gf2n.h

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#ifndef CRYPTOPP_GF2N_H
#define CRYPTOPP_GF2N_H
 
/*! \file */
 
#include "cryptlib.h"
#include "secblock.h"
#include "algebra.h"
#include "misc.h"
#include "asn.h"
 
#include <iosfwd>
 
NAMESPACE_BEGIN(CryptoPP)
 
//! Polynomial with Coefficients in GF(2)
/*! \nosubgrouping */
class CRYPTOPP_DLL PolynomialMod2
{
public:
    //! \name ENUMS, EXCEPTIONS, and TYPEDEFS
    //@{
        //! divide by zero exception
        class DivideByZero : public Exception
        {
        public:
            DivideByZero() : Exception(OTHER_ERROR, "PolynomialMod2: division by zero") {}
        };
 
        typedef unsigned int RandomizationParameter;
    //@}
 
    //! \name CREATORS
    //@{
        //! creates the zero polynomial
        PolynomialMod2();
        //! copy constructor
        PolynomialMod2(const PolynomialMod2& t);
 
        //! convert from word
        /*! value should be encoded with the least significant bit as coefficient to x^0
            and most significant bit as coefficient to x^(WORD_BITS-1)
            bitLength denotes how much memory to allocate initially
        */
        PolynomialMod2(word value, size_t bitLength=WORD_BITS);
 
        //! convert from big-endian byte array
        PolynomialMod2(const byte *encodedPoly, size_t byteCount)
            {Decode(encodedPoly, byteCount);}
 
        //! convert from big-endian form stored in a BufferedTransformation
        PolynomialMod2(BufferedTransformation &encodedPoly, size_t byteCount)
            {Decode(encodedPoly, byteCount);}
 
        //! create a random polynomial uniformly distributed over all polynomials with degree less than bitcount
        PolynomialMod2(RandomNumberGenerator &rng, size_t bitcount)
            {Randomize(rng, bitcount);}
 
        //! return x^i
        static PolynomialMod2 CRYPTOPP_API Monomial(size_t i);
        //! return x^t0 + x^t1 + x^t2
        //! The coefficients should be provided in descending order. That is, t0 > t1 > t2.
        static PolynomialMod2 CRYPTOPP_API Trinomial(size_t t0, size_t t1, size_t t2);
        //! return x^t0 + x^t1 + x^t2 + x^t3 + x^t4
        //! The coefficients should be provided in descending order. That is, t0 > t1 > t2 > t3 > t4.
        static PolynomialMod2 CRYPTOPP_API Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4);
        //! return x^(n-1) + ... + x + 1
        static PolynomialMod2 CRYPTOPP_API AllOnes(size_t n);
 
        //!
        static const PolynomialMod2 & CRYPTOPP_API Zero();
        //!
        static const PolynomialMod2 & CRYPTOPP_API One();
    //@}
 
    //! \name ENCODE/DECODE
    //@{
        //! minimum number of bytes to encode this polynomial
        /*! MinEncodedSize of 0 is 1 */
        unsigned int MinEncodedSize() const {return STDMAX(1U, ByteCount());}
 
        //! encode in big-endian format
        /*! if outputLen < MinEncodedSize, the most significant bytes will be dropped
            if outputLen > MinEncodedSize, the most significant bytes will be padded
        */
        void Encode(byte *output, size_t outputLen) const;
        //!
        void Encode(BufferedTransformation &bt, size_t outputLen) const;
 
        //!
        void Decode(const byte *input, size_t inputLen);
        //!
        //* Precondition: bt.MaxRetrievable() >= inputLen
        void Decode(BufferedTransformation &bt, size_t inputLen);
 
        //! encode value as big-endian octet string
        void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const;
        //! decode value as big-endian octet string
        void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length);
    //@}
 
    //! \name ACCESSORS
    //@{
        //! number of significant bits = Degree() + 1
        unsigned int BitCount() const;
        //! number of significant bytes = ceiling(BitCount()/8)
        unsigned int ByteCount() const;
        //! number of significant words = ceiling(ByteCount()/sizeof(word))
        unsigned int WordCount() const;
 
        //! return the n-th bit, n=0 being the least significant bit
        bool GetBit(size_t n) const {return GetCoefficient(n)!=0;}
        //! return the n-th byte
        byte GetByte(size_t n) const;
 
        //! the zero polynomial will return a degree of -1
        signed int Degree() const {return (signed int)(BitCount()-1U);}
        //! degree + 1
        unsigned int CoefficientCount() const {return BitCount();}
        //! return coefficient for x^i
        int GetCoefficient(size_t i) const
            {return (i/WORD_BITS < reg.size()) ? int(reg[i/WORD_BITS] >> (i % WORD_BITS)) & 1 : 0;}
        //! return coefficient for x^i
        int operator[](unsigned int i) const {return GetCoefficient(i);}
 
        //!
        bool IsZero() const {return !*this;}
        //!
        bool Equals(const PolynomialMod2 &rhs) const;
    //@}
 
    //! \name MANIPULATORS
    //@{
        //!
        PolynomialMod2&  operator=(const PolynomialMod2& t);
        //!
        PolynomialMod2&  operator&=(const PolynomialMod2& t);
        //!
        PolynomialMod2&  operator^=(const PolynomialMod2& t);
        //!
        PolynomialMod2&  operator+=(const PolynomialMod2& t) {return *this ^= t;}
        //!
        PolynomialMod2&  operator-=(const PolynomialMod2& t) {return *this ^= t;}
        //!
        PolynomialMod2&  operator*=(const PolynomialMod2& t);
        //!
        PolynomialMod2&  operator/=(const PolynomialMod2& t);
        //!
        PolynomialMod2&  operator%=(const PolynomialMod2& t);
        //!
        PolynomialMod2&  operator<<=(unsigned int);
        //!
        PolynomialMod2&  operator>>=(unsigned int);
 
        //!
        void Randomize(RandomNumberGenerator &rng, size_t bitcount);
 
        //!
        void SetBit(size_t i, int value = 1);
        //! set the n-th byte to value
        void SetByte(size_t n, byte value);
 
        //!
        void SetCoefficient(size_t i, int value) {SetBit(i, value);}
 
        //!
        void swap(PolynomialMod2 &a) {reg.swap(a.reg);}
    //@}
 
    //! \name UNARY OPERATORS
    //@{
        //!
        bool            operator!() const;
        //!
        PolynomialMod2  operator+() const {return *this;}
        //!
        PolynomialMod2  operator-() const {return *this;}
    //@}
 
    //! \name BINARY OPERATORS
    //@{
        //!
        PolynomialMod2 And(const PolynomialMod2 &b) const;
        //!
        PolynomialMod2 Xor(const PolynomialMod2 &b) const;
        //!
        PolynomialMod2 Plus(const PolynomialMod2 &b) const {return Xor(b);}
        //!
        PolynomialMod2 Minus(const PolynomialMod2 &b) const {return Xor(b);}
        //!
        PolynomialMod2 Times(const PolynomialMod2 &b) const;
        //!
        PolynomialMod2 DividedBy(const PolynomialMod2 &b) const;
        //!
        PolynomialMod2 Modulo(const PolynomialMod2 &b) const;
 
        //!
        PolynomialMod2 operator>>(unsigned int n) const;
        //!
        PolynomialMod2 operator<<(unsigned int n) const;
    //@}
 
    //! \name OTHER ARITHMETIC FUNCTIONS
    //@{
        //! sum modulo 2 of all coefficients
        unsigned int Parity() const;
 
        //! check for irreducibility
        bool IsIrreducible() const;
 
        //! is always zero since we're working modulo 2
        PolynomialMod2 Doubled() const {return Zero();}
        //!
        PolynomialMod2 Squared() const;
 
        //! only 1 is a unit
        bool IsUnit() const {return Equals(One());}
        //! return inverse if *this is a unit, otherwise return 0
        PolynomialMod2 MultiplicativeInverse() const {return IsUnit() ? One() : Zero();}
 
        //! greatest common divisor
        static PolynomialMod2 CRYPTOPP_API Gcd(const PolynomialMod2 &a, const PolynomialMod2 &n);
        //! calculate multiplicative inverse of *this mod n
        PolynomialMod2 InverseMod(const PolynomialMod2 &) const;
 
        //! calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))
        static void CRYPTOPP_API Divide(PolynomialMod2 &r, PolynomialMod2 &q, const PolynomialMod2 &a, const PolynomialMod2 &d);
    //@}
 
    //! \name INPUT/OUTPUT
    //@{
        //!
        friend std::ostream& operator<<(std::ostream& out, const PolynomialMod2 &a);
    //@}
 
private:
    friend class GF2NT;
 
    SecWordBlock reg;
};
 
//!
inline bool operator==(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
{return a.Equals(b);}
//!
inline bool operator!=(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
{return !(a==b);}
//! compares degree
inline bool operator> (const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
{return a.Degree() > b.Degree();}
//! compares degree
inline bool operator>=(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
{return a.Degree() >= b.Degree();}
//! compares degree
inline bool operator< (const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
{return a.Degree() < b.Degree();}
//! compares degree
inline bool operator<=(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
{return a.Degree() <= b.Degree();}
//!
inline CryptoPP::PolynomialMod2 operator&(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.And(b);}
//!
inline CryptoPP::PolynomialMod2 operator^(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Xor(b);}
//!
inline CryptoPP::PolynomialMod2 operator+(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Plus(b);}
//!
inline CryptoPP::PolynomialMod2 operator-(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Minus(b);}
//!
inline CryptoPP::PolynomialMod2 operator*(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Times(b);}
//!
inline CryptoPP::PolynomialMod2 operator/(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.DividedBy(b);}
//!
inline CryptoPP::PolynomialMod2 operator%(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Modulo(b);}
 
// CodeWarrior 8 workaround: put these template instantiations after overloaded operator declarations,
// but before the use of QuotientRing<EuclideanDomainOf<PolynomialMod2> > for VC .NET 2003
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<PolynomialMod2>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<PolynomialMod2>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<PolynomialMod2>;
CRYPTOPP_DLL_TEMPLATE_CLASS EuclideanDomainOf<PolynomialMod2>;
CRYPTOPP_DLL_TEMPLATE_CLASS QuotientRing<EuclideanDomainOf<PolynomialMod2> >;
 
//! GF(2^n) with Polynomial Basis
class CRYPTOPP_DLL GF2NP : public QuotientRing<EuclideanDomainOf<PolynomialMod2> >
{
public:
    GF2NP(const PolynomialMod2 &modulus);
 
    virtual GF2NP * Clone() const {return new GF2NP(*this);}
    virtual void DEREncode(BufferedTransformation &bt) const
        {CRYPTOPP_UNUSED(bt); assert(false);}   // no ASN.1 syntax yet for general polynomial basis
 
    void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
    void BERDecodeElement(BufferedTransformation &in, Element &a) const;
 
    bool Equal(const Element &a, const Element &b) const
        {assert(a.Degree() < m_modulus.Degree() && b.Degree() < m_modulus.Degree()); return a.Equals(b);}
 
    bool IsUnit(const Element &a) const
        {assert(a.Degree() < m_modulus.Degree()); return !!a;}
 
    unsigned int MaxElementBitLength() const
        {return m;}
 
    unsigned int MaxElementByteLength() const
        {return (unsigned int)BitsToBytes(MaxElementBitLength());}
 
    Element SquareRoot(const Element &a) const;
 
    Element HalfTrace(const Element &a) const;
 
    // returns z such that z^2 + z == a
    Element SolveQuadraticEquation(const Element &a) const;
 
protected:
    unsigned int m;
};
 
//! GF(2^n) with Trinomial Basis
class CRYPTOPP_DLL GF2NT : public GF2NP
{
public:
    // polynomial modulus = x^t0 + x^t1 + x^t2, t0 > t1 > t2
    GF2NT(unsigned int t0, unsigned int t1, unsigned int t2);
 
    GF2NP * Clone() const {return new GF2NT(*this);}
    void DEREncode(BufferedTransformation &bt) const;
 
    const Element& Multiply(const Element &a, const Element &b) const;
 
    const Element& Square(const Element &a) const
        {return Reduced(a.Squared());}
 
    const Element& MultiplicativeInverse(const Element &a) const;
 
private:
    const Element& Reduced(const Element &a) const;
 
    unsigned int t0, t1;
    mutable PolynomialMod2 result;
};
 
//! GF(2^n) with Pentanomial Basis
class CRYPTOPP_DLL GF2NPP : public GF2NP
{
public:
    // polynomial modulus = x^t0 + x^t1 + x^t2 + x^t3 + x^t4, t0 > t1 > t2 > t3 > t4
    GF2NPP(unsigned int t0, unsigned int t1, unsigned int t2, unsigned int t3, unsigned int t4)
        : GF2NP(PolynomialMod2::Pentanomial(t0, t1, t2, t3, t4)), t0(t0), t1(t1), t2(t2), t3(t3) {}
 
    GF2NP * Clone() const {return new GF2NPP(*this);}
    void DEREncode(BufferedTransformation &bt) const;
 
private:
    unsigned int t0, t1, t2, t3;
};
 
// construct new GF2NP from the ASN.1 sequence Characteristic-two
CRYPTOPP_DLL GF2NP * CRYPTOPP_API BERDecodeGF2NP(BufferedTransformation &bt);
 
NAMESPACE_END
 
#ifndef __BORLANDC__
NAMESPACE_BEGIN(std)
template<> inline void swap(CryptoPP::PolynomialMod2 &a, CryptoPP::PolynomialMod2 &b)
{
    a.swap(b);
}
NAMESPACE_END
#endif
 
#endif