algebra.h
#ifndef CRYPTOPP_ALGEBRA_H
#define CRYPTOPP_ALGEBRA_H
#include "config.h"
NAMESPACE_BEGIN(CryptoPP)
class Integer;
// "const Element&" 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:
// abcd = group.Add(group.Add(a,b), group.Add(c,d));
// But this should be fine:
// abcd = group.Add(a, group.Add(b, group.Add(c,d));
//! Abstract Group
template <class T> class CRYPTOPP_NO_VTABLE AbstractGroup
{
public:
typedef T Element;
virtual ~AbstractGroup() {}
virtual bool Equal(const Element &a, const Element &b) const =0;
virtual const Element& Identity() const =0;
virtual const Element& Add(const Element &a, const Element &b) const =0;
virtual const Element& Inverse(const Element &a) const =0;
virtual bool InversionIsFast() const {return false;}
virtual const Element& Double(const Element &a) const;
virtual const Element& Subtract(const Element &a, const Element &b) const;
virtual Element& Accumulate(Element &a, const Element &b) const;
virtual Element& Reduce(Element &a, const Element &b) const;
virtual Element ScalarMultiply(const Element &a, const Integer &e) const;
virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
virtual void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
};
//! Abstract Ring
template <class T> class CRYPTOPP_NO_VTABLE AbstractRing : public AbstractGroup<T>
{
public:
typedef T Element;
AbstractRing() {m_mg.m_pRing = this;}
AbstractRing(const AbstractRing &source) {m_mg.m_pRing = this;}
AbstractRing& operator=(const AbstractRing &source) {return *this;}
virtual bool IsUnit(const Element &a) const =0;
virtual const Element& MultiplicativeIdentity() const =0;
virtual const Element& Multiply(const Element &a, const Element &b) const =0;
virtual const Element& MultiplicativeInverse(const Element &a) const =0;
virtual const Element& Square(const Element &a) const;
virtual const Element& Divide(const Element &a, const Element &b) const;
virtual Element Exponentiate(const Element &a, const Integer &e) const;
virtual Element CascadeExponentiate(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
virtual void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
virtual const AbstractGroup<T>& MultiplicativeGroup() const
{return m_mg;}
private:
class MultiplicativeGroupT : public AbstractGroup<T>
{
public:
const AbstractRing<T>& GetRing() const
{return *m_pRing;}
bool Equal(const Element &a, const Element &b) const
{return GetRing().Equal(a, b);}
const Element& Identity() const
{return GetRing().MultiplicativeIdentity();}
const Element& Add(const Element &a, const Element &b) const
{return GetRing().Multiply(a, b);}
Element& Accumulate(Element &a, const Element &b) const
{return a = GetRing().Multiply(a, b);}
const Element& Inverse(const Element &a) const
{return GetRing().MultiplicativeInverse(a);}
const Element& Subtract(const Element &a, const Element &b) const
{return GetRing().Divide(a, b);}
Element& Reduce(Element &a, const Element &b) const
{return a = GetRing().Divide(a, b);}
const Element& Double(const Element &a) const
{return GetRing().Square(a);}
Element ScalarMultiply(const Element &a, const Integer &e) const
{return GetRing().Exponentiate(a, e);}
Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
{return GetRing().CascadeExponentiate(x, e1, y, e2);}
void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
{GetRing().SimultaneousExponentiate(results, base, exponents, exponentsCount);}
const AbstractRing<T> *m_pRing;
};
MultiplicativeGroupT m_mg;
};
// ********************************************************
//! Base and Exponent
template <class T, class E = Integer>
struct BaseAndExponent
{
public:
BaseAndExponent() {}
BaseAndExponent(const T &base, const E &exponent) : base(base), exponent(exponent) {}
bool operator<(const BaseAndExponent<T, E> &rhs) const {return exponent < rhs.exponent;}
T base;
E exponent;
};
// VC60 workaround: incomplete member template support
template <class Element, class Iterator>
Element GeneralCascadeMultiplication(const AbstractGroup<Element> &group, Iterator begin, Iterator end);
template <class Element, class Iterator>
Element GeneralCascadeExponentiation(const AbstractRing<Element> &ring, Iterator begin, Iterator end);
// ********************************************************
//! Abstract Euclidean Domain
template <class T> class CRYPTOPP_NO_VTABLE AbstractEuclideanDomain : public AbstractRing<T>
{
public:
typedef T Element;
virtual void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const =0;
virtual const Element& Mod(const Element &a, const Element &b) const =0;
virtual const Element& Gcd(const Element &a, const Element &b) const;
protected:
mutable Element result;
};
// ********************************************************
//! EuclideanDomainOf
template <class T> class EuclideanDomainOf : public AbstractEuclideanDomain<T>
{
public:
typedef T Element;
EuclideanDomainOf() {}
bool Equal(const Element &a, const Element &b) const
{return a==b;}
const Element& Identity() const
{return Element::Zero();}
const Element& Add(const Element &a, const Element &b) const
{return result = a+b;}
Element& Accumulate(Element &a, const Element &b) const
{return a+=b;}
const Element& Inverse(const Element &a) const
{return result = -a;}
const Element& Subtract(const Element &a, const Element &b) const
{return result = a-b;}
Element& Reduce(Element &a, const Element &b) const
{return a-=b;}
const Element& Double(const Element &a) const
{return result = a.Doubled();}
const Element& MultiplicativeIdentity() const
{return Element::One();}
const Element& Multiply(const Element &a, const Element &b) const
{return result = a*b;}
const Element& Square(const Element &a) const
{return result = a.Squared();}
bool IsUnit(const Element &a) const
{return a.IsUnit();}
const Element& MultiplicativeInverse(const Element &a) const
{return result = a.MultiplicativeInverse();}
const Element& Divide(const Element &a, const Element &b) const
{return result = a/b;}
const Element& Mod(const Element &a, const Element &b) const
{return result = a%b;}
void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const
{Element::Divide(r, q, a, d);}
bool operator==(const EuclideanDomainOf<T> &rhs) const
{return true;}
private:
mutable Element result;
};
//! Quotient Ring
template <class T> class QuotientRing : public AbstractRing<typename T::Element>
{
public:
typedef T EuclideanDomain;
typedef typename T::Element Element;
QuotientRing(const EuclideanDomain &domain, const Element &modulus)
: m_domain(domain), m_modulus(modulus) {}
const EuclideanDomain & GetDomain() const
{return m_domain;}
const Element& GetModulus() const
{return m_modulus;}
bool Equal(const Element &a, const Element &b) const
{return m_domain.Equal(m_domain.Mod(m_domain.Subtract(a, b), m_modulus), m_domain.Identity());}
const Element& Identity() const
{return m_domain.Identity();}
const Element& Add(const Element &a, const Element &b) const
{return m_domain.Add(a, b);}
Element& Accumulate(Element &a, const Element &b) const
{return m_domain.Accumulate(a, b);}
const Element& Inverse(const Element &a) const
{return m_domain.Inverse(a);}
const Element& Subtract(const Element &a, const Element &b) const
{return m_domain.Subtract(a, b);}
Element& Reduce(Element &a, const Element &b) const
{return m_domain.Reduce(a, b);}
const Element& Double(const Element &a) const
{return m_domain.Double(a);}
bool IsUnit(const Element &a) const
{return m_domain.IsUnit(m_domain.Gcd(a, m_modulus));}
const Element& MultiplicativeIdentity() const
{return m_domain.MultiplicativeIdentity();}
const Element& Multiply(const Element &a, const Element &b) const
{return m_domain.Mod(m_domain.Multiply(a, b), m_modulus);}
const Element& Square(const Element &a) const
{return m_domain.Mod(m_domain.Square(a), m_modulus);}
const Element& MultiplicativeInverse(const Element &a) const;
bool operator==(const QuotientRing<T> &rhs) const
{return m_domain == rhs.m_domain && m_modulus == rhs.m_modulus;}
protected:
EuclideanDomain m_domain;
Element m_modulus;
};
NAMESPACE_END
#ifdef CRYPTOPP_MANUALLY_INSTANTIATE_TEMPLATES
#include "algebra.cpp"
#endif
#endif
AbstractEuclideanDomain
Abstract Euclidean Domain.
Definition: algebra.h:138
Square
Square
Definition: square.h:19
QuotientRing
Quotient Ring.
Definition: algebra.h:218
AbstractRing
Abstract Ring.
Definition: algebra.h:44
Integer
multiple precision integer and basic arithmetics
Definition: integer.h:26
AbstractGroup
Abstract Group.
Definition: algebra.h:19
EuclideanDomainOf
EuclideanDomainOf.
Definition: algebra.h:155
BaseAndExponent
Base and Exponent.
Definition: algebra.h:119