gf2n.h
Go to the documentation of this file.
#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
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
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
AbstractGroup< PolynomialMod2 >
SecWordBlock
SecBlock<word> typedef.
Definition: secblock.h:734
PolynomialMod2::operator[]
int operator[](unsigned int i) const
return coefficient for x^i
Definition: gf2n.h:122
QuotientRing
Quotient ring.
Definition: algebra.h:386
PolynomialMod2::Doubled
PolynomialMod2 Doubled() const
is always zero since we're working modulo 2
Definition: gf2n.h:210
PolynomialMod2
Polynomial with Coefficients in GF(2)
Definition: gf2n.h:18
secblock.h
Classes and functions for secure memory allocations.
BufferedTransformation
Interface for buffered transformations.
Definition: cryptlib.h:1352
PolynomialMod2::PolynomialMod2
PolynomialMod2(const byte *encodedPoly, size_t byteCount)
convert from big-endian byte array
Definition: gf2n.h:48
PolynomialMod2::MinEncodedSize
unsigned int MinEncodedSize() const
minimum number of bytes to encode this polynomial
Definition: gf2n.h:78
QuotientRing< EuclideanDomainOf< PolynomialMod2 > >::MultiplicativeInverse
const Element & MultiplicativeInverse(const Element &a) const
Definition: algebra.cpp:70
PolynomialMod2::PolynomialMod2
PolynomialMod2(RandomNumberGenerator &rng, size_t bitcount)
create a random polynomial uniformly distributed over all polynomials with degree less than bitcount
Definition: gf2n.h:56
GetByte
unsigned int GetByte(ByteOrder order, T value, unsigned int index)
Gets a byte from a value.
Definition: misc.h:1694
PolynomialMod2::MultiplicativeInverse
PolynomialMod2 MultiplicativeInverse() const
return inverse if *this is a unit, otherwise return 0
Definition: gf2n.h:217
GF2NP::IsUnit
bool IsUnit(const Element &a) const
Determines whether an element is a unit in the group.
Definition: gf2n.h:297
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1186
operator>
bool operator>(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
Definition: gf2n.h:247
BitsToBytes
size_t BitsToBytes(size_t bitCount)
Returns the number of 8-bit bytes or octets required for the specified number of bits.
Definition: misc.h:740
Exception
Base class for all exceptions thrown by the library.
Definition: cryptlib.h:139
operator==
bool operator==(const OID &lhs, const OID &rhs)
Compare two OIDs for equality.
misc.h
Utility functions for the Crypto++ library.
PolynomialMod2::Degree
signed int Degree() const
the zero polynomial will return a degree of -1
Definition: gf2n.h:115
EuclideanDomainOf< PolynomialMod2 >
operator<=
bool operator<=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
Definition: gf2n.h:256
PolynomialMod2::Pentanomial
static PolynomialMod2 Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4)
return x^t0 + x^t1 + x^t2 + x^t3 + x^t4
Definition: gf2n.cpp:108
STDMAX
const T & STDMAX(const T &a, const T &b)
Replacement function for std::max.
Definition: misc.h:477
GF2NT::Square
const Element & Square(const Element &a) const
Square an element in the group.
Definition: gf2n.h:329
PolynomialMod2::GetCoefficient
int GetCoefficient(size_t i) const
return coefficient for x^i
Definition: gf2n.h:119
GF2NP
GF(2^n) with Polynomial Basis.
Definition: gf2n.h:282
GF2NPP
GF(2^n) with Pentanomial Basis.
Definition: gf2n.h:342
asn.h
Classes and functions for working with ANS.1 objects.
AbstractEuclideanDomain< PolynomialMod2 >
PolynomialMod2::IsUnit
bool IsUnit() const
only 1 is a unit
Definition: gf2n.h:215
PolynomialMod2::GetBit
bool GetBit(size_t n) const
return the n-th bit, n=0 being the least significant bit
Definition: gf2n.h:110
PolynomialMod2::CoefficientCount
unsigned int CoefficientCount() const
degree + 1
Definition: gf2n.h:117
PolynomialMod2::PolynomialMod2
PolynomialMod2(BufferedTransformation &encodedPoly, size_t byteCount)
convert from big-endian form stored in a BufferedTransformation
Definition: gf2n.h:52
GF2NP::Equal
bool Equal(const Element &a, const Element &b) const
Compare two elements for equality.
Definition: gf2n.h:294
QuotientRing< EuclideanDomainOf< PolynomialMod2 > >::Multiply
const Element & Multiply(const Element &a, const Element &b) const
Definition: algebra.h:431
PolynomialMod2::DivideByZero
divide by zero exception
Definition: gf2n.h:24
algebra.h
Classes for performing mathematics over different fields.
CryptoPP
Crypto++ library namespace.
operator>=
bool operator>=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
Definition: gf2n.h:250
operator+
OID operator+(const OID &lhs, unsigned long rhs)
Append a value to an OID.
operator!=
bool operator!=(const OID &lhs, const OID &rhs)
Compare two OIDs for inequality.
Parity
unsigned int Parity(T value)
Returns the parity of a value.
Definition: misc.h:612
AbstractRing< PolynomialMod2 >
operator*
inline ::Integer operator*(const ::Integer &a, const ::Integer &b)
Definition: integer.h:595
cryptlib.h
Abstract base classes that provide a uniform interface to this library.
operator<
bool operator<(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
Definition: gf2n.h:253
GF2NT
GF(2^n) with Trinomial Basis.
Definition: gf2n.h:318