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Diffstat (limited to 'CryptoPP/polynomi.h')
| -rw-r--r-- | CryptoPP/polynomi.h | 459 |
1 files changed, 459 insertions, 0 deletions
diff --git a/CryptoPP/polynomi.h b/CryptoPP/polynomi.h new file mode 100644 index 000000000..cddadaeaf --- /dev/null +++ b/CryptoPP/polynomi.h @@ -0,0 +1,459 @@ +#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 ¶meter, 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 ¶meter, 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 typename B::DivideByZero DivideByZero; + typedef typename B::RandomizationParameter RandomizationParameter; + + //! \name CREATORS + //@{ + //! creates the zero polynomial + PolynomialOverFixedRing(unsigned int count = 0) : B(ms_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, ms_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 ¶meter) : B(rng, parameter, ms_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(ms_fixedRing);} + //! degree + 1 + unsigned int CoefficientCount() const {return B::CoefficientCount(ms_fixedRing);} + //! return coefficient for x^i + CoefficientType GetCoefficient(unsigned int i) const {return B::GetCoefficient(i, ms_fixedRing);} + //! return coefficient for x^i + CoefficientType operator[](unsigned int i) const {return B::GetCoefficient(i, ms_fixedRing);} + //@} + + //! \name MANIPULATORS + //@{ + //! + ThisType& operator=(const ThisType& t) {B::operator=(t); return *this;} + //! + ThisType& operator+=(const ThisType& t) {Accumulate(t, ms_fixedRing); return *this;} + //! + ThisType& operator-=(const ThisType& t) {Reduce(t, ms_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, ms_fixedRing); return *this;} + //! + ThisType& operator>>=(unsigned int n) {ShiftRight(n, ms_fixedRing); return *this;} + + //! set the coefficient for x^i to value + void SetCoefficient(unsigned int i, const CoefficientType &value) {B::SetCoefficient(i, value, ms_fixedRing);} + + //! + void Randomize(RandomNumberGenerator &rng, const RandomizationParameter ¶meter) {B::Randomize(rng, parameter, ms_fixedRing);} + + //! + void Negate() {B::Negate(ms_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(ms_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(ms_fixedRing));} + //! + bool IsUnit() const {return B::IsUnit(ms_fixedRing);} + + //! + ThisType Doubled() const {return ThisType(B::Doubled(ms_fixedRing));} + //! + ThisType Squared() const {return ThisType(B::Squared(ms_fixedRing));} + + CoefficientType EvaluateAt(const CoefficientType &x) const {return B::EvaluateAt(x, ms_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, ms_fixedRing);} + //@} + + //! \name INPUT/OUTPUT + //@{ + //! + friend std::istream& operator>>(std::istream& in, ThisType &a) + {return a.Input(in, ms_fixedRing);} + //! + friend std::ostream& operator<<(std::ostream& out, const ThisType &a) + {return a.Output(out, ms_fixedRing);} + //@} + +private: + struct NewOnePolynomial + { + ThisType * operator()() const + { + return new ThisType(ms_fixedRing.MultiplicativeIdentity()); + } + }; + + static const Ring ms_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 typename Element::CoefficientType CoefficientType; + typedef typename Element::RandomizationParameter RandomizationParameter; + + RingOfPolynomialsOver(const CoefficientRing &ring) : m_ring(ring) {} + + Element RandomElement(RandomNumberGenerator &rng, const RandomizationParameter ¶meter) + {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 this->result = m_ring.Identity();} + + const Element& Add(const Element &a, const Element &b) const + {return this->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 this->result = a.Inverse(m_ring);} + + const Element& Subtract(const Element &a, const Element &b) const + {return this->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 this->result = a.Doubled(m_ring);} + + const Element& MultiplicativeIdentity() const + {return this->result = m_ring.MultiplicativeIdentity();} + + const Element& Multiply(const Element &a, const Element &b) const + {return this->result = a.Times(b, m_ring);} + + const Element& Square(const Element &a) const + {return this->result = a.Squared(m_ring);} + + bool IsUnit(const Element &a) const + {return a.IsUnit(m_ring);} + + const Element& MultiplicativeInverse(const Element &a) const + {return this->result = a.MultiplicativeInverse(m_ring);} + + const Element& Divide(const Element &a, const Element &b) const + {return this->result = a.DividedBy(b, m_ring);} + + const Element& Mod(const Element &a, const Element &b) const + {return this->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, a.ms_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, a.ms_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, a.ms_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, a.ms_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, a.ms_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, a.ms_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 |