17#if CRYPTOPP_MSC_VERSION
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);
138 bool IsZero()
const {
return !*
this;}
170 void SetBit(
size_t i,
int value = 1);
175 void SetCoefficient(
size_t i,
int value) {SetBit(i, value);}
184 bool operator!()
const;
249 friend class GF2NT233;
255inline bool operator==(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
258inline bool operator!=(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
261inline bool operator> (
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
262{
return a.Degree() > b.Degree();}
264inline bool operator>=(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
265{
return a.Degree() >= b.Degree();}
267inline bool operator< (
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
268{
return a.Degree() < b.Degree();}
270inline bool operator<=(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b)
271{
return a.Degree() <= b.Degree();}
273inline CryptoPP::PolynomialMod2 operator&(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.And(b);}
275inline CryptoPP::PolynomialMod2 operator^(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Xor(b);}
277inline CryptoPP::PolynomialMod2
operator+(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Plus(b);}
279inline CryptoPP::PolynomialMod2 operator-(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Minus(b);}
281inline CryptoPP::PolynomialMod2 operator*(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Times(b);}
283inline CryptoPP::PolynomialMod2 operator/(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.DividedBy(b);}
285inline CryptoPP::PolynomialMod2 operator%(
const CryptoPP::PolynomialMod2 &a,
const CryptoPP::PolynomialMod2 &b) {
return a.Modulo(b);}
296class CRYPTOPP_DLL GF2NP :
public QuotientRing<EuclideanDomainOf<PolynomialMod2> >
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;
332class CRYPTOPP_DLL GF2NT :
public GF2NP
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;
358class CRYPTOPP_DLL GF2NT233 :
public GF2NT
362 GF2NT233(
unsigned int t0,
unsigned int t1,
unsigned int t2);
364 GF2NP * Clone()
const {
return new GF2NT233(*
this);}
366 const Element&
Multiply(
const Element &a,
const Element &b)
const;
368 const Element&
Square(
const Element &a)
const;
372class CRYPTOPP_DLL GF2NPP :
public GF2NP
376 GF2NPP(
unsigned int t0,
unsigned int t1,
unsigned int t2,
unsigned int t3,
unsigned int t4)
379 GF2NP * Clone()
const {
return new GF2NPP(*
this);}
383 unsigned int t1, t2, t3;
393template<>
inline void swap(CryptoPP::PolynomialMod2 &a, CryptoPP::PolynomialMod2 &b)
400#if CRYPTOPP_MSC_VERSION
Classes for performing mathematics over different fields.
Classes and functions for working with ANS.1 objects.
std::ostream & operator<<(std::ostream &out, const OID &oid)
Print a OID value.
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 equality.
bool operator!=(const OID &lhs, const OID &rhs)
Compare two OIDs for inequality.
Abstract Euclidean domain.
Exception(ErrorType errorType, const std::string &s)
Construct a new Exception.
@ OTHER_ERROR
Some other error occurred not belonging to other categories.
GF(2^n) with Polynomial Basis.
bool Equal(const Element &a, const Element &b) const
Compare two elements for equality.
bool IsUnit(const Element &a) const
Determines whether an element is a unit in the group.
const Element & Multiply(const Element &a, const Element &b) const
Multiplies elements in the group.
const Element & Square(const Element &a) const
Square an element in the group.
const Element & MultiplicativeInverse(const Element &a) const
Calculate the multiplicative inverse of an element in the group.
const Element & Square(const Element &a) const
Square an element in the group.
const Element & Multiply(const Element &a, const Element &b) const
Multiplies elements in the group.
Polynomial with Coefficients in GF(2)
unsigned int MinEncodedSize() const
minimum number of bytes to encode this polynomial
void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const
encode value as big-endian octet string
PolynomialMod2 MultiplicativeInverse() const
return inverse if *this is a unit, otherwise return 0
void Encode(byte *output, size_t outputLen) const
encode in big-endian format
static PolynomialMod2 Monomial(size_t i)
Provides x^i.
signed int Degree() const
the zero polynomial will return a degree of -1
static const PolynomialMod2 & One()
The One polinomial.
bool IsIrreducible() const
check for irreducibility
PolynomialMod2(RandomNumberGenerator &rng, size_t bitcount)
Create a uniformly distributed random polynomial.
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.
bool IsUnit() const
only 1 is a unit
PolynomialMod2(word value, size_t bitLength=WORD_BITS)
Construct a PolynomialMod2 from a word.
PolynomialMod2 Doubled() const
is always zero since we're working modulo 2
PolynomialMod2(const PolynomialMod2 &t)
Copy construct a PolynomialMod2.
void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length)
decode value as big-endian octet string
byte GetByte(size_t n) const
return the n-th byte
unsigned int BitCount() const
number of significant bits = Degree() + 1
unsigned int WordCount() const
number of significant words = ceiling(ByteCount()/sizeof(word))
static PolynomialMod2 AllOnes(size_t n)
Provides x^(n-1) + ... + x + 1.
static PolynomialMod2 Trinomial(size_t t0, size_t t1, size_t t2)
Provides x^t0 + x^t1 + x^t2.
unsigned int CoefficientCount() const
degree + 1
PolynomialMod2 InverseMod(const PolynomialMod2 &) const
calculate multiplicative inverse of *this mod n
PolynomialMod2(BufferedTransformation &encodedPoly, size_t byteCount)
Construct a PolynomialMod2 from big-endian form stored in a BufferedTransformation.
int operator[](unsigned int i) const
return coefficient for x^i
unsigned int Parity() const
sum modulo 2 of all coefficients
PolynomialMod2()
Construct the zero polynomial.
static const PolynomialMod2 & Zero()
The Zero polinomial.
unsigned int ByteCount() const
number of significant bytes = ceiling(BitCount()/8)
static void Divide(PolynomialMod2 &r, PolynomialMod2 &q, const PolynomialMod2 &a, const PolynomialMod2 &d)
calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))
static PolynomialMod2 Gcd(const PolynomialMod2 &a, const PolynomialMod2 &n)
greatest common divisor
PolynomialMod2(const byte *encodedPoly, size_t byteCount)
Construct a PolynomialMod2 from big-endian byte array.
void SetByte(size_t n, byte value)
set the n-th byte to value
int GetCoefficient(size_t i) const
return coefficient for x^i
bool GetBit(size_t n) const
return the n-th bit, n=0 being the least significant bit
Interface for random number generators.
#define CRYPTOPP_API
Win32 calling convention.
#define CRYPTOPP_DLL_TEMPLATE_CLASS
Instantiate templates in a dynamic library.
word64 word
Full word used for multiprecision integer arithmetic.
const unsigned int WORD_BITS
Size of a platform word in bits.
Abstract base classes that provide a uniform interface to this library.
bool operator>(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
bool operator>=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
bool operator<(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
bool operator<=(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
Utility functions for the Crypto++ library.
const T & STDMAX(const T &a, const T &b)
Replacement function for std::max.
size_t BitsToBytes(size_t bitCount)
Returns the number of 8-bit bytes or octets required for the specified number of bits.
Crypto++ library namespace.
Classes and functions for secure memory allocations.
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.