Crypto++
8.6
Free C++ class library of cryptographic schemes
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Go to the documentation of this file.
6 #ifndef CRYPTOPP_GF2N_H
7 #define CRYPTOPP_GF2N_H
17 #if CRYPTOPP_MSC_VERSION
18 # pragma warning(push)
19 # pragma warning(disable: 4231 4275)
38 typedef unsigned int RandomizationParameter;
56 {Decode(encodedPoly, byteCount);}
60 {Decode(encodedPoly, byteCount);}
65 {Randomize(rng, bitcount);}
97 void Encode(
byte *output,
size_t outputLen)
const;
102 void Decode(
const byte *input,
size_t inputLen);
116 unsigned int BitCount()
const;
118 unsigned int ByteCount()
const;
120 unsigned int WordCount()
const;
123 bool GetBit(
size_t n)
const {
return GetCoefficient(n)!=0;}
128 signed int Degree()
const {
return (
signed int)(BitCount()-1U);}
135 int operator[](
unsigned int i)
const {
return GetCoefficient(i);}
138 bool IsZero()
const {
return !*
this;}
170 void SetBit(
size_t i,
int value = 1);
172 void SetByte(
size_t n,
byte value);
175 void SetCoefficient(
size_t i,
int value) {SetBit(i, value);}
184 bool operator!()
const;
217 unsigned int Parity()
const;
220 bool IsIrreducible()
const;
228 bool IsUnit()
const {
return Equals(One());}
255 inline bool operator==(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
256 {
return a.Equals(b);}
258 inline bool operator!=(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
261 inline bool operator> (
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
262 {
return a.Degree() > b.Degree();}
264 inline bool operator>=(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
265 {
return a.Degree() >= b.Degree();}
267 inline bool operator< (
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
268 {
return a.Degree() < b.Degree();}
270 inline bool operator<=(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
271 {
return a.Degree() <= b.Degree();}
273 inline CryptoPP::PolynomialMod2
operator&(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.And(b);}
275 inline CryptoPP::PolynomialMod2
operator^(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Xor(b);}
277 inline CryptoPP::PolynomialMod2
operator+(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Plus(b);}
279 inline CryptoPP::PolynomialMod2
operator-(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Minus(b);}
281 inline CryptoPP::PolynomialMod2
operator*(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Times(b);}
283 inline CryptoPP::PolynomialMod2 operator/(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.DividedBy(b);}
285 inline CryptoPP::PolynomialMod2 operator%(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Modulo(b);}
301 virtual GF2NP * Clone()
const {
return new GF2NP(*
this);}
308 bool Equal(
const Element &a,
const Element &b)
const
309 {
CRYPTOPP_ASSERT(a.Degree() < m_modulus.Degree() && b.Degree() < m_modulus.Degree());
return a.Equals(b);}
314 unsigned int MaxElementBitLength()
const
317 unsigned int MaxElementByteLength()
const
318 {
return (
unsigned int)
BitsToBytes(MaxElementBitLength());}
320 Element SquareRoot(
const Element &a)
const;
322 Element HalfTrace(
const Element &a)
const;
325 Element SolveQuadraticEquation(
const Element &a)
const;
336 GF2NT(
unsigned int t0,
unsigned int t1,
unsigned int t2);
338 GF2NP * Clone()
const {
return new GF2NT(*
this);}
341 const Element&
Multiply(
const Element &a,
const Element &b)
const;
343 const Element&
Square(
const Element &a)
const
344 {
return Reduced(a.Squared());}
349 const Element& Reduced(
const Element &a)
const;
362 GF2NT233(
unsigned int t0,
unsigned int t1,
unsigned int t2);
366 const Element&
Multiply(
const Element &a,
const Element &b)
const;
368 const Element&
Square(
const Element &a)
const;
376 GF2NPP(
unsigned int t0,
unsigned int t1,
unsigned int t2,
unsigned int t3,
unsigned int t4)
383 unsigned int t1, t2, t3;
393 template<>
inline void swap(CryptoPP::PolynomialMod2 &a, CryptoPP::PolynomialMod2 &b)
400 #if CRYPTOPP_MSC_VERSION
401 # pragma warning(pop)
void swap(::SecBlock< T, A > &a, ::SecBlock< T, A > &b)
Swap two SecBlocks.
int operator[](unsigned int i) const
return coefficient for x^i
PolynomialMod2 Doubled() const
is always zero since we're working modulo 2
Polynomial with Coefficients in GF(2)
Classes and functions for secure memory allocations.
PolynomialMod2(const byte *encodedPoly, size_t byteCount)
Construct a PolynomialMod2 from big-endian byte array.
unsigned int MinEncodedSize() const
minimum number of bytes to encode this polynomial
const Element & MultiplicativeInverse(const Element &a) const
static PolynomialMod2 Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4)
Provides x^t0 + x^t1 + x^t2 + x^t3 + x^t4.
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
inline ::Integer operator-(const ::Integer &a, const ::Integer &b)
Subtraction.
PolynomialMod2(RandomNumberGenerator &rng, size_t bitcount)
Create a uniformly distributed random polynomial.
unsigned int GetByte(ByteOrder order, T value, unsigned int index)
Gets a byte from a value.
inline ::Integer operator&(const ::Integer &a, const ::Integer &b)
Bitwise AND.
PolynomialMod2 MultiplicativeInverse() const
return inverse if *this is a unit, otherwise return 0
bool IsUnit(const Element &a) const
Determines whether an element is a unit in the group.
const unsigned int WORD_BITS
Size of a platform word in bits.
Interface for random number generators.
GF(2^n) for b233 and k233.
bool operator>(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
size_t BitsToBytes(size_t bitCount)
Returns the number of 8-bit bytes or octets required for the specified number of bits.
Base class for all exceptions thrown by the library.
bool operator==(const OID &lhs, const OID &rhs)
Compare two OIDs for equality.
Utility functions for the Crypto++ library.
signed int Degree() const
the zero polynomial will return a degree of -1
bool operator<=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
word64 word
Full word used for multiprecision integer arithmetic.
const T & STDMAX(const T &a, const T &b)
Replacement function for std::max.
const Element & Square(const Element &a) const
Square an element in the group.
int GetCoefficient(size_t i) const
return coefficient for x^i
GF(2^n) with Polynomial Basis.
GF(2^n) with Pentanomial Basis.
Classes and functions for working with ANS.1 objects.
bool IsUnit() const
only 1 is a unit
bool GetBit(size_t n) const
return the n-th bit, n=0 being the least significant bit
std::ostream & operator<<(std::ostream &out, const OID &oid)
Print a OID value.
unsigned int CoefficientCount() const
degree + 1
PolynomialMod2(BufferedTransformation &encodedPoly, size_t byteCount)
Construct a PolynomialMod2 from big-endian form stored in a BufferedTransformation.
bool Equal(const Element &a, const Element &b) const
Compare two elements for equality.
const Element & Multiply(const Element &a, const Element &b) const
inline ::Integer operator^(const ::Integer &a, const ::Integer &b)
Bitwise XOR.
Exception thrown when divide by zero is encountered.
Classes for performing mathematics over different fields.
Crypto++ library namespace.
#define CRYPTOPP_API
Win32 calling convention.
#define CRYPTOPP_DLL_TEMPLATE_CLASS
Instantiate templates in a dynamic library.
bool operator>=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
OID operator+(const OID &lhs, unsigned long rhs)
Append a value to an OID.
bool operator!=(const OID &lhs, const OID &rhs)
Compare two OIDs for inequality.
const Element & Multiply(const Element &a, const Element &b) const
Multiplies elements in the group.
unsigned int Parity(T value)
Returns the parity of a value.
inline ::Integer operator*(const ::Integer &a, const ::Integer &b)
Multiplication.
Abstract base classes that provide a uniform interface to this library.
bool operator<(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
GF(2^n) with Trinomial Basis.