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<div class="title">algebra.cpp</div> </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">// algebra.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_ALGEBRA_CPP // SunCC workaround: compiler could cause this file to be included twice</span>
<a name="l00006"></a>00006 <span class="preprocessor"></span><span class="preprocessor">#define CRYPTOPP_ALGEBRA_CPP</span>
<a name="l00007"></a>00007 <span class="preprocessor"></span>
<a name="l00008"></a>00008 <span class="preprocessor">#include "algebra.h"</span>
<a name="l00009"></a>00009 <span class="preprocessor">#include "<a class="code" href="integer_8h.html">integer.h</a>"</span>
<a name="l00010"></a>00010
<a name="l00011"></a>00011 <span class="preprocessor">#include <vector></span>
<a name="l00012"></a>00012
<a name="l00013"></a>00013 NAMESPACE_BEGIN(CryptoPP)
<a name="l00014"></a>00014
<a name="l00015"></a>00015 template <class T> const T& <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup</a><T>::Double(const Element &a)<span class="keyword"> const</span>
<a name="l00016"></a>00016 <span class="keyword"></span>{
<a name="l00017"></a>00017 <span class="keywordflow">return</span> Add(a, a);
<a name="l00018"></a>00018 }
<a name="l00019"></a>00019
<a name="l00020"></a>00020 <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> T& <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T>::Subtract</a>(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00021"></a>00021 <span class="keyword"></span>{
<a name="l00022"></a>00022 <span class="comment">// make copy of a in case Inverse() overwrites it</span>
<a name="l00023"></a>00023 Element a1(a);
<a name="l00024"></a>00024 <span class="keywordflow">return</span> Add(a1, Inverse(b));
<a name="l00025"></a>00025 }
<a name="l00026"></a>00026
<a name="l00027"></a>00027 <span class="keyword">template</span> <<span class="keyword">class</span> T> T& <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T>::Accumulate</a>(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00028"></a>00028 <span class="keyword"></span>{
<a name="l00029"></a>00029 <span class="keywordflow">return</span> a = Add(a, b);
<a name="l00030"></a>00030 }
<a name="l00031"></a>00031
<a name="l00032"></a>00032 <span class="keyword">template</span> <<span class="keyword">class</span> T> T& <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T>::Reduce</a>(Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00033"></a>00033 <span class="keyword"></span>{
<a name="l00034"></a>00034 <span class="keywordflow">return</span> a = Subtract(a, b);
<a name="l00035"></a>00035 }
<a name="l00036"></a>00036
<a name="l00037"></a>00037 <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> T& <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T>::Square</a>(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00038"></a>00038 <span class="keyword"></span>{
<a name="l00039"></a>00039 <span class="keywordflow">return</span> Multiply(a, a);
<a name="l00040"></a>00040 }
<a name="l00041"></a>00041
<a name="l00042"></a>00042 <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> T& <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T>::Divide</a>(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00043"></a>00043 <span class="keyword"></span>{
<a name="l00044"></a>00044 <span class="comment">// make copy of a in case MultiplicativeInverse() overwrites it</span>
<a name="l00045"></a>00045 Element a1(a);
<a name="l00046"></a>00046 <span class="keywordflow">return</span> Multiply(a1, MultiplicativeInverse(b));
<a name="l00047"></a>00047 }
<a name="l00048"></a>00048
<a name="l00049"></a>00049 <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> T& <a class="code" href="class_abstract_euclidean_domain.html" title="Abstract Euclidean Domain.">AbstractEuclideanDomain<T>::Mod</a>(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00050"></a>00050 <span class="keyword"></span>{
<a name="l00051"></a>00051 Element q;
<a name="l00052"></a>00052 DivisionAlgorithm(result, q, a, b);
<a name="l00053"></a>00053 <span class="keywordflow">return</span> result;
<a name="l00054"></a>00054 }
<a name="l00055"></a>00055
<a name="l00056"></a>00056 <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> T& <a class="code" href="class_abstract_euclidean_domain.html" title="Abstract Euclidean Domain.">AbstractEuclideanDomain<T>::Gcd</a>(<span class="keyword">const</span> Element &a, <span class="keyword">const</span> Element &b)<span class="keyword"> const</span>
<a name="l00057"></a>00057 <span class="keyword"></span>{
<a name="l00058"></a>00058 Element g[3]={b, a};
<a name="l00059"></a>00059 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i0=0, i1=1, i2=2;
<a name="l00060"></a>00060
<a name="l00061"></a>00061 <span class="keywordflow">while</span> (!Equal(g[i1], this->Identity()))
<a name="l00062"></a>00062 {
<a name="l00063"></a>00063 g[i2] = Mod(g[i0], g[i1]);
<a name="l00064"></a>00064 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t = i0; i0 = i1; i1 = i2; i2 = t;
<a name="l00065"></a>00065 }
<a name="l00066"></a>00066
<a name="l00067"></a>00067 <span class="keywordflow">return</span> result = g[i0];
<a name="l00068"></a>00068 }
<a name="l00069"></a>00069
<a name="l00070"></a>00070 <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> <span class="keyword">typename</span> QuotientRing<T>::Element& <a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing<T>::MultiplicativeInverse</a>(<span class="keyword">const</span> Element &a)<span class="keyword"> const</span>
<a name="l00071"></a>00071 <span class="keyword"></span>{
<a name="l00072"></a>00072 Element g[3]={m_modulus, a};
<a name="l00073"></a>00073 Element v[3]={m_domain.Identity(), m_domain.MultiplicativeIdentity()};
<a name="l00074"></a>00074 Element y;
<a name="l00075"></a>00075 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i0=0, i1=1, i2=2;
<a name="l00076"></a>00076
<a name="l00077"></a>00077 <span class="keywordflow">while</span> (!Equal(g[i1], Identity()))
<a name="l00078"></a>00078 {
<a name="l00079"></a>00079 <span class="comment">// y = g[i0] / g[i1];</span>
<a name="l00080"></a>00080 <span class="comment">// g[i2] = g[i0] % g[i1];</span>
<a name="l00081"></a>00081 m_domain.DivisionAlgorithm(g[i2], y, g[i0], g[i1]);
<a name="l00082"></a>00082 <span class="comment">// v[i2] = v[i0] - (v[i1] * y);</span>
<a name="l00083"></a>00083 v[i2] = m_domain.Subtract(v[i0], m_domain.Multiply(v[i1], y));
<a name="l00084"></a>00084 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> t = i0; i0 = i1; i1 = i2; i2 = t;
<a name="l00085"></a>00085 }
<a name="l00086"></a>00086
<a name="l00087"></a>00087 <span class="keywordflow">return</span> m_domain.IsUnit(g[i0]) ? m_domain.Divide(v[i0], g[i0]) : m_domain.Identity();
<a name="l00088"></a>00088 }
<a name="l00089"></a>00089
<a name="l00090"></a>00090 <span class="keyword">template</span> <<span class="keyword">class</span> T> T <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T>::ScalarMultiply</a>(<span class="keyword">const</span> Element &base, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &exponent)<span class="keyword"> const</span>
<a name="l00091"></a>00091 <span class="keyword"></span>{
<a name="l00092"></a>00092 Element result;
<a name="l00093"></a>00093 SimultaneousMultiply(&result, base, &exponent, 1);
<a name="l00094"></a>00094 <span class="keywordflow">return</span> result;
<a name="l00095"></a>00095 }
<a name="l00096"></a>00096
<a name="l00097"></a>00097 <span class="keyword">template</span> <<span class="keyword">class</span> T> T <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T>::CascadeScalarMultiply</a>(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e2)<span class="keyword"> const</span>
<a name="l00098"></a>00098 <span class="keyword"></span>{
<a name="l00099"></a>00099 <span class="keyword">const</span> <span class="keywordtype">unsigned</span> expLen = STDMAX(e1.<a class="code" href="class_integer.html#a178398002ab175e788a3bc224e5e5a8d" title="number of significant bits = floor(log2(abs(*this))) + 1">BitCount</a>(), e2.<a class="code" href="class_integer.html#a178398002ab175e788a3bc224e5e5a8d" title="number of significant bits = floor(log2(abs(*this))) + 1">BitCount</a>());
<a name="l00100"></a>00100 <span class="keywordflow">if</span> (expLen==0)
<a name="l00101"></a>00101 <span class="keywordflow">return</span> Identity();
<a name="l00102"></a>00102
<a name="l00103"></a>00103 <span class="keyword">const</span> <span class="keywordtype">unsigned</span> w = (expLen <= 46 ? 1 : (expLen <= 260 ? 2 : 3));
<a name="l00104"></a>00104 <span class="keyword">const</span> <span class="keywordtype">unsigned</span> tableSize = 1<<w;
<a name="l00105"></a>00105 std::vector<Element> powerTable(tableSize << w);
<a name="l00106"></a>00106
<a name="l00107"></a>00107 powerTable[1] = x;
<a name="l00108"></a>00108 powerTable[tableSize] = y;
<a name="l00109"></a>00109 <span class="keywordflow">if</span> (w==1)
<a name="l00110"></a>00110 powerTable[3] = Add(x,y);
<a name="l00111"></a>00111 <span class="keywordflow">else</span>
<a name="l00112"></a>00112 {
<a name="l00113"></a>00113 powerTable[2] = Double(x);
<a name="l00114"></a>00114 powerTable[2*tableSize] = Double(y);
<a name="l00115"></a>00115
<a name="l00116"></a>00116 <span class="keywordtype">unsigned</span> i, j;
<a name="l00117"></a>00117
<a name="l00118"></a>00118 <span class="keywordflow">for</span> (i=3; i<tableSize; i+=2)
<a name="l00119"></a>00119 powerTable[i] = Add(powerTable[i-2], powerTable[2]);
<a name="l00120"></a>00120 <span class="keywordflow">for</span> (i=1; i<tableSize; i+=2)
<a name="l00121"></a>00121 <span class="keywordflow">for</span> (j=i+tableSize; j<(tableSize<<w); j+=tableSize)
<a name="l00122"></a>00122 powerTable[j] = Add(powerTable[j-tableSize], y);
<a name="l00123"></a>00123
<a name="l00124"></a>00124 <span class="keywordflow">for</span> (i=3*tableSize; i<(tableSize<<w); i+=2*tableSize)
<a name="l00125"></a>00125 powerTable[i] = Add(powerTable[i-2*tableSize], powerTable[2*tableSize]);
<a name="l00126"></a>00126 <span class="keywordflow">for</span> (i=tableSize; i<(tableSize<<w); i+=2*tableSize)
<a name="l00127"></a>00127 <span class="keywordflow">for</span> (j=i+2; j<i+tableSize; j+=2)
<a name="l00128"></a>00128 powerTable[j] = Add(powerTable[j-1], x);
<a name="l00129"></a>00129 }
<a name="l00130"></a>00130
<a name="l00131"></a>00131 Element result;
<a name="l00132"></a>00132 <span class="keywordtype">unsigned</span> power1 = 0, power2 = 0, prevPosition = expLen-1;
<a name="l00133"></a>00133 <span class="keywordtype">bool</span> firstTime = <span class="keyword">true</span>;
<a name="l00134"></a>00134
<a name="l00135"></a>00135 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = expLen-1; i>=0; i--)
<a name="l00136"></a>00136 {
<a name="l00137"></a>00137 power1 = 2*power1 + e1.<a class="code" href="class_integer.html#a2814c3b82849bd8f6f44cc36974f1717" title="return the i-th bit, i=0 being the least significant bit">GetBit</a>(i);
<a name="l00138"></a>00138 power2 = 2*power2 + e2.<a class="code" href="class_integer.html#a2814c3b82849bd8f6f44cc36974f1717" title="return the i-th bit, i=0 being the least significant bit">GetBit</a>(i);
<a name="l00139"></a>00139
<a name="l00140"></a>00140 <span class="keywordflow">if</span> (i==0 || 2*power1 >= tableSize || 2*power2 >= tableSize)
<a name="l00141"></a>00141 {
<a name="l00142"></a>00142 <span class="keywordtype">unsigned</span> squaresBefore = prevPosition-i;
<a name="l00143"></a>00143 <span class="keywordtype">unsigned</span> squaresAfter = 0;
<a name="l00144"></a>00144 prevPosition = i;
<a name="l00145"></a>00145 <span class="keywordflow">while</span> ((power1 || power2) && power1%2 == 0 && power2%2==0)
<a name="l00146"></a>00146 {
<a name="l00147"></a>00147 power1 /= 2;
<a name="l00148"></a>00148 power2 /= 2;
<a name="l00149"></a>00149 squaresBefore--;
<a name="l00150"></a>00150 squaresAfter++;
<a name="l00151"></a>00151 }
<a name="l00152"></a>00152 <span class="keywordflow">if</span> (firstTime)
<a name="l00153"></a>00153 {
<a name="l00154"></a>00154 result = powerTable[(power2<<w) + power1];
<a name="l00155"></a>00155 firstTime = <span class="keyword">false</span>;
<a name="l00156"></a>00156 }
<a name="l00157"></a>00157 <span class="keywordflow">else</span>
<a name="l00158"></a>00158 {
<a name="l00159"></a>00159 <span class="keywordflow">while</span> (squaresBefore--)
<a name="l00160"></a>00160 result = Double(result);
<a name="l00161"></a>00161 <span class="keywordflow">if</span> (power1 || power2)
<a name="l00162"></a>00162 Accumulate(result, powerTable[(power2<<w) + power1]);
<a name="l00163"></a>00163 }
<a name="l00164"></a>00164 <span class="keywordflow">while</span> (squaresAfter--)
<a name="l00165"></a>00165 result = Double(result);
<a name="l00166"></a>00166 power1 = power2 = 0;
<a name="l00167"></a>00167 }
<a name="l00168"></a>00168 }
<a name="l00169"></a>00169 <span class="keywordflow">return</span> result;
<a name="l00170"></a>00170 }
<a name="l00171"></a>00171
<a name="l00172"></a>00172 <span class="keyword">template</span> <<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator> Element GeneralCascadeMultiplication(<span class="keyword">const</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<Element></a> &group, Iterator begin, Iterator end)
<a name="l00173"></a>00173 {
<a name="l00174"></a>00174 <span class="keywordflow">if</span> (end-begin == 1)
<a name="l00175"></a>00175 <span class="keywordflow">return</span> group.ScalarMultiply(begin->base, begin->exponent);
<a name="l00176"></a>00176 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (end-begin == 2)
<a name="l00177"></a>00177 <span class="keywordflow">return</span> group.CascadeScalarMultiply(begin->base, begin->exponent, (begin+1)->base, (begin+1)->exponent);
<a name="l00178"></a>00178 <span class="keywordflow">else</span>
<a name="l00179"></a>00179 {
<a name="l00180"></a>00180 <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> q, t;
<a name="l00181"></a>00181 Iterator last = end;
<a name="l00182"></a>00182 --last;
<a name="l00183"></a>00183
<a name="l00184"></a>00184 std::make_heap(begin, end);
<a name="l00185"></a>00185 std::pop_heap(begin, end);
<a name="l00186"></a>00186
<a name="l00187"></a>00187 <span class="keywordflow">while</span> (!!begin->exponent)
<a name="l00188"></a>00188 {
<a name="l00189"></a>00189 <span class="comment">// last->exponent is largest exponent, begin->exponent is next largest</span>
<a name="l00190"></a>00190 t = last->exponent;
<a name="l00191"></a>00191 <a class="code" href="class_integer.html#a567c89aa176b354143c99d558d05a5fb" title="calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))">Integer::Divide</a>(last->exponent, q, t, begin->exponent);
<a name="l00192"></a>00192
<a name="l00193"></a>00193 <span class="keywordflow">if</span> (q == <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638" title="avoid calling constructors for these frequently used integers">Integer::One</a>())
<a name="l00194"></a>00194 group.Accumulate(begin->base, last->base); <span class="comment">// avoid overhead of ScalarMultiply()</span>
<a name="l00195"></a>00195 <span class="keywordflow">else</span>
<a name="l00196"></a>00196 group.Accumulate(begin->base, group.ScalarMultiply(last->base, q));
<a name="l00197"></a>00197
<a name="l00198"></a>00198 std::push_heap(begin, end);
<a name="l00199"></a>00199 std::pop_heap(begin, end);
<a name="l00200"></a>00200 }
<a name="l00201"></a>00201
<a name="l00202"></a>00202 <span class="keywordflow">return</span> group.ScalarMultiply(last->base, last->exponent);
<a name="l00203"></a>00203 }
<a name="l00204"></a>00204 }
<a name="l00205"></a>00205
<a name="l00206"></a><a class="code" href="struct_window_slider.html">00206</a> <span class="keyword">struct </span><a class="code" href="struct_window_slider.html">WindowSlider</a>
<a name="l00207"></a>00207 {
<a name="l00208"></a>00208 <a class="code" href="struct_window_slider.html">WindowSlider</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &expIn, <span class="keywordtype">bool</span> fastNegate, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> windowSizeIn=0)
<a name="l00209"></a>00209 : exp(expIn), windowModulus(<a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638" title="avoid calling constructors for these frequently used integers">Integer::One</a>()), windowSize(windowSizeIn), windowBegin(0), fastNegate(fastNegate), firstTime(<span class="keyword">true</span>), finished(<span class="keyword">false</span>)
<a name="l00210"></a>00210 {
<a name="l00211"></a>00211 <span class="keywordflow">if</span> (windowSize == 0)
<a name="l00212"></a>00212 {
<a name="l00213"></a>00213 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expLen = exp.<a class="code" href="class_integer.html#a178398002ab175e788a3bc224e5e5a8d" title="number of significant bits = floor(log2(abs(*this))) + 1">BitCount</a>();
<a name="l00214"></a>00214 windowSize = expLen <= 17 ? 1 : (expLen <= 24 ? 2 : (expLen <= 70 ? 3 : (expLen <= 197 ? 4 : (expLen <= 539 ? 5 : (expLen <= 1434 ? 6 : 7)))));
<a name="l00215"></a>00215 }
<a name="l00216"></a>00216 windowModulus <<= windowSize;
<a name="l00217"></a>00217 }
<a name="l00218"></a>00218
<a name="l00219"></a>00219 <span class="keywordtype">void</span> FindNextWindow()
<a name="l00220"></a>00220 {
<a name="l00221"></a>00221 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expLen = exp.<a class="code" href="class_integer.html#aa8ecc9cc334b338ee805f91e6b289396" title="number of significant words = ceiling(ByteCount()/sizeof(word))">WordCount</a>() * WORD_BITS;
<a name="l00222"></a>00222 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> skipCount = firstTime ? 0 : windowSize;
<a name="l00223"></a>00223 firstTime = <span class="keyword">false</span>;
<a name="l00224"></a>00224 <span class="keywordflow">while</span> (!exp.<a class="code" href="class_integer.html#a2814c3b82849bd8f6f44cc36974f1717" title="return the i-th bit, i=0 being the least significant bit">GetBit</a>(skipCount))
<a name="l00225"></a>00225 {
<a name="l00226"></a>00226 <span class="keywordflow">if</span> (skipCount >= expLen)
<a name="l00227"></a>00227 {
<a name="l00228"></a>00228 finished = <span class="keyword">true</span>;
<a name="l00229"></a>00229 <span class="keywordflow">return</span>;
<a name="l00230"></a>00230 }
<a name="l00231"></a>00231 skipCount++;
<a name="l00232"></a>00232 }
<a name="l00233"></a>00233
<a name="l00234"></a>00234 exp >>= skipCount;
<a name="l00235"></a>00235 windowBegin += skipCount;
<a name="l00236"></a>00236 expWindow = word32(exp % (word(1) << windowSize));
<a name="l00237"></a>00237
<a name="l00238"></a>00238 <span class="keywordflow">if</span> (fastNegate && exp.<a class="code" href="class_integer.html#a2814c3b82849bd8f6f44cc36974f1717" title="return the i-th bit, i=0 being the least significant bit">GetBit</a>(windowSize))
<a name="l00239"></a>00239 {
<a name="l00240"></a>00240 negateNext = <span class="keyword">true</span>;
<a name="l00241"></a>00241 expWindow = (word32(1) << windowSize) - expWindow;
<a name="l00242"></a>00242 exp += windowModulus;
<a name="l00243"></a>00243 }
<a name="l00244"></a>00244 <span class="keywordflow">else</span>
<a name="l00245"></a>00245 negateNext = <span class="keyword">false</span>;
<a name="l00246"></a>00246 }
<a name="l00247"></a>00247
<a name="l00248"></a>00248 <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> exp, windowModulus;
<a name="l00249"></a>00249 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> windowSize, windowBegin;
<a name="l00250"></a>00250 word32 expWindow;
<a name="l00251"></a>00251 <span class="keywordtype">bool</span> fastNegate, negateNext, firstTime, finished;
<a name="l00252"></a>00252 };
<a name="l00253"></a>00253
<a name="l00254"></a>00254 <span class="keyword">template</span> <<span class="keyword">class</span> T>
<a name="l00255"></a>00255 <span class="keywordtype">void</span> <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup<T>::SimultaneousMultiply</a>(T *results, <span class="keyword">const</span> T &base, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> *expBegin, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expCount)<span class="keyword"> const</span>
<a name="l00256"></a>00256 <span class="keyword"></span>{
<a name="l00257"></a>00257 std::vector<std::vector<Element> > buckets(expCount);
<a name="l00258"></a>00258 std::vector<WindowSlider> exponents;
<a name="l00259"></a>00259 exponents.reserve(expCount);
<a name="l00260"></a>00260 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;
<a name="l00261"></a>00261
<a name="l00262"></a>00262 <span class="keywordflow">for</span> (i=0; i<expCount; i++)
<a name="l00263"></a>00263 {
<a name="l00264"></a>00264 assert(expBegin->NotNegative());
<a name="l00265"></a>00265 exponents.push_back(<a class="code" href="struct_window_slider.html">WindowSlider</a>(*expBegin++, InversionIsFast(), 0));
<a name="l00266"></a>00266 exponents[i].FindNextWindow();
<a name="l00267"></a>00267 buckets[i].resize(1<<(exponents[i].windowSize-1), Identity());
<a name="l00268"></a>00268 }
<a name="l00269"></a>00269
<a name="l00270"></a>00270 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expBitPosition = 0;
<a name="l00271"></a>00271 Element g = base;
<a name="l00272"></a>00272 <span class="keywordtype">bool</span> notDone = <span class="keyword">true</span>;
<a name="l00273"></a>00273
<a name="l00274"></a>00274 <span class="keywordflow">while</span> (notDone)
<a name="l00275"></a>00275 {
<a name="l00276"></a>00276 notDone = <span class="keyword">false</span>;
<a name="l00277"></a>00277 <span class="keywordflow">for</span> (i=0; i<expCount; i++)
<a name="l00278"></a>00278 {
<a name="l00279"></a>00279 <span class="keywordflow">if</span> (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)
<a name="l00280"></a>00280 {
<a name="l00281"></a>00281 Element &bucket = buckets[i][exponents[i].expWindow/2];
<a name="l00282"></a>00282 <span class="keywordflow">if</span> (exponents[i].negateNext)
<a name="l00283"></a>00283 Accumulate(bucket, Inverse(g));
<a name="l00284"></a>00284 <span class="keywordflow">else</span>
<a name="l00285"></a>00285 Accumulate(bucket, g);
<a name="l00286"></a>00286 exponents[i].FindNextWindow();
<a name="l00287"></a>00287 }
<a name="l00288"></a>00288 notDone = notDone || !exponents[i].finished;
<a name="l00289"></a>00289 }
<a name="l00290"></a>00290
<a name="l00291"></a>00291 <span class="keywordflow">if</span> (notDone)
<a name="l00292"></a>00292 {
<a name="l00293"></a>00293 g = Double(g);
<a name="l00294"></a>00294 expBitPosition++;
<a name="l00295"></a>00295 }
<a name="l00296"></a>00296 }
<a name="l00297"></a>00297
<a name="l00298"></a>00298 <span class="keywordflow">for</span> (i=0; i<expCount; i++)
<a name="l00299"></a>00299 {
<a name="l00300"></a>00300 Element &r = *results++;
<a name="l00301"></a>00301 r = buckets[i][buckets[i].size()-1];
<a name="l00302"></a>00302 <span class="keywordflow">if</span> (buckets[i].size() > 1)
<a name="l00303"></a>00303 {
<a name="l00304"></a>00304 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = (<span class="keywordtype">int</span>)buckets[i].size()-2; j >= 1; j--)
<a name="l00305"></a>00305 {
<a name="l00306"></a>00306 Accumulate(buckets[i][j], buckets[i][j+1]);
<a name="l00307"></a>00307 Accumulate(r, buckets[i][j]);
<a name="l00308"></a>00308 }
<a name="l00309"></a>00309 Accumulate(buckets[i][0], buckets[i][1]);
<a name="l00310"></a>00310 r = Add(Double(r), buckets[i][0]);
<a name="l00311"></a>00311 }
<a name="l00312"></a>00312 }
<a name="l00313"></a>00313 }
<a name="l00314"></a>00314
<a name="l00315"></a>00315 <span class="keyword">template</span> <<span class="keyword">class</span> T> T <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T>::Exponentiate</a>(<span class="keyword">const</span> Element &base, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &exponent)<span class="keyword"> const</span>
<a name="l00316"></a>00316 <span class="keyword"></span>{
<a name="l00317"></a>00317 Element result;
<a name="l00318"></a>00318 SimultaneousExponentiate(&result, base, &exponent, 1);
<a name="l00319"></a>00319 <span class="keywordflow">return</span> result;
<a name="l00320"></a>00320 }
<a name="l00321"></a>00321
<a name="l00322"></a>00322 <span class="keyword">template</span> <<span class="keyword">class</span> T> T <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T>::CascadeExponentiate</a>(<span class="keyword">const</span> Element &x, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e1, <span class="keyword">const</span> Element &y, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &e2)<span class="keyword"> const</span>
<a name="l00323"></a>00323 <span class="keyword"></span>{
<a name="l00324"></a>00324 <span class="keywordflow">return</span> MultiplicativeGroup().AbstractGroup<T>::CascadeScalarMultiply(x, e1, y, e2);
<a name="l00325"></a>00325 }
<a name="l00326"></a>00326
<a name="l00327"></a>00327 <span class="keyword">template</span> <<span class="keyword">class</span> Element, <span class="keyword">class</span> Iterator> Element GeneralCascadeExponentiation(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<Element></a> &ring, Iterator begin, Iterator end)
<a name="l00328"></a>00328 {
<a name="l00329"></a>00329 <span class="keywordflow">return</span> GeneralCascadeMultiplication<Element>(ring.MultiplicativeGroup(), begin, end);
<a name="l00330"></a>00330 }
<a name="l00331"></a>00331
<a name="l00332"></a>00332 <span class="keyword">template</span> <<span class="keyword">class</span> T>
<a name="l00333"></a>00333 <span class="keywordtype">void</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<T>::SimultaneousExponentiate</a>(T *results, <span class="keyword">const</span> T &base, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> expCount)<span class="keyword"> const</span>
<a name="l00334"></a>00334 <span class="keyword"></span>{
<a name="l00335"></a>00335 MultiplicativeGroup().AbstractGroup<T>::SimultaneousMultiply(results, base, exponents, expCount);
<a name="l00336"></a>00336 }
<a name="l00337"></a>00337
<a name="l00338"></a>00338 NAMESPACE_END
<a name="l00339"></a>00339
<a name="l00340"></a>00340 <span class="preprocessor">#endif</span>
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