modarith.hpp

/*
   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 modarith.h from CryptoPP */


#ifndef TAO_CRYPT_MODARITH_HPP
#define TAO_CRYPT_MODARITH_HPP

#include "misc.hpp"
#include "algebra.hpp"

namespace TaoCrypt {


// ModularArithmetic
class ModularArithmetic : public AbstractRing
{
public:

    typedef int RandomizationParameter;
    typedef Integer Element;

    ModularArithmetic(const Integer &modulus = Integer::One())
        : modulus(modulus), result((word)0, modulus.reg_.size()) {}

    ModularArithmetic(const ModularArithmetic &ma)
        : AbstractRing(),
        modulus(ma.modulus), result((word)0, modulus.reg_.size()) {}

    const Integer& GetModulus() const {return modulus;}
    void SetModulus(const Integer &newModulus) 
    {   
        modulus = newModulus;
        result.reg_.resize(modulus.reg_.size());
    }

    virtual bool IsMontgomeryRepresentation() const {return false;}

    virtual Integer ConvertIn(const Integer &a) const
        {return a%modulus;}

    virtual Integer ConvertOut(const Integer &a) const
        {return a;}

    const Integer& Half(const Integer &a) const;

    bool Equal(const Integer &a, const Integer &b) const
        {return a==b;}

    const Integer& Identity() const
        {return Integer::Zero();}

    const Integer& Add(const Integer &a, const Integer &b) const;

    Integer& Accumulate(Integer &a, const Integer &b) const;

    const Integer& Inverse(const Integer &a) const;

    const Integer& Subtract(const Integer &a, const Integer &b) const;

    Integer& Reduce(Integer &a, const Integer &b) const;

    const Integer& Double(const Integer &a) const
        {return Add(a, a);}

    const Integer& MultiplicativeIdentity() const
        {return Integer::One();}

    const Integer& Multiply(const Integer &a, const Integer &b) const
        {return result1 = a*b%modulus;}

    const Integer& Square(const Integer &a) const
        {return result1 = a.Squared()%modulus;}

    bool IsUnit(const Integer &a) const
        {return Integer::Gcd(a, modulus).IsUnit();}

    const Integer& MultiplicativeInverse(const Integer &a) const
        {return result1 = a.InverseMod(modulus);}

    const Integer& Divide(const Integer &a, const Integer &b) const
        {return Multiply(a, MultiplicativeInverse(b));}

    Integer CascadeExponentiate(const Integer &x, const Integer &e1,
                                const Integer &y, const Integer &e2) const;

    void SimultaneousExponentiate(Element *results, const Element &base,
                  const Integer *exponents, unsigned int exponentsCount) const;

    unsigned int MaxElementBitLength() const
        {return (modulus-1).BitCount();}

    unsigned int MaxElementByteLength() const
        {return (modulus-1).ByteCount();}


    static const RandomizationParameter DefaultRandomizationParameter;

protected:
    Integer modulus;
    mutable Integer result, result1;

};



class MontgomeryRepresentation : public ModularArithmetic
{
public:
    MontgomeryRepresentation(const Integer &modulus);   // modulus must be odd

    bool IsMontgomeryRepresentation() const {return true;}

    Integer ConvertIn(const Integer &a) const
        {return (a<<(WORD_BITS*modulus.reg_.size()))%modulus;}

    Integer ConvertOut(const Integer &a) const;

    const Integer& MultiplicativeIdentity() const
     {return result1 = Integer::Power2(WORD_BITS*modulus.reg_.size())%modulus;}

    const Integer& Multiply(const Integer &a, const Integer &b) const;

    const Integer& Square(const Integer &a) const;

    const Integer& MultiplicativeInverse(const Integer &a) const;

    Integer CascadeExponentiate(const Integer &x, const Integer &e1,
                                const Integer &y, const Integer &e2) const
        {return AbstractRing::CascadeExponentiate(x, e1, y, e2);}

    void SimultaneousExponentiate(Element *results, const Element &base,
            const Integer *exponents, unsigned int exponentsCount) const
        {AbstractRing::SimultaneousExponentiate(results, base,
                                                exponents, exponentsCount);}

private:
    Integer u;
    mutable AlignedWordBlock workspace;
};




} // namespace

#endif // TAO_CRYPT_MODARITH_HPP