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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 //! ring of congruence classes modulo n
    00018 /*! \note this implementation represents each congruence class as the smallest non-negative integer in that class */
    00019 class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
    00020 {
    00021 public:
    00022
    00023     typedef int RandomizationParameter;
    00024     typedef Integer Element;
    00025
    00026     ModularArithmetic(const Integer &modulus = Integer::One())
    00027         : m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
    00028
    00029     ModularArithmetic(const ModularArithmetic &ma)
    00030         : m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {}
    00031
    00032     ModularArithmetic(BufferedTransformation &bt);  // construct from BER encoded parameters
    00033
    00034     virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
    00035
    00036     void DEREncode(BufferedTransformation &bt) const;
    00037
    00038     void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
    00039     void BERDecodeElement(BufferedTransformation &in, Element &a) const;
    00040
    00041     const Integer& GetModulus() const {return m_modulus;}
    00042     void SetModulus(const Integer &newModulus) {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}
    00043
    00044     virtual bool IsMontgomeryRepresentation() const {return false;}
    00045
    00046     virtual Integer ConvertIn(const Integer &a) const
    00047         {return a%m_modulus;}
    00048
    00049     virtual Integer ConvertOut(const Integer &a) const
    00050         {return a;}
    00051
    00052     const Integer& Half(const Integer &a) const;
    00053
    00054     bool Equal(const Integer &a, const Integer &b) const
    00055         {return a==b;}
    00056
    00057     const Integer& Identity() const
    00058         {return Integer::Zero();}
    00059
    00060     const Integer& Add(const Integer &a, const Integer &b) const;
    00061
    00062     Integer& Accumulate(Integer &a, const Integer &b) const;
    00063
    00064     const Integer& Inverse(const Integer &a) const;
    00065
    00066     const Integer& Subtract(const Integer &a, const Integer &b) const;
    00067
    00068     Integer& Reduce(Integer &a, const Integer &b) const;
    00069
    00070     const Integer& Double(const Integer &a) const
    00071         {return Add(a, a);}
    00072
    00073     const Integer& MultiplicativeIdentity() const
    00074         {return Integer::One();}
    00075
    00076     const Integer& Multiply(const Integer &a, const Integer &b) const
    00077         {return m_result1 = a*b%m_modulus;}
    00078
    00079     const Integer& Square(const Integer &a) const
    00080         {return m_result1 = a.Squared()%m_modulus;}
    00081
    00082     bool IsUnit(const Integer &a) const
    00083         {return Integer::Gcd(a, m_modulus).IsUnit();}
    00084
    00085     const Integer& MultiplicativeInverse(const Integer &a) const
    00086         {return m_result1 = a.InverseMod(m_modulus);}
    00087
    00088     const Integer& Divide(const Integer &a, const Integer &b) const
    00089         {return Multiply(a, MultiplicativeInverse(b));}
    00090
    00091     Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;
    00092
    00093     void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
    00094
    00095     unsigned int MaxElementBitLength() const
    00096         {return (m_modulus-1).BitCount();}
    00097
    00098     unsigned int MaxElementByteLength() const
    00099         {return (m_modulus-1).ByteCount();}
    00100
    00101     Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const
    00102         // left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
    00103     {
    00104         return Element( rng , Integer( (long) 0) , m_modulus - Integer( (long) 1 )   ) ;
    00105     }
    00106
    00107     bool operator==(const ModularArithmetic &rhs) const
    00108         {return m_modulus == rhs.m_modulus;}
    00109
    00110     static const RandomizationParameter DefaultRandomizationParameter ;
    00111
    00112 protected:
    00113     Integer m_modulus;
    00114     mutable Integer m_result, m_result1;
    00115
    00116 };
    00117
    00118 // const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;
    00119
    00120 //! do modular arithmetics in Montgomery representation for increased speed
    00121 /*! \note the Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2 */
    00122 class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
    00123 {
    00124 public:
    00125     MontgomeryRepresentation(const Integer &modulus);   // modulus must be odd
    00126
    00127     virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}
    00128
    00129     bool IsMontgomeryRepresentation() const {return true;}
    00130
    00131     Integer ConvertIn(const Integer &a) const
    00132         {return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}
    00133
    00134     Integer ConvertOut(const Integer &a) const;
    00135
    00136     const Integer& MultiplicativeIdentity() const
    00137         {return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_modulus;}
    00138
    00139     const Integer& Multiply(const Integer &a, const Integer &b) const;
    00140
    00141     const Integer& Square(const Integer &a) const;
    00142
    00143     const Integer& MultiplicativeInverse(const Integer &a) const;
    00144
    00145     Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
    00146         {return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);}
    00147
    00148     void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
    00149         {AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}
    00150
    00151 private:
    00152     Integer m_u;
    00153     mutable IntegerSecBlock m_workspace;
    00154 };
    00155
    00156 NAMESPACE_END
    00157
    00158 #endif