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

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