a name="l00637"></a>00637
<a name="l00638"></a>00638 <span class="keywordflow">if</span> (i==1)
<a name="l00639"></a>00639 {
<a name="l00640"></a>00640 ShiftWordsRightByBits(f, fgLen, 1);
<a name="l00641"></a>00641 t=ShiftWordsLeftByBits(c, bcLen, 1);
<a name="l00642"></a>00642 }
<a name="l00643"></a>00643 <span class="keywordflow">else</span>
<a name="l00644"></a>00644 {
<a name="l00645"></a>00645 ShiftWordsRightByBits(f, fgLen, i);
<a name="l00646"></a>00646 t=ShiftWordsLeftByBits(c, bcLen, i);
<a name="l00647"></a>00647 }
<a name="l00648"></a>00648 <span class="keywordflow">if</span> (t)
<a name="l00649"></a>00649 {
<a name="l00650"></a>00650 c[bcLen] = t;
<a name="l00651"></a>00651 bcLen++;
<a name="l00652"></a>00652 assert(bcLen <= m_modulus.reg.size());
<a name="l00653"></a>00653 }
<a name="l00654"></a>00654
<a name="l00655"></a>00655 <span class="keywordflow">if</span> (f[fgLen-1]==0 && g[fgLen-1]==0)
<a name="l00656"></a>00656 fgLen--;
<a name="l00657"></a>00657
<a name="l00658"></a>00658 <span class="keywordflow">if</span> (f[fgLen-1] < g[fgLen-1])
<a name="l00659"></a>00659 {
<a name="l00660"></a>00660 std::swap(f, g);
<a name="l00661"></a>00661 std::swap(b, c);
<a name="l00662"></a>00662 }
<a name="l00663"></a>00663
<a name="l00664"></a>00664 XorWords(f, g, fgLen);
<a name="l00665"></a>00665 XorWords(b, c, bcLen);
<a name="l00666"></a>00666 }
<a name="l00667"></a>00667
<a name="l00668"></a>00668 <span class="keywordflow">while</span> (k >= WORD_BITS)
<a name="l00669"></a>00669 {
<a name="l00670"></a>00670 word temp = b[0];
<a name="l00671"></a>00671 <span class="comment">// right shift b</span>
<a name="l00672"></a>00672 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i=0; i+1<BitsToWords(m); i++)
<a name="l00673"></a>00673 b[i] = b[i+1];
<a name="l00674"></a>00674 b[BitsToWords(m)-1] = 0;
<a name="l00675"></a>00675
<a name="l00676"></a>00676 <span class="keywordflow">if</span> (t1 < WORD_BITS)
<a name="l00677"></a>00677 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j<WORD_BITS-t1; j++)
<a name="l00678"></a>00678 temp ^= ((temp >> j) & 1) << (t1 + j);
<a name="l00679"></a>00679 <span class="keywordflow">else</span>
<a name="l00680"></a>00680 b[t1/WORD_BITS-1] ^= temp << t1%WORD_BITS;
<a name="l00681"></a>00681
<a name="l00682"></a>00682 <span class="keywordflow">if</span> (t1 % WORD_BITS)
<a name="l00683"></a>00683 b[t1/WORD_BITS] ^= temp >> (WORD_BITS - t1%WORD_BITS);
<a name="l00684"></a>00684
<a name="l00685"></a>00685 <span class="keywordflow">if</span> (t0%WORD_BITS)
<a name="l00686"></a>00686 {
<a name="l00687"></a>00687 b[t0/WORD_BITS-1] ^= temp << t0%WORD_BITS;
<a name="l00688"></a>00688 b[t0/WORD_BITS] ^= temp >> (WORD_BITS - t0%WORD_BITS);
<a name="l00689"></a>00689 }
<a name="l00690"></a>00690 <span class="keywordflow">else</span>
<a name="l00691"></a>00691 b[t0/WORD_BITS-1] ^= temp;
<a name="l00692"></a>00692
<a name="l00693"></a>00693 k -= WORD_BITS;
<a name="l00694"></a>00694 }
<a name="l00695"></a>00695
<a name="l00696"></a>00696 <span class="keywordflow">if</span> (k)
<a name="l00697"></a>00697 {
<a name="l00698"></a>00698 word temp = b[0] << (WORD_BITS - k);
<a name="l00699"></a>00699 ShiftWordsRightByBits(b, BitsToWords(m), k);
<a name="l00700"></a>00700
<a name="l00701"></a>00701 <span class="keywordflow">if</span> (t1 < WORD_BITS)
<a name="l00702"></a>00702 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j<WORD_BITS-t1; j++)
<a name="l00703"></a>00703 temp ^= ((temp >> j) & 1) << (t1 + j);
<a name="l00704"></a>00704 <span class="keywordflow">else</span>
<a name="l00705"></a>00705 b[t1/WORD_BITS-1] ^= temp << t1%WORD_BITS;
<a name="l00706"></a>00706
<a name="l00707"></a>00707 <span class="keywordflow">if</span> (t1 % WORD_BITS)
<a name="l00708"></a>00708 b[t1/WORD_BITS] ^= temp >> (WORD_BITS - t1%WORD_BITS);
<a name="l00709"></a>00709
<a name="l00710"></a>00710 <span class="keywordflow">if</span> (t0%WORD_BITS)
<a name="l00711"></a>00711 {
<a name="l00712"></a>00712 b[t0/WORD_BITS-1] ^= temp << t0%WORD_BITS;
<a name="l00713"></a>00713 b[t0/WORD_BITS] ^= temp >> (WORD_BITS - t0%WORD_BITS);
<a name="l00714"></a>00714 }
<a name="l00715"></a>00715 <span class="keywordflow">else</span>
<a name="l00716"></a>00716 b[t0/WORD_BITS-1] ^= temp;
<a name="l00717"></a>00717 }
<a name="l00718"></a>00718
<a name="l00719"></a>00719 CopyWords(result.reg.begin(), b, result.reg.size());
<a name="l00720"></a>00720 <span class="keywordflow">return</span> result;
<a name="l00721"></a>00721 }
<a name="l00722"></a>00722
<a name="l00723"></a>00723 <span class="keyword">const</span> GF2NT::Element& GF2NT::Multiply(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00724"></a>00724 <span class="keyword"></span>{
<a name="l00725"></a>00725 <span class="keywordtype">size_t</span> aSize = STDMIN(a.reg.size(), result.reg.size());
<a name="l00726"></a>00726 Element r((word)0, m);
<a name="l00727"></a>00727
<a name="l00728"></a>00728 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=m-1; i>=0; i--)
<a name="l00729"></a>00729 {
<a name="l00730"></a>00730 <span class="keywordflow">if</span> (r[m-1])
<a name="l00731"></a>00731 {
<a name="l00732"></a>00732 ShiftWordsLeftByBits(r.reg.begin(), r.reg.size(), 1);
<a name="l00733"></a>00733 XorWords(r.reg.begin(), m_modulus.reg, r.reg.size());
<a name="l00734"></a>00734 }
<a name="l00735"></a>00735 <span class="keywordflow">else</span>
<a name="l00736"></a>00736 ShiftWordsLeftByBits(r.reg.begin(), r.reg.size(), 1);
<a name="l00737"></a>00737
<a name="l00738"></a>00738 <span class="keywordflow">if</span> (b[i])
<a name="l00739"></a>00739 XorWords(r.reg.begin(), a.reg, aSize);
<a name="l00740"></a>00740 }
<a name="l00741"></a>00741
<a name="l00742"></a>00742 <span class="keywordflow">if</span> (m%WORD_BITS)
<a name="l00743"></a>00743 r.reg.begin()[r.reg.size()-1] = (word)Crop(r.reg[r.reg.size()-1], m%WORD_BITS);
<a name="l00744"></a>00744
<a name="l00745"></a>00745 CopyWords(result.reg.begin(), r.reg.begin(), result.reg.size());
<a name="l00746"></a>00746 <span class="keywordflow">return</span> result;
<a name="l00747"></a>00747 }
<a name="l00748"></a>00748
<a name="l00749"></a>00749 <span class="keyword">const</span> GF2NT::Element& GF2NT::Reduced(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00750"></a>00750 <span class="keyword"></span>{
<a name="l00751"></a>00751 <span class="keywordflow">if</span> (t0-t1 < WORD_BITS)
<a name="l00752"></a>00752 <span class="keywordflow">return</span> m_domain.Mod(a, m_modulus);
<a name="l00753"></a>00753
<a name="l00754"></a>00754 <a class="code" href="class_sec_block.html">SecWordBlock</a> b(a.reg);
<a name="l00755"></a>00755
<a name="l00756"></a>00756 <span class="keywordtype">size_t</span> i;
<a name="l00757"></a>00757 <span class="keywordflow">for</span> (i=b.size()-1; i>=BitsToWords(t0); i--)
<a name="l00758"></a>00758 {
<a name="l00759"></a>00759 word temp = b[i];
<a name="l00760"></a>00760
<a name="l00761"></a>00761 <span class="keywordflow">if</span> (t0%WORD_BITS)
<a name="l00762"></a>00762 {
<a name="l00763"></a>00763 b[i-t0/WORD_BITS] ^= temp >> t0%WORD_BITS;
<a name="l00764"></a>00764 b[i-t0/WORD_BITS-1] ^= temp << (WORD_BITS - t0%WORD_BITS);
<a name="l00765"></a>00765 }
<a name="l00766"></a>00766 <span class="keywordflow">else</span>
<a name="l00767"></a>00767 b[i-t0/WORD_BITS] ^= temp;
<a name="l00768"></a>00768
<a name="l00769"></a>00769 <span class="keywordflow">if</span> ((t0-t1)%WORD_BITS)
<a name="l00770"></a>00770 {
<a name="l00771"></a>00771 b[i-(t0-t1)/WORD_BITS] ^= temp >> (t0-t1)%WORD_BITS;
<a name="l00772"></a>00772 b[i-(t0-t1)/WORD_BITS-1] ^= temp << (WORD_BITS - (t0-t1)%WORD_BITS);
<a name="l00773"></a>00773 }
<a name="l00774"></a>00774 <span class="keywordflow">else</span>
<a name="l00775"></a>00775 b[i-(t0-t1)/WORD_BITS] ^= temp;
<a name="l00776"></a>00776 }
<a name="l00777"></a>00777
<a name="l00778"></a>00778 <span class="keywordflow">if</span> (i==BitsToWords(t0)-1 && t0%WORD_BITS)
<a name="l00779"></a>00779 {
<a name="l00780"></a>00780 word mask = ((word)1<<(t0%WORD_BITS))-1;
<a name="l00781"></a>00781 word temp = b[i] & ~mask;
<a name="l00782"></a>00782 b[i] &= mask;
<a name="l00783"></a>00783
<a name="l00784"></a>00784 b[i-t0/WORD_BITS] ^= temp >> t0%WORD_BITS;
<a name="l00785"></a>00785
<a name="l00786"></a>00786 <span class="keywordflow">if</span> ((t0-t1)%WORD_BITS)
<a name="l00787"></a>00787 {
<a name="l00788"></a>00788 b[i-(t0-t1)/WORD_BITS] ^= temp >> (t0-t1)%WORD_BITS;
<a name="l00789"></a>00789 <span class="keywordflow">if</span> ((t0-t1)%WORD_BITS > t0%WORD_BITS)
<a name="l00790"></a>00790 b[i-(t0-t1)/WORD_BITS-1] ^= temp << (WORD_BITS - (t0-t1)%WORD_BITS);
<a name="l00791"></a>00791 <span class="keywordflow">else</span>
<a name="l00792"></a>00792 assert(temp << (WORD_BITS - (t0-t1)%WORD_BITS) == 0);
<a name="l00793"></a>00793 }
<a name="l00794"></a>00794 <span class="keywordflow">else</span>
<a name="l00795"></a>00795 b[i-(t0-t1)/WORD_BITS] ^= temp;
<a name="l00796"></a>00796 }
<a name="l00797"></a>00797
<a name="l00798"></a>00798 SetWords(result.reg.begin(), 0, result.reg.size());
<a name="l00799"></a>00799 CopyWords(result.reg.begin(), b, STDMIN(b.size(), result.reg.size()));
<a name="l00800"></a>00800 <span class="keywordflow">return</span> result;
<a name="l00801"></a>00801 }
<a name="l00802"></a>00802
<a name="l00803"></a>00803 <span class="keywordtype">void</span> GF2NP::DEREncodeElement(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &out, <span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00804"></a>00804 <span class="keyword"></span>{
<a name="l00805"></a>00805 a.DEREncodeAsOctetString(out, MaxElementByteLength());
<a name="l00806"></a>00806 }
<a name="l00807"></a>00807
<a name="l00808"></a>00808 <span class="keywordtype">void</span> GF2NP::BERDecodeElement(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &in, Element &a)<span class="keyword"> const</span>
<a name="l00809"></a>00809 <span class="keyword"></span>{
<a name="l00810"></a>00810 a.BERDecodeAsOctetString(in, MaxElementByteLength());
<a name="l00811"></a>00811 }
<a name="l00812"></a>00812
<a name="l00813"></a>00813 <span class="keywordtype">void</span> GF2NT::DEREncode(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt)<span class="keyword"> const</span>
<a name="l00814"></a>00814 <span class="keyword"></span>{
<a name="l00815"></a>00815 <a class="code" href="class_d_e_r_sequence_encoder.html" title="DER Sequence Encoder.">DERSequenceEncoder</a> seq(bt);
<a name="l00816"></a>00816 ASN1::characteristic_two_field().DEREncode(seq);
<a name="l00817"></a>00817 <a class="code" href="class_d_e_r_sequence_encoder.html" title="DER Sequence Encoder.">DERSequenceEncoder</a> parameters(seq);
<a name="l00818"></a>00818 DEREncodeUnsigned(parameters, m);
<a name="l00819"></a>00819 ASN1::tpBasis().DEREncode(parameters);
<a name="l00820"></a>00820 DEREncodeUnsigned(parameters, t1);
<a name="l00821"></a>00821 parameters.MessageEnd();
<a name="l00822"></a>00822 seq.MessageEnd();
<a name="l00823"></a>00823 }
<a name="l00824"></a>00824
<a name="l00825"></a>00825 <span class="keywordtype">void</span> GF2NPP::DEREncode(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt)<span class="keyword"> const</span>
<a name="l00826"></a>00826 <span class="keyword"></span>{
<a name="l00827"></a>00827 <a class="code" href="class_d_e_r_sequence_encoder.html" title="DER Sequence Encoder.">DERSequenceEncoder</a> seq(bt);
<a name="l00828"></a>00828 ASN1::characteristic_two_field().DEREncode(seq);
<a name="l00829"></a>00829 <a class="code" href="class_d_e_r_sequence_encoder.html" title="DER Sequence Encoder.">DERSequenceEncoder</a> parameters(seq);
<a name="l00830"></a>00830 DEREncodeUnsigned(parameters, m);
<a name="l00831"></a>00831 ASN1::ppBasis().DEREncode(parameters);
<a name="l00832"></a>00832 <a class="code" href="class_d_e_r_sequence_encoder.html" title="DER Sequence Encoder.">DERSequenceEncoder</a> pentanomial(parameters);
<a name="l00833"></a>00833 DEREncodeUnsigned(pentanomial, t3);
<a name="l00834"></a>00834 DEREncodeUnsigned(pentanomial, t2);
<a name="l00835"></a>00835 DEREncodeUnsigned(pentanomial, t1);
<a name="l00836"></a>00836 pentanomial.MessageEnd();
<a name="l00837"></a>00837 parameters.MessageEnd();
<a name="l00838"></a>00838 seq.MessageEnd();
<a name="l00839"></a>00839 }
<a name="l00840"></a>00840
<a name="l00841"></a>00841 <a class="code" href="class_g_f2_n_p.html" title="GF(2^n) with Polynomial Basis.">GF2NP</a> * BERDecodeGF2NP(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt)
<a name="l00842"></a>00842 {
<a name="l00843"></a>00843 <span class="comment">// VC60 workaround: auto_ptr lacks reset()</span>
<a name="l00844"></a>00844 <a class="code" href="classmember__ptr.html">member_ptr<GF2NP></a> result;
<a name="l00845"></a>00845
<a name="l00846"></a>00846 <a class="code" href="class_b_e_r_sequence_decoder.html" title="BER Sequence Decoder.">BERSequenceDecoder</a> seq(bt);
<a name="l00847"></a>00847 <span class="keywordflow">if</span> (<a class="code" href="class_o_i_d.html" title="Object Identifier.">OID</a>(seq) != ASN1::characteristic_two_field())
<a name="l00848"></a>00848 BERDecodeError();
<a name="l00849"></a>00849 <a class="code" href="class_b_e_r_sequence_decoder.html" title="BER Sequence Decoder.">BERSequenceDecoder</a> parameters(seq);
<a name="l00850"></a>00850 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> m;
<a name="l00851"></a>00851 BERDecodeUnsigned(parameters, m);
<a name="l00852"></a>00852 <a class="code" href="class_o_i_d.html" title="Object Identifier.">OID</a> oid(parameters);
<a name="l00853"></a>00853 <span class="keywordflow">if</span> (oid == ASN1::tpBasis())
<a name="l00854"></a>00854 {
<a name="l00855"></a>00855 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t1;
<a name="l00856"></a>00856 BERDecodeUnsigned(parameters, t1);
<a name="l00857"></a>00857 result.reset(<span class="keyword">new</span> <a class="code" href="class_g_f2_n_t.html" title="GF(2^n) with Trinomial Basis.">GF2NT</a>(m, t1, 0));
<a name="l00858"></a>00858 }
<a name="l00859"></a>00859 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (oid == ASN1::ppBasis())
<a name="l00860"></a>00860 {
<a name="l00861"></a>00861 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t1, t2, t3;
<a name="l00862"></a>00862 <a class="code" href="class_b_e_r_sequence_decoder.html" title="BER Sequence Decoder.">BERSequenceDecoder</a> pentanomial(parameters);
<a name="l00863"></a>00863 BERDecodeUnsigned(pentanomial, t3);
<a name="l00864"></a>00864 BERDecodeUnsigned(pentanomial, t2);
<a name="l00865"></a>00865 BERDecodeUnsigned(pentanomial, t1);
<a name="l00866"></a>00866 pentanomial.MessageEnd();
<a name="l00867"></a>00867 result.reset(<span class="keyword">new</span> <a class="code" href="class_g_f2_n_p_p.html" title="GF(2^n) with Pentanomial Basis.">GF2NPP</a>(m, t3, t2, t1, 0));
<a name="l00868"></a>00868 }
<a name="l00869"></a>00869 <span class="keywordflow">else</span>
<a name="l00870"></a>00870 {
<a name="l00871"></a>00871 BERDecodeError();
<a name="l00872"></a>00872 <span class="keywordflow">return</span> NULL;
<a name="l00873"></a>00873 }
<a name="l00874"></a>00874 parameters.MessageEnd();
<a name="l00875"></a>00875 seq.MessageEnd();
<a name="l00876"></a>00876
<a name="l00877"></a>00877 <span class="keywordflow">return</span> result.release();
<a name="l00878"></a>00878 }
<a name="l00879"></a>00879
<a name="l00880"></a>00880 NAMESPACE_END
<a name="l00881"></a>00881
<a name="l00882"></a>00882 <span class="preprocessor">#endif</span>
</pre></div></div>
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