00001 #ifndef CRYPTOPP_MODARITH_H
00002 #define CRYPTOPP_MODARITH_H
00003
00004
00005
00006 #include "cryptlib.h"
00007 #include "misc.h"
00008 #include "integer.h"
00009 #include "algebra.h"
00010
00011 NAMESPACE_BEGIN(CryptoPP)
00012
00013 #ifndef SKIP_EXPLICIT_INSTANTIATION
00014 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
00015 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
00016 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;
00017 #endif // SKIP_EXPLICIT_INSTANTIATION
00018
00019
00020
00021 class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
00022 {
00023 public:
00024
00025 typedef int RandomizationParameter;
00026 typedef Integer Element;
00027
00028 ModularArithmetic(const Integer &modulus = Integer::One())
00029 : m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
00030
00031 ModularArithmetic(const ModularArithmetic &ma)
00032 : m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {}
00033
00034 ModularArithmetic(BufferedTransformation &bt);
00035
00036 virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
00037
00038 void DEREncode(BufferedTransformation &bt) const;
00039
00040 void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
00041 void BERDecodeElement(BufferedTransformation &in, Element &a) const;
00042
00043 const Integer& GetModulus() const {return m_modulus;}
00044 void SetModulus(const Integer &newModulus) {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}
00045
00046 virtual bool IsMontgomeryRepresentation() const {return false;}
00047
00048 virtual Integer ConvertIn(const Integer &a) const
00049 {return a%m_modulus;}
00050
00051 virtual Integer ConvertOut(const Integer &a) const
00052 {return a;}
00053
00054 const Integer& Half(const Integer &a) const;
00055
00056 bool Equal(const Integer &a, const Integer &b) const
00057 {return a==b;}
00058
00059 const Integer& Identity() const
00060 {return Integer::Zero();}
00061
00062 const Integer& Add(const Integer &a, const Integer &b) const;
00063
00064 Integer& Accumulate(Integer &a, const Integer &b) const;
00065
00066 const Integer& Inverse(const Integer &a) const;
00067
00068 const Integer& Subtract(const Integer &a, const Integer &b) const;
00069
00070 Integer& Reduce(Integer &a, const Integer &b) const;
00071
00072 const Integer& Double(const Integer &a) const
00073 {return Add(a, a);}
00074
00075 const Integer& MultiplicativeIdentity() const
00076 {return Integer::One();}
00077
00078 const Integer& Multiply(const Integer &a, const Integer &b) const
00079 {return m_result1 = a*b%m_modulus;}
00080
00081 const Integer& Square(const Integer &a) const
00082 {return m_result1 = a.Squared()%m_modulus;}
00083
00084 bool IsUnit(const Integer &a) const
00085 {return Integer::Gcd(a, m_modulus).IsUnit();}
00086
00087 const Integer& MultiplicativeInverse(const Integer &a) const
00088 {return m_result1 = a.InverseMod(m_modulus);}
00089
00090 const Integer& Divide(const Integer &a, const Integer &b) const
00091 {return Multiply(a, MultiplicativeInverse(b));}
00092
00093 Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;
00094
00095 void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
00096
00097 unsigned int MaxElementBitLength() const
00098 {return (m_modulus-1).BitCount();}
00099
00100 unsigned int MaxElementByteLength() const
00101 {return (m_modulus-1).ByteCount();}
00102
00103 Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const
00104
00105 {
00106 return Element( rng , Integer( (long) 0) , m_modulus - Integer( (long) 1 ) ) ;
00107 }
00108
00109 bool operator==(const ModularArithmetic &rhs) const
00110 {return m_modulus == rhs.m_modulus;}
00111
00112 static const RandomizationParameter DefaultRandomizationParameter ;
00113
00114 protected:
00115 Integer m_modulus;
00116 mutable Integer m_result, m_result1;
00117
00118 };
00119
00120
00121
00122
00123
00124 class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
00125 {
00126 public:
00127 MontgomeryRepresentation(const Integer &modulus);
00128
00129 virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}
00130
00131 bool IsMontgomeryRepresentation() const {return true;}
00132
00133 Integer ConvertIn(const Integer &a) const
00134 {return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}
00135
00136 Integer ConvertOut(const Integer &a) const;
00137
00138 const Integer& MultiplicativeIdentity() const
00139 {return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_modulus;}
00140
00141 const Integer& Multiply(const Integer &a, const Integer &b) const;
00142
00143 const Integer& Square(const Integer &a) const;
00144
00145 const Integer& MultiplicativeInverse(const Integer &a) const;
00146
00147 Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
00148 {return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);}
00149
00150 void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
00151 {AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}
00152
00153 private:
00154 Integer m_u;
00155 mutable SecAlignedWordBlock m_workspace;
00156 };
00157
00158 NAMESPACE_END
00159
00160 #endif