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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="preprocessor">#ifndef CRYPTOPP_MODARITH_H</span>
<a name="l00002"></a>00002 <span class="preprocessor"></span><span class="preprocessor">#define CRYPTOPP_MODARITH_H</span>
<a name="l00003"></a>00003 <span class="preprocessor"></span>
<a name="l00004"></a>00004 <span class="comment">// implementations are in integer.cpp</span>
<a name="l00005"></a>00005
<a name="l00006"></a>00006 <span class="preprocessor">#include "<a class="code" href="cryptlib_8h.html">cryptlib.h</a>"</span>
<a name="l00007"></a>00007 <span class="preprocessor">#include "misc.h"</span>
<a name="l00008"></a>00008 <span class="preprocessor">#include "<a class="code" href="integer_8h.html">integer.h</a>"</span>
<a name="l00009"></a>00009 <span class="preprocessor">#include "algebra.h"</span>
<a name="l00010"></a>00010
<a name="l00011"></a>00011 NAMESPACE_BEGIN(CryptoPP)
<a name="l00012"></a>00012
<a name="l00013"></a>00013 CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_group.html" title="Abstract Group.">AbstractGroup</a><<a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>>;
<a name="l00014"></a>00014 CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a><Integer>;
<a name="l00015"></a>00015 CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_euclidean_domain.html" title="Abstract Euclidean Domain.">AbstractEuclideanDomain</a><Integer>;
<a name="l00016"></a>00016 <span class="comment"></span>
<a name="l00017"></a>00017 <span class="comment">//! ring of congruence classes modulo n</span>
<a name="l00018"></a>00018 <span class="comment"></span><span class="comment">/*! \note this implementation represents each congruence class as the smallest non-negative integer in that class */</span>
<a name="l00019"></a><a class="code" href="class_modular_arithmetic.html">00019</a> class CRYPTOPP_DLL <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> : public <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing</a><Integer>
<a name="l00020"></a>00020 {
<a name="l00021"></a>00021 <span class="keyword">public</span>:
<a name="l00022"></a>00022
<a name="l00023"></a>00023 <span class="keyword">typedef</span> <span class="keywordtype">int</span> RandomizationParameter;
<a name="l00024"></a>00024 <span class="keyword">typedef</span> Integer <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Element</a>;
<a name="l00025"></a>00025
<a name="l00026"></a>00026 <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a>(<span class="keyword">const</span> Integer &modulus = <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638" title="avoid calling constructors for these frequently used integers">Integer::One</a>())
<a name="l00027"></a>00027 : m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
<a name="l00028"></a>00028
<a name="l00029"></a>00029 <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a>(<span class="keyword">const</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> &ma)
<a name="l00030"></a>00030 : m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {}
<a name="l00031"></a>00031
<a name="l00032"></a>00032 <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a>(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt); <span class="comment">// construct from BER encoded parameters</span>
<a name="l00033"></a>00033
<a name="l00034"></a>00034 <span class="keyword">virtual</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> * Clone()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a>(*<span class="keyword">this</span>);}
<a name="l00035"></a>00035
<a name="l00036"></a>00036 <span class="keywordtype">void</span> DEREncode(<a class="code" href="class_buffered_transformation.html" title="interface for buffered transformations">BufferedTransformation</a> &bt) <span class="keyword">const</span>;
<a name="l00037"></a>00037
<a name="l00038"></a>00038 <span class="keywordtype">void</span> 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="l00039"></a>00039 <span class="keywordtype">void</span> 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="l00040"></a>00040
<a name="l00041"></a>00041 <span class="keyword">const</span> Integer& GetModulus()<span class="keyword"> const </span>{<span class="keywordflow">return</span> m_modulus;}
<a name="l00042"></a>00042 <span class="keywordtype">void</span> SetModulus(<span class="keyword">const</span> Integer &newModulus) {m_modulus = newModulus; m_result.reg.<a class="code" href="class_sec_block.html#af9e98d3f4a7af1156fcf3e6e68f4ae5a" title="change size and preserve contents">resize</a>(m_modulus.reg.size());}
<a name="l00043"></a>00043
<a name="l00044"></a>00044 <span class="keyword">virtual</span> <span class="keywordtype">bool</span> IsMontgomeryRepresentation()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">false</span>;}
<a name="l00045"></a>00045
<a name="l00046"></a>00046 <span class="keyword">virtual</span> Integer ConvertIn(<span class="keyword">const</span> Integer &a)<span class="keyword"> const</span>
<a name="l00047"></a>00047 <span class="keyword"> </span>{<span class="keywordflow">return</span> a%m_modulus;}
<a name="l00048"></a>00048
<a name="l00049"></a>00049 <span class="keyword">virtual</span> Integer ConvertOut(<span class="keyword">const</span> Integer &a)<span class="keyword"> const</span>
<a name="l00050"></a>00050 <span class="keyword"> </span>{<span class="keywordflow">return</span> a;}
<a name="l00051"></a>00051
<a name="l00052"></a>00052 <span class="keyword">const</span> Integer& Half(<span class="keyword">const</span> Integer &a) <span class="keyword">const</span>;
<a name="l00053"></a>00053
<a name="l00054"></a>00054 <span class="keywordtype">bool</span> Equal(<span class="keyword">const</span> Integer &a, <span class="keyword">const</span> Integer &b)<span class="keyword"> const</span>
<a name="l00055"></a>00055 <span class="keyword"> </span>{<span class="keywordflow">return</span> a==b;}
<a name="l00056"></a>00056
<a name="l00057"></a>00057 <span class="keyword">const</span> Integer& Identity()<span class="keyword"> const</span>
<a name="l00058"></a>00058 <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_integer.html#a19b7e6d48b1b57bd4846160ea2928175" title="avoid calling constructors for these frequently used integers">Integer::Zero</a>();}
<a name="l00059"></a>00059
<a name="l00060"></a>00060 <span class="keyword">const</span> Integer& Add(<span class="keyword">const</span> Integer &a, <span class="keyword">const</span> Integer &b) <span class="keyword">const</span>;
<a name="l00061"></a>00061
<a name="l00062"></a>00062 Integer& Accumulate(Integer &a, <span class="keyword">const</span> Integer &b) <span class="keyword">const</span>;
<a name="l00063"></a>00063
<a name="l00064"></a>00064 <span class="keyword">const</span> Integer& Inverse(<span class="keyword">const</span> Integer &a) <span class="keyword">const</span>;
<a name="l00065"></a>00065
<a name="l00066"></a>00066 <span class="keyword">const</span> Integer& Subtract(<span class="keyword">const</span> Integer &a, <span class="keyword">const</span> Integer &b) <span class="keyword">const</span>;
<a name="l00067"></a>00067
<a name="l00068"></a>00068 Integer& Reduce(Integer &a, <span class="keyword">const</span> Integer &b) <span class="keyword">const</span>;
<a name="l00069"></a>00069
<a name="l00070"></a>00070 <span class="keyword">const</span> Integer& Double(<span class="keyword">const</span> Integer &a)<span class="keyword"> const</span>
<a name="l00071"></a>00071 <span class="keyword"> </span>{<span class="keywordflow">return</span> Add(a, a);}
<a name="l00072"></a>00072
<a name="l00073"></a>00073 <span class="keyword">const</span> Integer& MultiplicativeIdentity()<span class="keyword"> const</span>
<a name="l00074"></a>00074 <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638" title="avoid calling constructors for these frequently used integers">Integer::One</a>();}
<a name="l00075"></a>00075
<a name="l00076"></a>00076 <span class="keyword">const</span> Integer& Multiply(<span class="keyword">const</span> Integer &a, <span class="keyword">const</span> Integer &b)<span class="keyword"> const</span>
<a name="l00077"></a>00077 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = a*b%m_modulus;}
<a name="l00078"></a>00078
<a name="l00079"></a>00079 <span class="keyword">const</span> Integer& <a class="code" href="class_square.html" title="Square">Square</a>(<span class="keyword">const</span> Integer &a)<span class="keyword"> const</span>
<a name="l00080"></a>00080 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = a.Squared()%m_modulus;}
<a name="l00081"></a>00081
<a name="l00082"></a>00082 <span class="keywordtype">bool</span> IsUnit(<span class="keyword">const</span> Integer &a)<span class="keyword"> const</span>
<a name="l00083"></a>00083 <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_integer.html#a2d4d29937f8ef666717530b30f137c37" title="greatest common divisor">Integer::Gcd</a>(a, m_modulus).<a class="code" href="class_integer.html#acbee0ebe94c7ef5b0da39beabe87c27b" title="is 1 or -1">IsUnit</a>();}
<a name="l00084"></a>00084
<a name="l00085"></a>00085 <span class="keyword">const</span> Integer& MultiplicativeInverse(<span class="keyword">const</span> Integer &a)<span class="keyword"> const</span>
<a name="l00086"></a>00086 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = a.<a class="code" href="class_integer.html#a881f9c714ee42f35718725a43d4d7db3" title="calculate multiplicative inverse of *this mod n">InverseMod</a>(m_modulus);}
<a name="l00087"></a>00087
<a name="l00088"></a>00088 <span class="keyword">const</span> Integer& Divide(<span class="keyword">const</span> Integer &a, <span class="keyword">const</span> Integer &b)<span class="keyword"> const</span>
<a name="l00089"></a>00089 <span class="keyword"> </span>{<span class="keywordflow">return</span> Multiply(a, MultiplicativeInverse(b));}
<a name="l00090"></a>00090
<a name="l00091"></a>00091 Integer CascadeExponentiate(<span class="keyword">const</span> Integer &x, <span class="keyword">const</span> Integer &e1, <span class="keyword">const</span> Integer &y, <span class="keyword">const</span> Integer &e2) <span class="keyword">const</span>;
<a name="l00092"></a>00092
<a name="l00093"></a>00093 <span class="keywordtype">void</span> SimultaneousExponentiate(Element *results, <span class="keyword">const</span> Element &base, <span class="keyword">const</span> Integer *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount) <span class="keyword">const</span>;
<a name="l00094"></a>00094
<a name="l00095"></a>00095 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> MaxElementBitLength()<span class="keyword"> const</span>
<a name="l00096"></a>00096 <span class="keyword"> </span>{<span class="keywordflow">return</span> (m_modulus-1).BitCount();}
<a name="l00097"></a>00097
<a name="l00098"></a>00098 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> MaxElementByteLength()<span class="keyword"> const</span>
<a name="l00099"></a>00099 <span class="keyword"> </span>{<span class="keywordflow">return</span> (m_modulus-1).ByteCount();}
<a name="l00100"></a>00100
<a name="l00101"></a>00101 Element RandomElement( <a class="code" href="class_random_number_generator.html" title="interface for random number generators">RandomNumberGenerator</a> &rng , <span class="keyword">const</span> RandomizationParameter &ignore_for_now = 0 ) <span class="keyword">const</span>
<a name="l00102"></a>00102 <span class="comment">// left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct</span>
<a name="l00103"></a>00103 {
<a name="l00104"></a>00104 <span class="keywordflow">return</span> Element( rng , Integer( (<span class="keywordtype">long</span>) 0) , m_modulus - Integer( (<span class="keywordtype">long</span>) 1 ) ) ;
<a name="l00105"></a>00105 }
<a name="l00106"></a>00106
<a name="l00107"></a>00107 <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> &rhs)<span class="keyword"> const</span>
<a name="l00108"></a>00108 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_modulus == rhs.m_modulus;}
<a name="l00109"></a>00109
<a name="l00110"></a>00110 <span class="keyword">static</span> <span class="keyword">const</span> RandomizationParameter DefaultRandomizationParameter ;
<a name="l00111"></a>00111
<a name="l00112"></a>00112 <span class="keyword">protected</span>:
<a name="l00113"></a>00113 Integer m_modulus;
<a name="l00114"></a>00114 <span class="keyword">mutable</span> Integer m_result, m_result1;
<a name="l00115"></a>00115
<a name="l00116"></a>00116 };
<a name="l00117"></a>00117
<a name="l00118"></a>00118 <span class="comment">// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;</span>
<a name="l00119"></a>00119 <span class="comment"></span>
<a name="l00120"></a>00120 <span class="comment">//! do modular arithmetics in Montgomery representation for increased speed</span>
<a name="l00121"></a>00121 <span class="comment"></span><span class="comment">/*! \note the Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2 */</span>
<a name="l00122"></a><a class="code" href="class_montgomery_representation.html">00122</a> <span class="keyword">class </span>CRYPTOPP_DLL <a class="code" href="class_montgomery_representation.html" title="do modular arithmetics in Montgomery representation for increased speed">MontgomeryRepresentation</a> : <span class="keyword">public</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a>
<a name="l00123"></a>00123 {
<a name="l00124"></a>00124 <span class="keyword">public</span>:
<a name="l00125"></a>00125 <a class="code" href="class_montgomery_representation.html" title="do modular arithmetics in Montgomery representation for increased speed">MontgomeryRepresentation</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &modulus); <span class="comment">// modulus must be odd</span>
<a name="l00126"></a>00126
<a name="l00127"></a>00127 <span class="keyword">virtual</span> <a class="code" href="class_modular_arithmetic.html" title="ring of congruence classes modulo n">ModularArithmetic</a> * Clone()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_montgomery_representation.html" title="do modular arithmetics in Montgomery representation for increased speed">MontgomeryRepresentation</a>(*<span class="keyword">this</span>);}
<a name="l00128"></a>00128
<a name="l00129"></a>00129 <span class="keywordtype">bool</span> IsMontgomeryRepresentation()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">true</span>;}
<a name="l00130"></a>00130
<a name="l00131"></a>00131 <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> ConvertIn(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &a)<span class="keyword"> const</span>
<a name="l00132"></a>00132 <span class="keyword"> </span>{<span class="keywordflow">return</span> (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}
<a name="l00133"></a>00133
<a name="l00134"></a>00134 <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> ConvertOut(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &a) <span class="keyword">const</span>;
<a name="l00135"></a>00135
<a name="l00136"></a>00136 <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>& MultiplicativeIdentity()<span class="keyword"> const</span>
<a name="l00137"></a>00137 <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c" title="return the integer 2**e">Integer::Power2</a>(WORD_BITS*m_modulus.reg.size())%m_modulus;}
<a name="l00138"></a>00138
<a name="l00139"></a>00139 <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>& Multiply(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &a, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &b) <span class="keyword">const</span>;
<a name="l00140"></a>00140
<a name="l00141"></a>00141 <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>& <a class="code" href="class_square.html" title="Square">Square</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &a) <span class="keyword">const</span>;
<a name="l00142"></a>00142
<a name="l00143"></a>00143 <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a>& MultiplicativeInverse(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> &a) <span class="keyword">const</span>;
<a name="l00144"></a>00144
<a name="l00145"></a>00145 <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> CascadeExponentiate(<span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</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_integer.html" title="multiple precision integer and basic arithmetics">Integer</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="l00146"></a>00146 <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<Integer>::CascadeExponentiate</a>(x, e1, y, e2);}
<a name="l00147"></a>00147
<a name="l00148"></a>00148 <span class="keywordtype">void</span> SimultaneousExponentiate(<a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Element</a> *results, <span class="keyword">const</span> <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Element</a> &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> exponentsCount)<span class="keyword"> const</span>
<a name="l00149"></a>00149 <span class="keyword"> </span>{<a class="code" href="class_abstract_ring.html" title="Abstract Ring.">AbstractRing<Integer>::SimultaneousExponentiate</a>(results, base, exponents, exponentsCount);}
<a name="l00150"></a>00150
<a name="l00151"></a>00151 <span class="keyword">private</span>:
<a name="l00152"></a>00152 <a class="code" href="class_integer.html" title="multiple precision integer and basic arithmetics">Integer</a> m_u;
<a name="l00153"></a>00153 <span class="keyword">mutable</span> <a class="code" href="class_sec_block.html">IntegerSecBlock</a> m_workspace;
<a name="l00154"></a>00154 };
<a name="l00155"></a>00155
<a name="l00156"></a>00156 NAMESPACE_END
<a name="l00157"></a>00157
<a name="l00158"></a>00158 <span class="preprocessor">#endif</span>
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