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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.h 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.h</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">// nbtheory.h - written and placed in the public domain by Wei Dai</span><a name="l00002"></a>00002 <a name="l00003"></a>00003 <span class="preprocessor">#ifndef CRYPTOPP_NBTHEORY_H</span><a name="l00004"></a>00004 <span class="preprocessor"></span><span class="preprocessor">#define CRYPTOPP_NBTHEORY_H</span><a name="l00005"></a>00005 <span class="preprocessor"></span><a name="l00006"></a>00006 <span class="preprocessor">#include "<a class="code" href="integer_8h.html">integer.h</a>"</span><a name="l00007"></a>00007 <span class="preprocessor">#include "algparam.h"</span><a name="l00008"></a>00008 <a name="l00009"></a>00009 NAMESPACE_BEGIN(CryptoPP)<a name="l00010"></a>00010 <a name="l00011"></a>00011 <span class="comment">// obtain pointer to small prime table and get its size</span><a name="l00012"></a>00012 CRYPTOPP_DLL const word16 * CRYPTOPP_API GetPrimeTable(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> &size);<a name="l00013"></a>00013 <a name="l00014"></a>00014 <span class="comment">// ************ primality testing ****************</span><a name="l00015"></a>00015 <a name="l00016"></a>00016 <span class="comment">// generate a provable prime</span><a name="l00017"></a>00017 CRYPTOPP_DLL <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> CRYPTOPP_API MaurerProvablePrime(<a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &rng, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> bits);<a name="l00018"></a>00018 CRYPTOPP_DLL <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> CRYPTOPP_API MihailescuProvablePrime(<a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &rng, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> bits);<a name="l00019"></a>00019 <a name="l00020"></a>00020 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API IsSmallPrime(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p);<a name="l00021"></a>00021 <a name="l00022"></a>00022 <span class="comment">// returns true if p is divisible by some prime less than bound</span><a name="l00023"></a>00023 <span class="comment">// bound not be greater than the largest entry in the prime table</span><a name="l00024"></a>00024 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API TrialDivision(const <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="l00025"></a>00025 <a name="l00026"></a>00026 <span class="comment">// returns true if p is NOT divisible by small primes</span><a name="l00027"></a>00027 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API SmallDivisorsTest(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p);<a name="l00028"></a>00028 <a name="l00029"></a>00029 <span class="comment">// These is no reason to use these two, use the ones below instead</span><a name="l00030"></a>00030 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API IsFermatProbablePrime(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &n, const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &b);<a name="l00031"></a>00031 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API IsLucasProbablePrime(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &n);<a name="l00032"></a>00032 <a name="l00033"></a>00033 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API IsStrongProbablePrime(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &n, const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &b);<a name="l00034"></a>00034 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API IsStrongLucasProbablePrime(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &n);<a name="l00035"></a>00035 <a name="l00036"></a>00036 <span class="comment">// Rabin-Miller primality test, i.e. repeating the strong probable prime test </span><a name="l00037"></a>00037 <span class="comment">// for several rounds with random bases</span><a name="l00038"></a>00038 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API RabinMillerTest(<a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &rng, const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &w, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> rounds);<a name="l00039"></a>00039 <a name="l00040"></a>00040 <span class="comment">// primality test, used to generate primes</span><a name="l00041"></a>00041 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API IsPrime(const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p);<a name="l00042"></a>00042 <a name="l00043"></a>00043 <span class="comment">// more reliable than IsPrime(), used to verify primes generated by others</span><a name="l00044"></a>00044 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API VerifyPrime(<a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &rng, const <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> level = 1);<a name="l00045"></a>00045 <a name="l00046"></a><a class="code" href="class_prime_selector.html">00046</a> class CRYPTOPP_DLL <a class="code" href="class_prime_selector.html">PrimeSelector</a><a name="l00047"></a>00047 {<a name="l00048"></a>00048 <span class="keyword">public</span>:<a name="l00049"></a><a class="code" href="class_prime_selector.html#0fb5aafa214283370841f019a7b36a4f">00049</a> <span class="keyword">const</span> PrimeSelector *GetSelectorPointer()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">this</span>;}<a name="l00050"></a>00050 <span class="keyword">virtual</span> <span class="keywordtype">bool</span> IsAcceptable(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &candidate) <span class="keyword">const</span> =0;<a name="l00051"></a>00051 };<a name="l00052"></a>00052 <a name="l00053"></a>00053 <span class="comment">// use a fast sieve to find the first probable prime in {x | p<=x<=max and x%mod==equiv}</span><a name="l00054"></a>00054 <span class="comment">// returns true iff successful, value of p is undefined if no such prime exists</span><a name="l00055"></a>00055 CRYPTOPP_DLL <span class="keywordtype">bool</span> CRYPTOPP_API FirstPrime(<a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &max, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &equiv, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &mod, <span class="keyword">const</span> <a class="code" href="class_prime_selector.html">PrimeSelector</a> *pSelector);<a name="l00056"></a>00056 <a name="l00057"></a>00057 CRYPTOPP_DLL <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> CRYPTOPP_API PrimeSearchInterval(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &max);<a name="l00058"></a>00058 <a name="l00059"></a>00059 CRYPTOPP_DLL <a class="code" href="class_algorithm_parameters.html">AlgorithmParameters<AlgorithmParameters<AlgorithmParameters<NullNameValuePairs, Integer::RandomNumberType></a>, <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>>, <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>><a name="l00060"></a>00060 CRYPTOPP_API MakeParametersForTwoPrimesOfEqualSize(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> productBitLength);<a name="l00061"></a>00061 ⌨️ 快捷键说明
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