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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++: nbtheory.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>nbtheory.cpp</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">// nbtheory.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 "nbtheory.h"</span><a name="l00008"></a>00008 <span class="preprocessor">#include "modarith.h"</span><a name="l00009"></a>00009 <span class="preprocessor">#include "algparam.h"</span><a name="l00010"></a>00010 <a name="l00011"></a>00011 <span class="preprocessor">#include <math.h></span><a name="l00012"></a>00012 <span class="preprocessor">#include <vector></span><a name="l00013"></a>00013 <a name="l00014"></a>00014 <span class="preprocessor">#ifdef _OPENMP</span><a name="l00015"></a>00015 <span class="preprocessor"></span><span class="comment">// needed in MSVC 2005 to generate correct manifest</span><a name="l00016"></a>00016 <span class="preprocessor">#include <omp.h></span><a name="l00017"></a>00017 <span class="preprocessor">#endif</span><a name="l00018"></a>00018 <span class="preprocessor"></span><a name="l00019"></a>00019 NAMESPACE_BEGIN(CryptoPP)<a name="l00020"></a>00020 <a name="l00021"></a>00021 const word s_lastSmallPrime = 32719;<a name="l00022"></a>00022 <a name="l00023"></a><a class="code" href="struct_new_prime_table.html">00023</a> struct <a class="code" href="struct_new_prime_table.html">NewPrimeTable</a><a name="l00024"></a>00024 {<a name="l00025"></a><a class="code" href="struct_new_prime_table.html#0c08a248d463c9dc410e934b1f370b0b">00025</a> std::vector<word16> * operator()()<span class="keyword"> const</span><a name="l00026"></a>00026 <span class="keyword"> </span>{<a name="l00027"></a>00027 <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> maxPrimeTableSize = 3511;<a name="l00028"></a>00028 <a name="l00029"></a>00029 std::auto_ptr<std::vector<word16> > pPrimeTable(<span class="keyword">new</span> std::vector<word16>);<a name="l00030"></a>00030 std::vector<word16> &primeTable = *pPrimeTable;<a name="l00031"></a>00031 primeTable.reserve(maxPrimeTableSize);<a name="l00032"></a>00032 <a name="l00033"></a>00033 primeTable.push_back(2);<a name="l00034"></a>00034 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> testEntriesEnd = 1;<a name="l00035"></a>00035 <a name="l00036"></a>00036 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> p=3; p<=s_lastSmallPrime; p+=2)<a name="l00037"></a>00037 {<a name="l00038"></a>00038 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j;<a name="l00039"></a>00039 <span class="keywordflow">for</span> (j=1; j<testEntriesEnd; j++)<a name="l00040"></a>00040 <span class="keywordflow">if</span> (p%primeTable[j] == 0)<a name="l00041"></a>00041 <span class="keywordflow">break</span>;<a name="l00042"></a>00042 <span class="keywordflow">if</span> (j == testEntriesEnd)<a name="l00043"></a>00043 {<a name="l00044"></a>00044 primeTable.push_back(p);<a name="l00045"></a>00045 testEntriesEnd = UnsignedMin(54U, primeTable.size());<a name="l00046"></a>00046 }<a name="l00047"></a>00047 }<a name="l00048"></a>00048 <a name="l00049"></a>00049 <span class="keywordflow">return</span> pPrimeTable.release();<a name="l00050"></a>00050 }<a name="l00051"></a>00051 };<a name="l00052"></a>00052 <a name="l00053"></a>00053 <span class="keyword">const</span> word16 * GetPrimeTable(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> &size)<a name="l00054"></a>00054 {<a name="l00055"></a>00055 <span class="keyword">const</span> std::vector<word16> &primeTable = <a class="code" href="class_singleton.html">Singleton<std::vector<word16></a>, <a class="code" href="struct_new_prime_table.html">NewPrimeTable</a>>().Ref();<a name="l00056"></a>00056 size = (<span class="keywordtype">unsigned</span> int)primeTable.size();<a name="l00057"></a>00057 <span class="keywordflow">return</span> &primeTable[0];<a name="l00058"></a>00058 }<a name="l00059"></a>00059 <a name="l00060"></a>00060 <span class="keywordtype">bool</span> IsSmallPrime(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p)<a name="l00061"></a>00061 {<a name="l00062"></a>00062 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;<a name="l00063"></a>00063 <span class="keyword">const</span> word16 * primeTable = GetPrimeTable(primeTableSize);<a name="l00064"></a>00064 <a name="l00065"></a>00065 <span class="keywordflow">if</span> (p.<a class="code" href="class_integer.html#13ddbfd8e9729932c2a99b0dff530978">IsPositive</a>() && p <= primeTable[primeTableSize-1])<a name="l00066"></a>00066 <span class="keywordflow">return</span> std::binary_search(primeTable, primeTable+primeTableSize, (word16)p.<a class="code" href="class_integer.html#2e90d8f4c5a13e203b94f9abc24d733f" title="return equivalent signed long if possible, otherwise undefined">ConvertToLong</a>());<a name="l00067"></a>00067 <span class="keywordflow">else</span><a name="l00068"></a>00068 <span class="keywordflow">return</span> <span class="keyword">false</span>;<a name="l00069"></a>00069 }<a name="l00070"></a>00070 <a name="l00071"></a>00071 <span class="keywordtype">bool</span> TrialDivision(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p, <span class="keywordtype">unsigned</span> bound)<a name="l00072"></a>00072 {<a name="l00073"></a>00073 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;<a name="l00074"></a>00074 <span class="keyword">const</span> word16 * primeTable = GetPrimeTable(primeTableSize);<a name="l00075"></a>00075 <a name="l00076"></a>00076 assert(primeTable[primeTableSize-1] >= bound);<a name="l00077"></a>00077 <a name="l00078"></a>00078 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;<a name="l00079"></a>00079 <span class="keywordflow">for</span> (i = 0; primeTable[i]<bound; i++)<a name="l00080"></a>00080 <span class="keywordflow">if</span> ((p % primeTable[i]) == 0)<a name="l00081"></a>00081 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00082"></a>00082 <a name="l00083"></a>00083 <span class="keywordflow">if</span> (bound == primeTable[i])<a name="l00084"></a>00084 <span class="keywordflow">return</span> (p % bound == 0);<a name="l00085"></a>00085 <span class="keywordflow">else</span><a name="l00086"></a>00086 <span class="keywordflow">return</span> <span class="keyword">false</span>;<a name="l00087"></a>00087 }<a name="l00088"></a>00088 <a name="l00089"></a>00089 <span class="keywordtype">bool</span> SmallDivisorsTest(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p)<a name="l00090"></a>00090 {<a name="l00091"></a>00091 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;<a name="l00092"></a>00092 <span class="keyword">const</span> word16 * primeTable = GetPrimeTable(primeTableSize);<a name="l00093"></a>00093 <span class="keywordflow">return</span> !TrialDivision(p, primeTable[primeTableSize-1]);<a name="l00094"></a>00094 }<a name="l00095"></a>00095 <a name="l00096"></a>00096 <span class="keywordtype">bool</span> IsFermatProbablePrime(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &n, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &b)<a name="l00097"></a>00097 {<a name="l00098"></a>00098 <span class="keywordflow">if</span> (n <= 3)<a name="l00099"></a>00099 <span class="keywordflow">return</span> n==2 || n==3;<a name="l00100"></a>00100 <a name="l00101"></a>00101 assert(n>3 && b>1 && b<n-1);<a name="l00102"></a>00102 <span class="keywordflow">return</span> a_exp_b_mod_c(b, n-1, n)==1;<a name="l00103"></a>00103 }<a name="l00104"></a>00104 <a name="l00105"></a>00105 <span class="keywordtype">bool</span> IsStrongProbablePrime(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &n, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &b)<a name="l00106"></a>00106 {<a name="l00107"></a>00107 <span class="keywordflow">if</span> (n <= 3)⌨️ 快捷键说明
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