/* algebra.hpp                                 * * Copyright (C) 2003 Sawtooth Consulting Ltd. * * This file is part of yaSSL. * * yaSSL is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * yaSSL is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA *//* based on Wei Dai's algebra.h from CryptoPP */#ifndef TAO_CRYPT_ALGEBRA_HPP#define TAO_CRYPT_ALGEBRA_HPP#include "integer.hpp"namespace TaoCrypt {// "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 Groupclass TAOCRYPT_NO_VTABLE AbstractGroup : public virtual_base{public:    typedef Integer 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 Ringclass TAOCRYPT_NO_VTABLE AbstractRing : public AbstractGroup{public:    typedef Integer Element;    AbstractRing() : AbstractGroup() {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&, const Element&) 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&,                  const Integer *exponents, unsigned int exponentsCount) const;    virtual const AbstractGroup& MultiplicativeGroup() const        {return m_mg;}private:    class MultiplicativeGroupT : public AbstractGroup    {    public:        const AbstractRing& 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* m_pRing;    };    MultiplicativeGroupT m_mg;};// Abstract Euclidean Domainclass TAOCRYPT_NO_VTABLE AbstractEuclideanDomain    : public AbstractRing{public:    typedef Integer 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;};// EuclideanDomainOfclass EuclideanDomainOf : public AbstractEuclideanDomain{public:    typedef Integer 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);}private:    mutable Element result;};} // namespace#endif // TAO_CRYPT_ALGEBRA_HPP