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modarith.h

00001 #ifndef CRYPTOPP_MODARITH_H
00002 #define CRYPTOPP_MODARITH_H
00003 
00004 // implementations are in integer.cpp
00005 
00006 #include "cryptlib.h"
00007 #include "misc.h"
00008 #include "integer.h"
00009 #include "algebra.h"
00010 
00011 NAMESPACE_BEGIN(CryptoPP)
00012 
00013 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
00014 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
00015 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;
00016 
00017 //! .
00018 class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
00019 {
00020 public:
00021 
00022         typedef int RandomizationParameter;
00023         typedef Integer Element;
00024 
00025         ModularArithmetic(const Integer &modulus = Integer::One())
00026                 : modulus(modulus), result((word)0, modulus.reg.size()) {}
00027 
00028         ModularArithmetic(const ModularArithmetic &ma)
00029                 : modulus(ma.modulus), result((word)0, modulus.reg.size()) {}
00030 
00031         ModularArithmetic(BufferedTransformation &bt);  // construct from BER encoded parameters
00032 
00033         virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
00034 
00035         void DEREncode(BufferedTransformation &bt) const;
00036 
00037         void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
00038         void BERDecodeElement(BufferedTransformation &in, Element &a) const;
00039 
00040         const Integer& GetModulus() const {return modulus;}
00041         void SetModulus(const Integer &newModulus) {modulus = newModulus; result.reg.resize(modulus.reg.size());}
00042 
00043         virtual bool IsMontgomeryRepresentation() const {return false;}
00044 
00045         virtual Integer ConvertIn(const Integer &a) const
00046                 {return a%modulus;}
00047 
00048         virtual Integer ConvertOut(const Integer &a) const
00049                 {return a;}
00050 
00051         const Integer& Half(const Integer &a) const;
00052 
00053         bool Equal(const Integer &a, const Integer &b) const
00054                 {return a==b;}
00055 
00056         const Integer& Identity() const
00057                 {return Integer::Zero();}
00058 
00059         const Integer& Add(const Integer &a, const Integer &b) const;
00060 
00061         Integer& Accumulate(Integer &a, const Integer &b) const;
00062 
00063         const Integer& Inverse(const Integer &a) const;
00064 
00065         const Integer& Subtract(const Integer &a, const Integer &b) const;
00066 
00067         Integer& Reduce(Integer &a, const Integer &b) const;
00068 
00069         const Integer& Double(const Integer &a) const
00070                 {return Add(a, a);}
00071 
00072         const Integer& MultiplicativeIdentity() const
00073                 {return Integer::One();}
00074 
00075         const Integer& Multiply(const Integer &a, const Integer &b) const
00076                 {return result1 = a*b%modulus;}
00077 
00078         const Integer& Square(const Integer &a) const
00079                 {return result1 = a.Squared()%modulus;}
00080 
00081         bool IsUnit(const Integer &a) const
00082                 {return Integer::Gcd(a, modulus).IsUnit();}
00083 
00084         const Integer& MultiplicativeInverse(const Integer &a) const
00085                 {return result1 = a.InverseMod(modulus);}
00086 
00087         const Integer& Divide(const Integer &a, const Integer &b) const
00088                 {return Multiply(a, MultiplicativeInverse(b));}
00089 
00090         Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;
00091 
00092         void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
00093 
00094         unsigned int MaxElementBitLength() const
00095                 {return (modulus-1).BitCount();}
00096 
00097         unsigned int MaxElementByteLength() const
00098                 {return (modulus-1).ByteCount();}
00099 
00100         Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const
00101                 // left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
00102         { 
00103                 return Element( rng , Integer( (long) 0) , modulus - Integer( (long) 1 )   ) ; 
00104         }   
00105 
00106         bool operator==(const ModularArithmetic &rhs) const
00107                 {return modulus == rhs.modulus;}
00108 
00109         static const RandomizationParameter DefaultRandomizationParameter ;
00110 
00111 protected:
00112         Integer modulus;
00113         mutable Integer result, result1;
00114 
00115 };
00116 
00117 // const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;
00118 
00119 //! do modular arithmetics in Montgomery representation for increased speed
00120 class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
00121 {
00122 public:
00123         MontgomeryRepresentation(const Integer &modulus);       // modulus must be odd
00124 
00125         virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}
00126 
00127         bool IsMontgomeryRepresentation() const {return true;}
00128 
00129         Integer ConvertIn(const Integer &a) const
00130                 {return (a<<(WORD_BITS*modulus.reg.size()))%modulus;}
00131 
00132         Integer ConvertOut(const Integer &a) const;
00133 
00134         const Integer& MultiplicativeIdentity() const
00135                 {return result1 = Integer::Power2(WORD_BITS*modulus.reg.size())%modulus;}
00136 
00137         const Integer& Multiply(const Integer &a, const Integer &b) const;
00138 
00139         const Integer& Square(const Integer &a) const;
00140 
00141         const Integer& MultiplicativeInverse(const Integer &a) const;
00142 
00143         Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
00144                 {return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);}
00145 
00146         void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
00147                 {AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}
00148 
00149 private:
00150         Integer u;
00151         mutable SecAlignedWordBlock workspace;
00152 };
00153 
00154 NAMESPACE_END
00155 
00156 #endif

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