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Diffstat (limited to 'src-cryptopp/algebra.h')
| -rw-r--r-- | src-cryptopp/algebra.h | 285 |
1 files changed, 285 insertions, 0 deletions
diff --git a/src-cryptopp/algebra.h b/src-cryptopp/algebra.h new file mode 100644 index 0000000..13038bd --- /dev/null +++ b/src-cryptopp/algebra.h @@ -0,0 +1,285 @@ +#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 |