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165 lines
4.9 KiB
C++
165 lines
4.9 KiB
C++
/*
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Copyright (C) 2000-2007 MySQL AB
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; version 2 of the License.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; see the file COPYING. If not, write to the
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Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
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MA 02110-1301 USA.
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*/
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/* based on Wei Dai's modarith.h from CryptoPP */
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#ifndef TAO_CRYPT_MODARITH_HPP
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#define TAO_CRYPT_MODARITH_HPP
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#include "misc.hpp"
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#include "algebra.hpp"
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namespace TaoCrypt {
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// ModularArithmetic
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class ModularArithmetic : public AbstractRing
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{
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public:
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typedef int RandomizationParameter;
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typedef Integer Element;
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ModularArithmetic(const Integer &modulus = Integer::One())
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: modulus(modulus), result((word)0, modulus.reg_.size()) {}
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ModularArithmetic(const ModularArithmetic &ma)
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: AbstractRing(),
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modulus(ma.modulus), result((word)0, modulus.reg_.size()) {}
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const Integer& GetModulus() const {return modulus;}
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void SetModulus(const Integer &newModulus)
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{
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modulus = newModulus;
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result.reg_.resize(modulus.reg_.size());
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}
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virtual bool IsMontgomeryRepresentation() const {return false;}
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virtual Integer ConvertIn(const Integer &a) const
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{return a%modulus;}
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virtual Integer ConvertOut(const Integer &a) const
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{return a;}
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const Integer& Half(const Integer &a) const;
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bool Equal(const Integer &a, const Integer &b) const
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{return a==b;}
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const Integer& Identity() const
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{return Integer::Zero();}
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const Integer& Add(const Integer &a, const Integer &b) const;
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Integer& Accumulate(Integer &a, const Integer &b) const;
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const Integer& Inverse(const Integer &a) const;
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const Integer& Subtract(const Integer &a, const Integer &b) const;
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Integer& Reduce(Integer &a, const Integer &b) const;
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const Integer& Double(const Integer &a) const
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{return Add(a, a);}
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const Integer& MultiplicativeIdentity() const
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{return Integer::One();}
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const Integer& Multiply(const Integer &a, const Integer &b) const
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{return result1 = a*b%modulus;}
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const Integer& Square(const Integer &a) const
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{return result1 = a.Squared()%modulus;}
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bool IsUnit(const Integer &a) const
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{return Integer::Gcd(a, modulus).IsUnit();}
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const Integer& MultiplicativeInverse(const Integer &a) const
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{return result1 = a.InverseMod(modulus);}
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const Integer& Divide(const Integer &a, const Integer &b) const
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{return Multiply(a, MultiplicativeInverse(b));}
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Integer CascadeExponentiate(const Integer &x, const Integer &e1,
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const Integer &y, const Integer &e2) const;
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void SimultaneousExponentiate(Element *results, const Element &base,
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const Integer *exponents, unsigned int exponentsCount) const;
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unsigned int MaxElementBitLength() const
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{return (modulus-1).BitCount();}
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unsigned int MaxElementByteLength() const
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{return (modulus-1).ByteCount();}
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static const RandomizationParameter DefaultRandomizationParameter;
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protected:
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Integer modulus;
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mutable Integer result, result1;
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};
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//! do modular arithmetics in Montgomery representation for increased speed
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class MontgomeryRepresentation : public ModularArithmetic
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{
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public:
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MontgomeryRepresentation(const Integer &modulus); // modulus must be odd
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bool IsMontgomeryRepresentation() const {return true;}
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Integer ConvertIn(const Integer &a) const
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{return (a<<(WORD_BITS*modulus.reg_.size()))%modulus;}
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Integer ConvertOut(const Integer &a) const;
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const Integer& MultiplicativeIdentity() const
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{return result1 = Integer::Power2(WORD_BITS*modulus.reg_.size())%modulus;}
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const Integer& Multiply(const Integer &a, const Integer &b) const;
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const Integer& Square(const Integer &a) const;
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const Integer& MultiplicativeInverse(const Integer &a) const;
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Integer CascadeExponentiate(const Integer &x, const Integer &e1,
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const Integer &y, const Integer &e2) const
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{return AbstractRing::CascadeExponentiate(x, e1, y, e2);}
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void SimultaneousExponentiate(Element *results, const Element &base,
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const Integer *exponents, unsigned int exponentsCount) const
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{AbstractRing::SimultaneousExponentiate(results, base,
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exponents, exponentsCount);}
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private:
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Integer u;
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mutable AlignedWordBlock workspace;
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};
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} // namespace
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#endif // TAO_CRYPT_MODARITH_HPP
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