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-/*
- Copyright (c) 2000, 2012, Oracle and/or its affiliates. All rights reserved.
-
- This program 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; version 2 of the License.
-
- This program 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; see the file COPYING. If not, write to the
- Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
- MA 02110-1301 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 Group
-class 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 Ring
-class TAOCRYPT_NO_VTABLE AbstractRing : public AbstractGroup
-{
-public:
- typedef Integer Element;
-
- AbstractRing() : AbstractGroup() {m_mg.m_pRing = this;}
- AbstractRing(const AbstractRing &source) : AbstractGroup()
- {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 Domain
-class 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;
-};
-
-
-// EuclideanDomainOf
-class 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