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/*
Copyright (C) 2000-2007 MySQL AB
Use is subject to license terms
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 02110-1335 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;
};
//! do modular arithmetics in Montgomery representation for increased speed
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
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