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