source: git/src-cryptopp/modarith.h

// modarith.h - written and placed in the public domain by Wei Dai

//! \file modarith.h
//! \brief Class file for performing modular arithmetic.

#ifndef CRYPTOPP_MODARITH_H
#define CRYPTOPP_MODARITH_H

// implementations are in integer.cpp

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

NAMESPACE_BEGIN(CryptoPP)

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

//! \class ModularArithmetic
//! \brief Ring of congruence classes modulo n
//! \details This implementation represents each congruence class as the smallest
//!   non-negative integer in that class.
//! \details <tt>const Element&</tt> returned by member functions are references
//!   to internal data members. Since each object may have only
//!   one such data member for holding results, the following code
//!   will produce incorrect results:
//!   <pre>    abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre>
//!   But this should be fine:
//!   <pre>    abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
{
public:

        typedef int RandomizationParameter;
        typedef Integer Element;

#ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
        virtual ~ModularArithmetic() {}
#endif

        //! \brief Construct a ModularArithmetic
        //! \param modulus congruence class modulus
        ModularArithmetic(const Integer &modulus = Integer::One())
                : AbstractRing<Integer>(), m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}

        //! \brief Copy construct a ModularArithmetic
        //! \param ma other ModularArithmetic
        ModularArithmetic(const ModularArithmetic &ma)
                : AbstractRing<Integer>(), m_modulus(ma.m_modulus), m_result((word)0, ma.m_modulus.reg.size()) {}

        //! \brief Construct a ModularArithmetic
        //! \param bt BER encoded ModularArithmetic
        ModularArithmetic(BufferedTransformation &bt);  // construct from BER encoded parameters

        //! \brief Clone a ModularArithmetic
        //! \returns pointer to a new ModularArithmetic
        //! \details Clone effectively copy constructs a new ModularArithmetic. The caller is
        //!   responsible for deleting the pointer returned from this method.
        virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}

        //! \brief Encodes in DER format
        //! \param bt BufferedTransformation object
        void DEREncode(BufferedTransformation &bt) const;

        //! \brief Encodes element in DER format
        //! \param out BufferedTransformation object
        //! \param a Element to encode
        void DEREncodeElement(BufferedTransformation &out, const Element &a) const;

        //! \brief Decodes element in DER format
        //! \param in BufferedTransformation object
        //! \param a Element to decode
        void BERDecodeElement(BufferedTransformation &in, Element &a) const;

        //! \brief Retrieves the modulus
        //! \returns the modulus
        const Integer& GetModulus() const {return m_modulus;}

        //! \brief Sets the modulus
        //! \param newModulus the new modulus
        void SetModulus(const Integer &newModulus)
                {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}

        //! \brief Retrieves the representation
        //! \returns true if the representation is MontgomeryRepresentation, false otherwise
        virtual bool IsMontgomeryRepresentation() const {return false;}

        //! \brief Reduces an element in the congruence class
        //! \param a element to convert
        //! \returns the reduced element
        //! \details ConvertIn is useful for derived classes, like MontgomeryRepresentation, which
        //!   must convert between representations.
        virtual Integer ConvertIn(const Integer &a) const
                {return a%m_modulus;}

        //! \brief Reduces an element in the congruence class
        //! \param a element to convert
        //! \returns the reduced element
        //! \details ConvertOut is useful for derived classes, like MontgomeryRepresentation, which
        //!   must convert between representations.
        virtual Integer ConvertOut(const Integer &a) const
                {return a;}

        //! \brief TODO
        //! \param a element to convert
        const Integer& Half(const Integer &a) const;

        //! \brief Compare two elements for equality
        //! \param a first element
        //! \param b second element
        //! \returns true if the elements are equal, false otherwise
        //! \details Equal() tests the elements for equality using <tt>a==b</tt>
        bool Equal(const Integer &a, const Integer &b) const
                {return a==b;}

        //! \brief Provides the Identity element
        //! \returns the Identity element
        const Integer& Identity() const
                {return Integer::Zero();}

        //! \brief Adds elements in the ring
        //! \param a first element
        //! \param b second element
        //! \returns the sum of <tt>a</tt> and <tt>b</tt>
        const Integer& Add(const Integer &a, const Integer &b) const;

        //! \brief TODO
        //! \param a first element
        //! \param b second element
        //! \returns TODO
        Integer& Accumulate(Integer &a, const Integer &b) const;

        //! \brief Inverts the element in the ring
        //! \param a first element
        //! \returns the inverse of the element
        const Integer& Inverse(const Integer &a) const;

        //! \brief Subtracts elements in the ring
        //! \param a first element
        //! \param b second element
        //! \returns the difference of <tt>a</tt> and <tt>b</tt>. The element <tt>a</tt> must provide a Subtract member function.
        const Integer& Subtract(const Integer &a, const Integer &b) const;

        //! \brief TODO
        //! \param a first element
        //! \param b second element
        //! \returns TODO
        Integer& Reduce(Integer &a, const Integer &b) const;

        //! \brief Doubles an element in the ring
        //! \param a the element
        //! \returns the element doubled
        //! \details Double returns <tt>Add(a, a)</tt>. The element <tt>a</tt> must provide an Add member function.
        const Integer& Double(const Integer &a) const
                {return Add(a, a);}

        //! \brief Retrieves the multiplicative identity
        //! \returns the multiplicative identity
        //! \details the base class implementations returns 1.
        const Integer& MultiplicativeIdentity() const
                {return Integer::One();}

        //! \brief Multiplies elements in the ring
        //! \param a the multiplicand
        //! \param b the multiplier
        //! \returns the product of a and b
        //! \details Multiply returns <tt>a*b\%n</tt>.
        const Integer& Multiply(const Integer &a, const Integer &b) const
                {return m_result1 = a*b%m_modulus;}

        //! \brief Square an element in the ring
        //! \param a the element
        //! \returns the element squared
        //! \details Square returns <tt>a*a\%n</tt>. The element <tt>a</tt> must provide a Square member function.
        const Integer& Square(const Integer &a) const
                {return m_result1 = a.Squared()%m_modulus;}

        //! \brief Determines whether an element is a unit in the ring
        //! \param a the element
        //! \returns true if the element is a unit after reduction, false otherwise.
        bool IsUnit(const Integer &a) const
                {return Integer::Gcd(a, m_modulus).IsUnit();}

        //! \brief Calculate the multiplicative inverse of an element in the ring
        //! \param a the element
        //! \details MultiplicativeInverse returns <tt>a<sup>-1</sup>\%n</tt>. The element <tt>a</tt> must
        //!   provide a InverseMod member function.
        const Integer& MultiplicativeInverse(const Integer &a) const
                {return m_result1 = a.InverseMod(m_modulus);}

        //! \brief Divides elements in the ring
        //! \param a the dividend
        //! \param b the divisor
        //! \returns the quotient
        //! \details Divide returns <tt>a*b<sup>-1</sup>\%n</tt>.
        const Integer& Divide(const Integer &a, const Integer &b) const
                {return Multiply(a, MultiplicativeInverse(b));}

        //! \brief TODO
        //! \param x first element
        //! \param e1 first exponent
        //! \param y second element
        //! \param e2 second exponent
        //! \returns TODO
        Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;

        //! \brief Exponentiates a base to multiple exponents in the ring
        //! \param results an array of Elements
        //! \param base the base to raise to the exponents
        //! \param exponents an array of exponents
        //! \param exponentsCount the number of exponents in the array
        //! \details SimultaneousExponentiate() raises the base to each exponent in the exponents array and stores the
        //!   result at the respective position in the results array.
        //! \details SimultaneousExponentiate() must be implemented in a derived class.
        //! \pre <tt>COUNTOF(results) == exponentsCount</tt>
        //! \pre <tt>COUNTOF(exponents) == exponentsCount</tt>
        void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;

        //! \brief Provides the maximum bit size of an element in the ring
        //! \returns maximum bit size of an element
        unsigned int MaxElementBitLength() const
                {return (m_modulus-1).BitCount();}

        //! \brief Provides the maximum byte size of an element in the ring
        //! \returns maximum byte size of an element
        unsigned int MaxElementByteLength() const
                {return (m_modulus-1).ByteCount();}

        //! \brief Provides a random element in the ring
        //! \param rng RandomNumberGenerator used to generate material
        //! \param ignore_for_now unused
        //! \returns a random element that is uniformly distributed
        //! \details RandomElement constructs a new element in the range <tt>[0,n-1]</tt>, inclusive.
        //!   The element's class must provide a constructor with the signature <tt>Element(RandomNumberGenerator rng,
        //!   Element min, Element max)</tt>.
        Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0) const
                // left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
        {
                CRYPTOPP_UNUSED(ignore_for_now);
                return Element(rng, Integer::Zero(), m_modulus - Integer::One()) ;
        }

        //! \brief Compares two ModularArithmetic for equality
        //! \param rhs other ModularArithmetic
        //! \returns true if this is equal to the other, false otherwise
        //! \details The operator tests for equality using <tt>this.m_modulus == rhs.m_modulus</tt>.
        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 ;

//! \class MontgomeryRepresentation
//! \brief Performs modular arithmetic in Montgomery representation for increased speed
//! \details The Montgomery representation represents each congruence class <tt>[a]</tt> as
//!   <tt>a*r\%n</tt>, where <tt>r</tt> is a convenient power of 2.
//! \details <tt>const Element&</tt> returned by member functions are references
//!   to internal data members. Since each object may have only
//!   one such data member for holding results, the following code
//!   will produce incorrect results:
//!   <pre>    abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre>
//!   But this should be fine:
//!   <pre>    abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
{
public:
#ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
        virtual ~MontgomeryRepresentation() {}
#endif

        //! \brief Construct a IsMontgomeryRepresentation
        //! \param modulus congruence class modulus
        //! \note The modulus must be odd.
        MontgomeryRepresentation(const Integer &modulus);

        //! \brief Clone a MontgomeryRepresentation
        //! \returns pointer to a new MontgomeryRepresentation
        //! \details Clone effectively copy constructs a new MontgomeryRepresentation. The caller is
        //!   responsible for deleting the pointer returned from this method.
        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 IntegerSecBlock m_workspace;
};

NAMESPACE_END

#endif