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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