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464 lines
17 KiB
C++
464 lines
17 KiB
C++
// polynomi.h - originally written and placed in the public domain by Wei Dai
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/// \file polynomi.h
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/// \brief Classes for polynomial basis and operations
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#ifndef CRYPTOPP_POLYNOMI_H
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#define CRYPTOPP_POLYNOMI_H
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#include "cryptlib.h"
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#include "secblock.h"
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#include "algebra.h"
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#include "misc.h"
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#include <iosfwd>
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#include <vector>
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NAMESPACE_BEGIN(CryptoPP)
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/// represents single-variable polynomials over arbitrary rings
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/*! \nosubgrouping */
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template <class T> class PolynomialOver
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{
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public:
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/// \name ENUMS, EXCEPTIONS, and TYPEDEFS
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//@{
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/// division by zero exception
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class DivideByZero : public Exception
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{
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public:
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DivideByZero() : Exception(OTHER_ERROR, "PolynomialOver<T>: division by zero") {}
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};
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/// specify the distribution for randomization functions
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class RandomizationParameter
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{
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public:
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RandomizationParameter(unsigned int coefficientCount, const typename T::RandomizationParameter &coefficientParameter )
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: m_coefficientCount(coefficientCount), m_coefficientParameter(coefficientParameter) {}
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private:
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unsigned int m_coefficientCount;
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typename T::RandomizationParameter m_coefficientParameter;
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friend class PolynomialOver<T>;
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};
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typedef T Ring;
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typedef typename T::Element CoefficientType;
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//@}
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/// \name CREATORS
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//@{
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/// creates the zero polynomial
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PolynomialOver() {}
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///
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PolynomialOver(const Ring &ring, unsigned int count)
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: m_coefficients((size_t)count, ring.Identity()) {}
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/// copy constructor
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PolynomialOver(const PolynomialOver<Ring> &t)
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: m_coefficients(t.m_coefficients.size()) {*this = t;}
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/// construct constant polynomial
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PolynomialOver(const CoefficientType &element)
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: m_coefficients(1, element) {}
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/// construct polynomial with specified coefficients, starting from coefficient of x^0
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template <typename Iterator> PolynomialOver(Iterator begin, Iterator end)
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: m_coefficients(begin, end) {}
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/// convert from string
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PolynomialOver(const char *str, const Ring &ring) {FromStr(str, ring);}
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/// convert from big-endian byte array
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PolynomialOver(const byte *encodedPolynomialOver, unsigned int byteCount);
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/// convert from Basic Encoding Rules encoded byte array
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explicit PolynomialOver(const byte *BEREncodedPolynomialOver);
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/// convert from BER encoded byte array stored in a BufferedTransformation object
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explicit PolynomialOver(BufferedTransformation &bt);
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/// create a random PolynomialOver<T>
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PolynomialOver(RandomNumberGenerator &rng, const RandomizationParameter ¶meter, const Ring &ring)
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{Randomize(rng, parameter, ring);}
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//@}
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/// \name ACCESSORS
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//@{
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/// the zero polynomial will return a degree of -1
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int Degree(const Ring &ring) const {return int(CoefficientCount(ring))-1;}
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///
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unsigned int CoefficientCount(const Ring &ring) const;
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/// return coefficient for x^i
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CoefficientType GetCoefficient(unsigned int i, const Ring &ring) const;
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//@}
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/// \name MANIPULATORS
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//@{
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///
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PolynomialOver<Ring>& operator=(const PolynomialOver<Ring>& t);
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///
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void Randomize(RandomNumberGenerator &rng, const RandomizationParameter ¶meter, const Ring &ring);
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/// set the coefficient for x^i to value
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void SetCoefficient(unsigned int i, const CoefficientType &value, const Ring &ring);
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///
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void Negate(const Ring &ring);
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///
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void swap(PolynomialOver<Ring> &t);
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//@}
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/// \name BASIC ARITHMETIC ON POLYNOMIALS
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//@{
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bool Equals(const PolynomialOver<Ring> &t, const Ring &ring) const;
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bool IsZero(const Ring &ring) const {return CoefficientCount(ring)==0;}
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PolynomialOver<Ring> Plus(const PolynomialOver<Ring>& t, const Ring &ring) const;
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PolynomialOver<Ring> Minus(const PolynomialOver<Ring>& t, const Ring &ring) const;
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PolynomialOver<Ring> Inverse(const Ring &ring) const;
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PolynomialOver<Ring> Times(const PolynomialOver<Ring>& t, const Ring &ring) const;
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PolynomialOver<Ring> DividedBy(const PolynomialOver<Ring>& t, const Ring &ring) const;
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PolynomialOver<Ring> Modulo(const PolynomialOver<Ring>& t, const Ring &ring) const;
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PolynomialOver<Ring> MultiplicativeInverse(const Ring &ring) const;
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bool IsUnit(const Ring &ring) const;
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PolynomialOver<Ring>& Accumulate(const PolynomialOver<Ring>& t, const Ring &ring);
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PolynomialOver<Ring>& Reduce(const PolynomialOver<Ring>& t, const Ring &ring);
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///
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PolynomialOver<Ring> Doubled(const Ring &ring) const {return Plus(*this, ring);}
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///
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PolynomialOver<Ring> Squared(const Ring &ring) const {return Times(*this, ring);}
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CoefficientType EvaluateAt(const CoefficientType &x, const Ring &ring) const;
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PolynomialOver<Ring>& ShiftLeft(unsigned int n, const Ring &ring);
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PolynomialOver<Ring>& ShiftRight(unsigned int n, const Ring &ring);
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/// calculate r and q such that (a == d*q + r) && (0 <= degree of r < degree of d)
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static void Divide(PolynomialOver<Ring> &r, PolynomialOver<Ring> &q, const PolynomialOver<Ring> &a, const PolynomialOver<Ring> &d, const Ring &ring);
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//@}
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/// \name INPUT/OUTPUT
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//@{
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std::istream& Input(std::istream &in, const Ring &ring);
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std::ostream& Output(std::ostream &out, const Ring &ring) const;
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//@}
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private:
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void FromStr(const char *str, const Ring &ring);
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std::vector<CoefficientType> m_coefficients;
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};
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/// Polynomials over a fixed ring
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/*! Having a fixed ring allows overloaded operators */
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template <class T, int instance> class PolynomialOverFixedRing : private PolynomialOver<T>
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{
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typedef PolynomialOver<T> B;
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typedef PolynomialOverFixedRing<T, instance> ThisType;
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public:
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typedef T Ring;
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typedef typename T::Element CoefficientType;
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typedef typename B::DivideByZero DivideByZero;
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typedef typename B::RandomizationParameter RandomizationParameter;
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/// \name CREATORS
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//@{
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/// creates the zero polynomial
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PolynomialOverFixedRing(unsigned int count = 0) : B(ms_fixedRing, count) {}
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/// copy constructor
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PolynomialOverFixedRing(const ThisType &t) : B(t) {}
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explicit PolynomialOverFixedRing(const B &t) : B(t) {}
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/// construct constant polynomial
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PolynomialOverFixedRing(const CoefficientType &element) : B(element) {}
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/// construct polynomial with specified coefficients, starting from coefficient of x^0
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template <typename Iterator> PolynomialOverFixedRing(Iterator first, Iterator last)
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: B(first, last) {}
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/// convert from string
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explicit PolynomialOverFixedRing(const char *str) : B(str, ms_fixedRing) {}
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/// convert from big-endian byte array
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PolynomialOverFixedRing(const byte *encodedPoly, unsigned int byteCount) : B(encodedPoly, byteCount) {}
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/// convert from Basic Encoding Rules encoded byte array
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explicit PolynomialOverFixedRing(const byte *BEREncodedPoly) : B(BEREncodedPoly) {}
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/// convert from BER encoded byte array stored in a BufferedTransformation object
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explicit PolynomialOverFixedRing(BufferedTransformation &bt) : B(bt) {}
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/// create a random PolynomialOverFixedRing
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PolynomialOverFixedRing(RandomNumberGenerator &rng, const RandomizationParameter ¶meter) : B(rng, parameter, ms_fixedRing) {}
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static const ThisType &Zero();
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static const ThisType &One();
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//@}
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/// \name ACCESSORS
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//@{
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/// the zero polynomial will return a degree of -1
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int Degree() const {return B::Degree(ms_fixedRing);}
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/// degree + 1
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unsigned int CoefficientCount() const {return B::CoefficientCount(ms_fixedRing);}
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/// return coefficient for x^i
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CoefficientType GetCoefficient(unsigned int i) const {return B::GetCoefficient(i, ms_fixedRing);}
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/// return coefficient for x^i
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CoefficientType operator[](unsigned int i) const {return B::GetCoefficient(i, ms_fixedRing);}
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//@}
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/// \name MANIPULATORS
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//@{
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///
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ThisType& operator=(const ThisType& t) {B::operator=(t); return *this;}
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///
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ThisType& operator+=(const ThisType& t) {Accumulate(t, ms_fixedRing); return *this;}
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///
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ThisType& operator-=(const ThisType& t) {Reduce(t, ms_fixedRing); return *this;}
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///
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ThisType& operator*=(const ThisType& t) {return *this = *this*t;}
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///
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ThisType& operator/=(const ThisType& t) {return *this = *this/t;}
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///
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ThisType& operator%=(const ThisType& t) {return *this = *this%t;}
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///
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ThisType& operator<<=(unsigned int n) {ShiftLeft(n, ms_fixedRing); return *this;}
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///
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ThisType& operator>>=(unsigned int n) {ShiftRight(n, ms_fixedRing); return *this;}
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/// set the coefficient for x^i to value
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void SetCoefficient(unsigned int i, const CoefficientType &value) {B::SetCoefficient(i, value, ms_fixedRing);}
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///
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void Randomize(RandomNumberGenerator &rng, const RandomizationParameter ¶meter) {B::Randomize(rng, parameter, ms_fixedRing);}
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///
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void Negate() {B::Negate(ms_fixedRing);}
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void swap(ThisType &t) {B::swap(t);}
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//@}
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/// \name UNARY OPERATORS
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//@{
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///
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bool operator!() const {return CoefficientCount()==0;}
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///
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ThisType operator+() const {return *this;}
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///
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ThisType operator-() const {return ThisType(Inverse(ms_fixedRing));}
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//@}
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/// \name BINARY OPERATORS
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//@{
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///
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friend ThisType operator>>(ThisType a, unsigned int n) {return ThisType(a>>=n);}
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///
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friend ThisType operator<<(ThisType a, unsigned int n) {return ThisType(a<<=n);}
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//@}
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/// \name OTHER ARITHMETIC FUNCTIONS
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//@{
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///
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ThisType MultiplicativeInverse() const {return ThisType(B::MultiplicativeInverse(ms_fixedRing));}
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///
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bool IsUnit() const {return B::IsUnit(ms_fixedRing);}
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///
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ThisType Doubled() const {return ThisType(B::Doubled(ms_fixedRing));}
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///
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ThisType Squared() const {return ThisType(B::Squared(ms_fixedRing));}
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CoefficientType EvaluateAt(const CoefficientType &x) const {return B::EvaluateAt(x, ms_fixedRing);}
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/// calculate r and q such that (a == d*q + r) && (0 <= r < abs(d))
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static void Divide(ThisType &r, ThisType &q, const ThisType &a, const ThisType &d)
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{B::Divide(r, q, a, d, ms_fixedRing);}
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//@}
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/// \name INPUT/OUTPUT
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//@{
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///
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friend std::istream& operator>>(std::istream& in, ThisType &a)
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{return a.Input(in, ms_fixedRing);}
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///
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friend std::ostream& operator<<(std::ostream& out, const ThisType &a)
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{return a.Output(out, ms_fixedRing);}
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//@}
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private:
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struct NewOnePolynomial
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{
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ThisType * operator()() const
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{
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return new ThisType(ms_fixedRing.MultiplicativeIdentity());
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}
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};
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static const Ring ms_fixedRing;
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};
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/// Ring of polynomials over another ring
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template <class T> class RingOfPolynomialsOver : public AbstractEuclideanDomain<PolynomialOver<T> >
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{
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public:
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typedef T CoefficientRing;
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typedef PolynomialOver<T> Element;
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typedef typename Element::CoefficientType CoefficientType;
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typedef typename Element::RandomizationParameter RandomizationParameter;
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RingOfPolynomialsOver(const CoefficientRing &ring) : m_ring(ring) {}
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Element RandomElement(RandomNumberGenerator &rng, const RandomizationParameter ¶meter)
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{return Element(rng, parameter, m_ring);}
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bool Equal(const Element &a, const Element &b) const
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{return a.Equals(b, m_ring);}
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const Element& Identity() const
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{return this->result = m_ring.Identity();}
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const Element& Add(const Element &a, const Element &b) const
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{return this->result = a.Plus(b, m_ring);}
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Element& Accumulate(Element &a, const Element &b) const
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{a.Accumulate(b, m_ring); return a;}
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const Element& Inverse(const Element &a) const
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{return this->result = a.Inverse(m_ring);}
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const Element& Subtract(const Element &a, const Element &b) const
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{return this->result = a.Minus(b, m_ring);}
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Element& Reduce(Element &a, const Element &b) const
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{return a.Reduce(b, m_ring);}
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const Element& Double(const Element &a) const
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{return this->result = a.Doubled(m_ring);}
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const Element& MultiplicativeIdentity() const
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{return this->result = m_ring.MultiplicativeIdentity();}
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const Element& Multiply(const Element &a, const Element &b) const
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{return this->result = a.Times(b, m_ring);}
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const Element& Square(const Element &a) const
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{return this->result = a.Squared(m_ring);}
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bool IsUnit(const Element &a) const
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{return a.IsUnit(m_ring);}
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const Element& MultiplicativeInverse(const Element &a) const
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{return this->result = a.MultiplicativeInverse(m_ring);}
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const Element& Divide(const Element &a, const Element &b) const
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{return this->result = a.DividedBy(b, m_ring);}
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const Element& Mod(const Element &a, const Element &b) const
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{return this->result = a.Modulo(b, m_ring);}
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void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const
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{Element::Divide(r, q, a, d, m_ring);}
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class InterpolationFailed : public Exception
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{
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public:
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InterpolationFailed() : Exception(OTHER_ERROR, "RingOfPolynomialsOver<T>: interpolation failed") {}
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};
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Element Interpolate(const CoefficientType x[], const CoefficientType y[], unsigned int n) const;
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// a faster version of Interpolate(x, y, n).EvaluateAt(position)
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CoefficientType InterpolateAt(const CoefficientType &position, const CoefficientType x[], const CoefficientType y[], unsigned int n) const;
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/*
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void PrepareBulkInterpolation(CoefficientType *w, const CoefficientType x[], unsigned int n) const;
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void PrepareBulkInterpolationAt(CoefficientType *v, const CoefficientType &position, const CoefficientType x[], const CoefficientType w[], unsigned int n) const;
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CoefficientType BulkInterpolateAt(const CoefficientType y[], const CoefficientType v[], unsigned int n) const;
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*/
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protected:
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void CalculateAlpha(std::vector<CoefficientType> &alpha, const CoefficientType x[], const CoefficientType y[], unsigned int n) const;
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CoefficientRing m_ring;
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};
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template <class Ring, class Element>
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void PrepareBulkPolynomialInterpolation(const Ring &ring, Element *w, const Element x[], unsigned int n);
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template <class Ring, class Element>
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void PrepareBulkPolynomialInterpolationAt(const Ring &ring, Element *v, const Element &position, const Element x[], const Element w[], unsigned int n);
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template <class Ring, class Element>
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Element BulkPolynomialInterpolateAt(const Ring &ring, const Element y[], const Element v[], unsigned int n);
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///
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template <class T, int instance>
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inline bool operator==(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return a.Equals(b, a.ms_fixedRing);}
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///
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template <class T, int instance>
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inline bool operator!=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return !(a==b);}
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///
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template <class T, int instance>
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inline bool operator> (const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return a.Degree() > b.Degree();}
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///
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template <class T, int instance>
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inline bool operator>=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return a.Degree() >= b.Degree();}
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///
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template <class T, int instance>
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inline bool operator< (const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return a.Degree() < b.Degree();}
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///
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template <class T, int instance>
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inline bool operator<=(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return a.Degree() <= b.Degree();}
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///
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template <class T, int instance>
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inline CryptoPP::PolynomialOverFixedRing<T, instance> operator+(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Plus(b, a.ms_fixedRing));}
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///
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template <class T, int instance>
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inline CryptoPP::PolynomialOverFixedRing<T, instance> operator-(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Minus(b, a.ms_fixedRing));}
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///
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template <class T, int instance>
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inline CryptoPP::PolynomialOverFixedRing<T, instance> operator*(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Times(b, a.ms_fixedRing));}
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///
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template <class T, int instance>
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inline CryptoPP::PolynomialOverFixedRing<T, instance> operator/(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.DividedBy(b, a.ms_fixedRing));}
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///
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template <class T, int instance>
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inline CryptoPP::PolynomialOverFixedRing<T, instance> operator%(const CryptoPP::PolynomialOverFixedRing<T, instance> &a, const CryptoPP::PolynomialOverFixedRing<T, instance> &b)
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{return CryptoPP::PolynomialOverFixedRing<T, instance>(a.Modulo(b, a.ms_fixedRing));}
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NAMESPACE_END
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NAMESPACE_BEGIN(std)
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template<class T> inline void swap(CryptoPP::PolynomialOver<T> &a, CryptoPP::PolynomialOver<T> &b)
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{
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a.swap(b);
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}
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template<class T, int i> inline void swap(CryptoPP::PolynomialOverFixedRing<T,i> &a, CryptoPP::PolynomialOverFixedRing<T,i> &b)
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{
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a.swap(b);
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}
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NAMESPACE_END
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#endif
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