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// 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
//! \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())
: AbstractRing<Integer>(), m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
ModularArithmetic(const ModularArithmetic &ma)
: AbstractRing<Integer>(), m_modulus(ma.m_modulus), m_result((word)0, ma.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
{
CRYPTOPP_UNUSED(ignore_for_now);
return Element(rng, Integer::Zero(), m_modulus - Integer::One()) ;
}
bool operator==(const ModularArithmetic &rhs) const
{return m_modulus == rhs.m_modulus;}
static const RandomizationParameter DefaultRandomizationParameter ;
#ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
virtual ~ModularArithmetic() {}
#endif
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 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);}
#ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
virtual ~MontgomeryRepresentation() {}
#endif
private:
Integer m_u;
mutable IntegerSecBlock m_workspace;
};
NAMESPACE_END
#endif
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