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316 lines
10 KiB
C++
316 lines
10 KiB
C++
/* algebra.hpp
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*
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* Copyright (C) 2003 Sawtooth Consulting Ltd.
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*
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* This file is part of yaSSL.
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*
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* yaSSL is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* yaSSL is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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*/
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/* based on Wei Dai's algebra.h from CryptoPP */
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#ifndef TAO_CRYPT_ALGEBRA_HPP
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#define TAO_CRYPT_ALGEBRA_HPP
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#include "misc.hpp"
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namespace TaoCrypt {
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class Integer;
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// "const Element&" returned by member functions are references
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// to internal data members. Since each object may have only
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// one such data member for holding results, the following code
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// will produce incorrect results:
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// abcd = group.Add(group.Add(a,b), group.Add(c,d));
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// But this should be fine:
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// abcd = group.Add(a, group.Add(b, group.Add(c,d));
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//! Abstract Group
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template <class T> class TAOCRYPT_NO_VTABLE AbstractGroup
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{
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public:
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typedef T Element;
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virtual ~AbstractGroup() {}
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virtual bool Equal(const Element &a, const Element &b) const =0;
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virtual const Element& Identity() const =0;
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virtual const Element& Add(const Element &a, const Element &b) const =0;
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virtual const Element& Inverse(const Element &a) const =0;
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virtual bool InversionIsFast() const {return false;}
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virtual const Element& Double(const Element &a) const;
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virtual const Element& Subtract(const Element &a, const Element &b) const;
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virtual Element& Accumulate(Element &a, const Element &b) const;
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virtual Element& Reduce(Element &a, const Element &b) const;
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virtual Element ScalarMultiply(const Element &a, const Integer &e) const;
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virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1,
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const Element &y, const Integer &e2) const;
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virtual void SimultaneousMultiply(Element *results, const Element &base,
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const Integer *exponents, unsigned int exponentsCount) const;
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};
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//! Abstract Ring
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template <class T> class TAOCRYPT_NO_VTABLE AbstractRing
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: public AbstractGroup<T>
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{
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public:
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typedef T Element;
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AbstractRing() {m_mg.m_pRing = this;}
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AbstractRing(const AbstractRing &source) {m_mg.m_pRing = this;}
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AbstractRing& operator=(const AbstractRing &source) {return *this;}
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virtual bool IsUnit(const Element &a) const =0;
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virtual const Element& MultiplicativeIdentity() const =0;
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virtual const Element& Multiply(const Element&, const Element&) const =0;
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virtual const Element& MultiplicativeInverse(const Element &a) const =0;
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virtual const Element& Square(const Element &a) const;
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virtual const Element& Divide(const Element &a, const Element &b) const;
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virtual Element Exponentiate(const Element &a, const Integer &e) const;
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virtual Element CascadeExponentiate(const Element &x, const Integer &e1,
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const Element &y, const Integer &e2) const;
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virtual void SimultaneousExponentiate(Element *results, const Element&,
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const Integer *exponents, unsigned int exponentsCount) const;
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virtual const AbstractGroup<T>& MultiplicativeGroup() const
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{return m_mg;}
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private:
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class MultiplicativeGroupT : public AbstractGroup<T>
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{
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public:
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const AbstractRing<T>& GetRing() const
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{return *m_pRing;}
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bool Equal(const Element &a, const Element &b) const
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{return GetRing().Equal(a, b);}
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const Element& Identity() const
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{return GetRing().MultiplicativeIdentity();}
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const Element& Add(const Element &a, const Element &b) const
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{return GetRing().Multiply(a, b);}
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Element& Accumulate(Element &a, const Element &b) const
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{return a = GetRing().Multiply(a, b);}
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const Element& Inverse(const Element &a) const
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{return GetRing().MultiplicativeInverse(a);}
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const Element& Subtract(const Element &a, const Element &b) const
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{return GetRing().Divide(a, b);}
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Element& Reduce(Element &a, const Element &b) const
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{return a = GetRing().Divide(a, b);}
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const Element& Double(const Element &a) const
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{return GetRing().Square(a);}
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Element ScalarMultiply(const Element &a, const Integer &e) const
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{return GetRing().Exponentiate(a, e);}
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Element CascadeScalarMultiply(const Element &x, const Integer &e1,
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const Element &y, const Integer &e2) const
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{return GetRing().CascadeExponentiate(x, e1, y, e2);}
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void SimultaneousMultiply(Element *results, const Element &base,
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const Integer *exponents, unsigned int exponentsCount) const
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{GetRing().SimultaneousExponentiate(results, base, exponents,
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exponentsCount);}
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const AbstractRing<T> *m_pRing;
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};
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MultiplicativeGroupT m_mg;
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};
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// ********************************************************
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//! Base and Exponent
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template <class T, class E = Integer>
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struct BaseAndExponent
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{
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public:
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BaseAndExponent() {}
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BaseAndExponent(const T &base, const E &exponent) : base(base),
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exponent(exponent) {}
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bool operator<(const BaseAndExponent<T, E> &rhs) const
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{return exponent < rhs.exponent;}
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T base;
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E exponent;
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};
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// VC60 workaround: incomplete member template support
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template <class Element, class Iterator>
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Element GeneralCascadeMultiplication(const AbstractGroup<Element> &group,
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Iterator begin, Iterator end);
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template <class Element, class Iterator>
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Element GeneralCascadeExponentiation(const AbstractRing<Element> &ring,
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Iterator begin, Iterator end);
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// ********************************************************
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//! Abstract Euclidean Domain
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template <class T> class TAOCRYPT_NO_VTABLE AbstractEuclideanDomain
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: public AbstractRing<T>
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{
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public:
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typedef T Element;
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virtual void DivisionAlgorithm(Element &r, Element &q, const Element &a,
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const Element &d) const =0;
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virtual const Element& Mod(const Element &a, const Element &b) const =0;
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virtual const Element& Gcd(const Element &a, const Element &b) const;
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protected:
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mutable Element result;
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};
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// ********************************************************
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//! EuclideanDomainOf
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template <class T> class EuclideanDomainOf : public AbstractEuclideanDomain<T>
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{
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public:
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typedef T Element;
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EuclideanDomainOf() {}
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bool Equal(const Element &a, const Element &b) const
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{return a==b;}
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const Element& Identity() const
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{return Element::Zero();}
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const Element& Add(const Element &a, const Element &b) const
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{return result = a+b;}
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Element& Accumulate(Element &a, const Element &b) const
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{return a+=b;}
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const Element& Inverse(const Element &a) const
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{return result = -a;}
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const Element& Subtract(const Element &a, const Element &b) const
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{return result = a-b;}
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Element& Reduce(Element &a, const Element &b) const
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{return a-=b;}
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const Element& Double(const Element &a) const
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{return result = a.Doubled();}
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const Element& MultiplicativeIdentity() const
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{return Element::One();}
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const Element& Multiply(const Element &a, const Element &b) const
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{return result = a*b;}
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const Element& Square(const Element &a) const
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{return result = a.Squared();}
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bool IsUnit(const Element &a) const
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{return a.IsUnit();}
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const Element& MultiplicativeInverse(const Element &a) const
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{return result = a.MultiplicativeInverse();}
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const Element& Divide(const Element &a, const Element &b) const
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{return result = a/b;}
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const Element& Mod(const Element &a, const Element &b) const
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{return result = a%b;}
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void DivisionAlgorithm(Element &r, Element &q, const Element &a,
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const Element &d) const
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{Element::Divide(r, q, a, d);}
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private:
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mutable Element result;
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};
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//! Quotient Ring
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template<class T> class QuotientRing : public AbstractRing<typename T::Element>
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{
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public:
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typedef T EuclideanDomain;
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typedef typename T::Element Element;
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QuotientRing(const EuclideanDomain &domain, const Element &modulus)
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: m_domain(domain), m_modulus(modulus) {}
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const EuclideanDomain & GetDomain() const
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{return m_domain;}
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const Element& GetModulus() const
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{return m_modulus;}
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bool Equal(const Element &a, const Element &b) const
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{return m_domain.Equal(m_domain.Mod(m_domain.Subtract(a, b),
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m_modulus), m_domain.Identity());}
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const Element& Identity() const
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{return m_domain.Identity();}
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const Element& Add(const Element &a, const Element &b) const
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{return m_domain.Add(a, b);}
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Element& Accumulate(Element &a, const Element &b) const
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{return m_domain.Accumulate(a, b);}
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const Element& Inverse(const Element &a) const
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{return m_domain.Inverse(a);}
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const Element& Subtract(const Element &a, const Element &b) const
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{return m_domain.Subtract(a, b);}
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Element& Reduce(Element &a, const Element &b) const
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{return m_domain.Reduce(a, b);}
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const Element& Double(const Element &a) const
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{return m_domain.Double(a);}
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bool IsUnit(const Element &a) const
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{return m_domain.IsUnit(m_domain.Gcd(a, m_modulus));}
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const Element& MultiplicativeIdentity() const
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{return m_domain.MultiplicativeIdentity();}
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const Element& Multiply(const Element &a, const Element &b) const
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{return m_domain.Mod(m_domain.Multiply(a, b), m_modulus);}
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const Element& Square(const Element &a) const
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{return m_domain.Mod(m_domain.Square(a), m_modulus);}
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const Element& MultiplicativeInverse(const Element &a) const;
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protected:
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EuclideanDomain m_domain;
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Element m_modulus;
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};
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} // namespace
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#endif // TAO_CRYPT_ALGEBRA_HPP
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