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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html><head><meta http-equiv="Content-Type" content="text/html;charset=UTF-8"><title>Crypto++: algebra.cpp Source File</title><link href="doxygen.css" rel="stylesheet" type="text/css"><link href="tabs.css" rel="stylesheet" type="text/css"></head><body><!-- Generated by Doxygen 1.5.2 --><div class="tabs"> <ul> <li><a href="index.html"><span>Main Page</span></a></li> <li><a href="namespaces.html"><span>Namespaces</span></a></li> <li><a href="classes.html"><span>Classes</span></a></li> <li class="current"><a href="files.html"><span>Files</span></a></li> </ul></div><div class="tabs"> <ul> <li><a href="files.html"><span>File List</span></a></li> <li><a href="globals.html"><span>File Members</span></a></li> </ul></div><h1>algebra.cpp</h1><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><a class="code" href="class_abstract_group.html#e54ef772d5f231729e188cbe3b9173f6">00015</a> 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><a class="code" href="class_abstract_group.html#a19e1bef00198fb30eb01df3f7076717">00020</a> <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#a19e1bef00198fb30eb01df3f7076717">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 <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> 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><a class="code" href="class_abstract_group.html#45aa7c2240cb2f87184c7ad90df298ec">00027</a> <span class="keyword">template</span> <<span class="keyword">class</span> T> T& <a class="code" href="class_abstract_group.html#45aa7c2240cb2f87184c7ad90df298ec">AbstractGroup<T>::Accumulate</a>(<a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &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><a class="code" href="class_abstract_group.html#2cc747d7e6b910e137942bd5c01e5b87">00032</a> <span class="keyword">template</span> <<span class="keyword">class</span> T> T& <a class="code" href="class_abstract_group.html#2cc747d7e6b910e137942bd5c01e5b87">AbstractGroup<T>::Reduce</a>(<a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &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 = <a class="code" href="class_abstract_group.html#a19e1bef00198fb30eb01df3f7076717">Subtract</a>(a, b);<a name="l00035"></a>00035 }<a name="l00036"></a>00036 <a name="l00037"></a><a class="code" href="class_abstract_ring.html#dce7ac629f07850d5c45b473bed72ab0">00037</a> <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#dce7ac629f07850d5c45b473bed72ab0">AbstractRing<T>::Square</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &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><a class="code" href="class_abstract_ring.html#a7ce20a30d89a8257088930d1d06d0b7">00042</a> <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#a7ce20a30d89a8257088930d1d06d0b7">AbstractRing<T>::Divide</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html#cd93e8ce4e2897173310c68fcb60f3e9">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_abstract_ring.html#cd93e8ce4e2897173310c68fcb60f3e9">Element</a> &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 <a class="code" href="class_abstract_ring.html#cd93e8ce4e2897173310c68fcb60f3e9">Element</a> 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><a class="code" href="class_abstract_euclidean_domain.html#aeaae5226cf710c9a8c583f5fc1d17b6">00049</a> <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#aeaae5226cf710c9a8c583f5fc1d17b6">AbstractEuclideanDomain<T>::Mod</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_ring.html#cd93e8ce4e2897173310c68fcb60f3e9">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_abstract_ring.html#cd93e8ce4e2897173310c68fcb60f3e9">Element</a> &b)<span class="keyword"> const</span><a name="l00050"></a>00050 <span class="keyword"></span>{<a name="l00051"></a>00051 <a class="code" href="class_abstract_euclidean_domain.html#02903b4c46289ca070e2e7668e532bdc">Element</a> q;<a name="l00052"></a>00052 DivisionAlgorithm(<a class="code" href="class_abstract_euclidean_domain.html#f1314f064e73c560b3d31982c4e26404">result</a>, q, a, b);<a name="l00053"></a>00053 <span class="keywordflow">return</span> <a class="code" href="class_abstract_euclidean_domain.html#f1314f064e73c560b3d31982c4e26404">result</a>;<a name="l00054"></a>00054 }<a name="l00055"></a>00055 <a name="l00056"></a><a class="code" href="class_abstract_euclidean_domain.html#2044146d4eb49414e1f4f880a9858161">00056</a> <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#2044146d4eb49414e1f4f880a9858161">AbstractEuclideanDomain<T>::Gcd</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_euclidean_domain.html#02903b4c46289ca070e2e7668e532bdc">Element</a> &a, <span class="keyword">const</span> <a class="code" href="class_abstract_euclidean_domain.html#02903b4c46289ca070e2e7668e532bdc">Element</a> &b)<span class="keyword"> const</span><a name="l00057"></a>00057 <span class="keyword"></span>{<a name="l00058"></a>00058 <a class="code" href="class_abstract_euclidean_domain.html#02903b4c46289ca070e2e7668e532bdc">Element</a> 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] = <a class="code" href="class_abstract_euclidean_domain.html#aeaae5226cf710c9a8c583f5fc1d17b6">Mod</a>(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> <a class="code" href="class_abstract_euclidean_domain.html#f1314f064e73c560b3d31982c4e26404">result</a> = g[i0];<a name="l00068"></a>00068 }<a name="l00069"></a>00069 <a name="l00070"></a><a class="code" href="class_quotient_ring.html#c4188ae1dccb83f17c118748afd60df8">00070</a> <span class="keyword">template</span> <<span class="keyword">class</span> T> <span class="keyword">const</span> <span class="keyword">typename</span> <a class="code" href="class_quotient_ring.html" title="Quotient Ring.">QuotientRing<T>::Element</a>& <a class="code" href="class_quotient_ring.html#c4188ae1dccb83f17c118748afd60df8">QuotientRing<T>::MultiplicativeInverse</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_euclidean_domain.html#02903b4c46289ca070e2e7668e532bdc">Element</a> &a)<span class="keyword"> const</span><a name="l00071"></a>00071 <span class="keyword"></span>{<a name="l00072"></a>00072 <a class="code" href="class_quotient_ring.html#a5fc43636ce1b8ab3c8aa4ec309242e0">Element</a> g[3]={<a class="code" href="class_quotient_ring.html#07127b18d71b1a503e29436fce18e5b4">m_modulus</a>, a};<a name="l00073"></a>00073 <a class="code" href="class_quotient_ring.html#a5fc43636ce1b8ab3c8aa4ec309242e0">Element</a> v[3]={<a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.Identity(), <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.MultiplicativeIdentity()};<a name="l00074"></a>00074 <a class="code" href="class_quotient_ring.html#a5fc43636ce1b8ab3c8aa4ec309242e0">Element</a> 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> (!<a class="code" href="class_quotient_ring.html#95a675aaca290e8cc05a56361c7d56f3">Equal</a>(g[i1], <a class="code" href="class_quotient_ring.html#80815f5757c80106ae7dc2db2799b835">Identity</a>()))<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 <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.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] = <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.Subtract(v[i0], <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.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> <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.IsUnit(g[i0]) ? <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.Divide(v[i0], g[i0]) : <a class="code" href="class_quotient_ring.html#fa96b7fc70b6b3abbc3a1eca196d7b6c">m_domain</a>.Identity();<a name="l00088"></a>00088 }<a name="l00089"></a>00089 <a name="l00090"></a><a class="code" href="class_abstract_group.html#c01536b91c4fa3d0e0f929917143595b">00090</a> <span class="keyword">template</span> <<span class="keyword">class</span> T> T <a class="code" href="class_abstract_group.html#c01536b91c4fa3d0e0f929917143595b">AbstractGroup<T>::ScalarMultiply</a>(<span class="keyword">const</span> <a class="code" href="class_quotient_ring.html#a5fc43636ce1b8ab3c8aa4ec309242e0">Element</a> &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 <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> result;<a name="l00093"></a>00093 <a class="code" href="class_abstract_group.html#00a5cd4b22aab947ec107ec93ad13122">SimultaneousMultiply</a>(&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><a class="code" href="class_abstract_group.html#ca3e1ca578003aff2595cc8d73522894">00097</a> <span class="keyword">template</span> <<span class="keyword">class</span> T> T <a class="code" href="class_abstract_group.html#ca3e1ca578003aff2595cc8d73522894">AbstractGroup<T>::CascadeScalarMultiply</a>(<span class="keyword">const</span> <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &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> <a class="code" href="class_abstract_group.html#4a2b3308fb5c13f70fcc5746be52ba7b">Element</a> &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#867356d88074424328d0ebb9bea63254" title="number of significant bits = floor(log2(abs(*this))) + 1">BitCount</a>(), e2.<a class="code" href="class_integer.html#867356d88074424328d0ebb9bea63254" 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 ⌨️ 快捷键说明
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