modarith.h

#ifndef CRYPTOPP_MODARITH_H
#define CRYPTOPP_MODARITH_H

// implementations are in integer.cpp

#include "cryptlib.h"
#include "misc.h"
#include "integer.h"
#include "algebra.h"

NAMESPACE_BEGIN(CryptoPP)

CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;

//! ring of congruence classes modulo n
/*! \note this implementation represents each congruence class as the smallest non-negative integer in that class */
class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
{
public:

        typedef int RandomizationParameter;
        typedef Integer Element;

        ModularArithmetic(const Integer &modulus = Integer::One())
                : m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}

        ModularArithmetic(const ModularArithmetic &ma)
                : m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {}

        ModularArithmetic(BufferedTransformation &bt);  // construct from BER encoded parameters

        virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}

        void DEREncode(BufferedTransformation &bt) const;

        void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
        void BERDecodeElement(BufferedTransformation &in, Element &a) const;

        const Integer& GetModulus() const {return m_modulus;}
        void SetModulus(const Integer &newModulus) {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}

        virtual bool IsMontgomeryRepresentation() const {return false;}

        virtual Integer ConvertIn(const Integer &a) const
                {return a%m_modulus;}

        virtual Integer ConvertOut(const Integer &a) const
                {return a;}

        const Integer& Half(const Integer &a) const;

        bool Equal(const Integer &a, const Integer &b) const
                {return a==b;}

        const Integer& Identity() const
                {return Integer::Zero();}

        const Integer& Add(const Integer &a, const Integer &b) const;

        Integer& Accumulate(Integer &a, const Integer &b) const;

        const Integer& Inverse(const Integer &a) const;

        const Integer& Subtract(const Integer &a, const Integer &b) const;

        Integer& Reduce(Integer &a, const Integer &b) const;

        const Integer& Double(const Integer &a) const
                {return Add(a, a);}

        const Integer& MultiplicativeIdentity() const
                {return Integer::One();}

        const Integer& Multiply(const Integer &a, const Integer &b) const
                {return m_result1 = a*b%m_modulus;}

        const Integer& Square(const Integer &a) const
                {return m_result1 = a.Squared()%m_modulus;}

        bool IsUnit(const Integer &a) const
                {return Integer::Gcd(a, m_modulus).IsUnit();}

        const Integer& MultiplicativeInverse(const Integer &a) const
                {return m_result1 = a.InverseMod(m_modulus);}

        const Integer& Divide(const Integer &a, const Integer &b) const
                {return Multiply(a, MultiplicativeInverse(b));}

        Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;

        void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;

        unsigned int MaxElementBitLength() const
                {return (m_modulus-1).BitCount();}

        unsigned int MaxElementByteLength() const
                {return (m_modulus-1).ByteCount();}

        Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const
                // left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
        { 
                return Element( rng , Integer( (long) 0) , m_modulus - Integer( (long) 1 )   ) ; 
        }   

        bool operator==(const ModularArithmetic &rhs) const
                {return m_modulus == rhs.m_modulus;}

        static const RandomizationParameter DefaultRandomizationParameter ;

protected:
        Integer m_modulus;
        mutable Integer m_result, m_result1;

};

// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;

//! do modular arithmetics in Montgomery representation for increased speed
/*! \note the Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2 */
class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
{
public:
        MontgomeryRepresentation(const Integer &modulus);       // modulus must be odd

        virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}

        bool IsMontgomeryRepresentation() const {return true;}

        Integer ConvertIn(const Integer &a) const
                {return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}

        Integer ConvertOut(const Integer &a) const;

        const Integer& MultiplicativeIdentity() const
                {return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_modulus;}

        const Integer& Multiply(const Integer &a, const Integer &b) const;

        const Integer& Square(const Integer &a) const;

        const Integer& MultiplicativeInverse(const Integer &a) const;

        Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
                {return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);}

        void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
                {AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}

private:
        Integer m_u;
        mutable SecAlignedWordBlock m_workspace;
};

NAMESPACE_END

#endif

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