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Файл:Документация по криптоалгоритмам / CRYPTO30 / algebra
.h#ifndef CRYPTOPP_ALGEBRA_H
#define CRYPTOPP_ALGEBRA_H
NAMESPACE_BEGIN(CryptoPP)
class Integer;
template <class T> class AbstractGroup
{
public:
typedef T Element;
virtual ~AbstractGroup() {}
virtual bool Equal(const Element &a, const Element &b) const =0;
virtual Element Zero() const =0;
virtual Element Add(const Element &a, const Element &b) const =0;
virtual Element Inverse(const Element &a) const =0;
virtual Element Double(const Element &a) const;
virtual 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 IntMultiply(const Element &a, const Integer &e) const;
virtual Element CascadeIntMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
};
template <class T> class AbstractRing : public AbstractGroup<T>
{
public:
typedef T Element;
virtual bool IsUnit(const Element &a) const =0;
virtual Element One() const =0;
virtual Element Multiply(const Element &a, const Element &b) const =0;
virtual Element MultiplicativeInverse(const Element &a) const =0;
virtual Element Square(const Element &a) const;
virtual 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;
};
// ********************************************************
// 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, class ConstIterator>
void SimultaneousMultiplication(Iterator result, const AbstractGroup<Element> &group, const Element &base, ConstIterator expBegin, ConstIterator expEnd);
template <class Element, class Iterator>
Element GeneralCascadeExponentiation(const AbstractRing<Element> &ring, Iterator begin, Iterator end);
template <class Element, class Iterator, class ConstIterator>
void SimultaneousExponentiation(Iterator result, const AbstractRing<Element> &ring, const Element &base, ConstIterator expBegin, ConstIterator expEnd);
// ********************************************************
template <class T> class AbstractField : public AbstractRing<T>
{
public:
bool IsUnit(const Element &a) const
{return !Equal(a, Zero());}
};
template <class T> class AbstractEuclideanDomain : public AbstractRing<T>
{
public:
typedef T Element;
virtual void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const =0;
virtual Element Mod(const Element &a, const Element &b) const;
virtual Element Gcd(const Element &a, const Element &b) const;
};
// ********************************************************
template <class T> class MultiplicativeGroup : public AbstractGroup<typename T::Element>
{
public:
typedef T Ring;
MultiplicativeGroup(const Ring &m_ring)
: m_ring(m_ring) {}
const Ring & GetRing() const
{return m_ring;}
bool Equal(const Element &a, const Element &b) const
{return m_ring.Equal(a, b);}
Element Zero() const
{return m_ring.One();}
Element Add(const Element &a, const Element &b) const
{return m_ring.Multiply(a, b);}
Element& Accumulate(Element &a, const Element &b) const
{return a = m_ring.Multiply(a, b);}
Element Inverse(const Element &a) const
{return m_ring.MultiplicativeInverse(a);}
Element Subtract(const Element &a, const Element &b) const
{return m_ring.Divide(a, b);}
Element& Reduce(Element &a, const Element &b) const
{return a = m_ring.Divide(a, b);}
Element Double(const Element &a) const
{return m_ring.Square(a);}
protected:
const Ring &m_ring;
};
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;}
Element Zero() const
{return Element::Zero();}
Element Add(const Element &a, const Element &b) const
{return a+b;}
Element& Accumulate(Element &a, const Element &b) const
{return a+=b;}
Element Inverse(const Element &a) const
{return -a;}
Element Subtract(const Element &a, const Element &b) const
{return a-b;}
Element& Reduce(Element &a, const Element &b) const
{return a-=b;}
Element Double(const Element &a) const
{return a.Doubled();}
Element One() const
{return Element::One();}
Element Multiply(const Element &a, const Element &b) const
{return a*b;}
Element Square(const Element &a) const
{return a.Squared();}
bool IsUnit(const Element &a) const
{return a.IsUnit();}
Element MultiplicativeInverse(const Element &a) const
{return a.MultiplicativeInverse();}
Element Divide(const Element &a, const Element &b) const
{return a/b;}
Element Mod(const Element &a, const Element &b) const
{return a%b;}
void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const
{Element::Divide(r, q, a, d);}
};
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.Zero());}
Element Zero() const
{return m_domain.Zero();}
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);}
Element Inverse(const Element &a) const
{return m_domain.Inverse(a);}
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);}
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));}
Element One() const
{return m_domain.One();}
Element Multiply(const Element &a, const Element &b) const
{return m_domain.Mod(m_domain.Multiply(a, b), m_modulus);}
Element Square(const Element &a) const
{return m_domain.Mod(m_domain.Square(a), m_modulus);}
Element MultiplicativeInverse(const Element &a) const;
protected:
const EuclideanDomain &m_domain;
Element m_modulus;
};
NAMESPACE_END
#endif
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