You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
405 lines
14 KiB
405 lines
14 KiB
![]()
4 years ago
|
// gf2n.h - originally written and placed in the public domain by Wei Dai
|
||
|
|
||
|
/// \file gf2n.h
|
||
|
/// \brief Classes and functions for schemes over GF(2^n)
|
||
|
|
||
|
#ifndef CRYPTOPP_GF2N_H
|
||
|
#define CRYPTOPP_GF2N_H
|
||
|
|
||
|
#include "cryptlib.h"
|
||
|
#include "secblock.h"
|
||
|
#include "algebra.h"
|
||
|
#include "misc.h"
|
||
|
#include "asn.h"
|
||
|
|
||
|
#include <iosfwd>
|
||
|
|
||
|
#if CRYPTOPP_MSC_VERSION
|
||
|
# pragma warning(push)
|
||
|
# pragma warning(disable: 4231 4275)
|
||
|
#endif
|
||
|
|
||
|
NAMESPACE_BEGIN(CryptoPP)
|
||
|
|
||
|
/// \brief Polynomial with Coefficients in GF(2)
|
||
|
/*! \nosubgrouping */
|
||
|
class CRYPTOPP_DLL PolynomialMod2
|
||
|
{
|
||
|
public:
|
||
|
/// \name ENUMS, EXCEPTIONS, and TYPEDEFS
|
||
|
//@{
|
||
|
/// \brief Excpetion thrown when divide by zero is encountered
|
||
|
class DivideByZero : public Exception
|
||
|
{
|
||
|
public:
|
||
|
DivideByZero() : Exception(OTHER_ERROR, "PolynomialMod2: division by zero") {}
|
||
|
};
|
||
|
|
||
|
typedef unsigned int RandomizationParameter;
|
||
|
//@}
|
||
|
|
||
|
/// \name CREATORS
|
||
|
//@{
|
||
|
/// \brief Construct the zero polynomial
|
||
|
PolynomialMod2();
|
||
|
/// Copy construct a PolynomialMod2
|
||
|
PolynomialMod2(const PolynomialMod2& t);
|
||
|
|
||
|
/// \brief Construct a PolynomialMod2 from a word
|
||
|
/// \details 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);
|
||
|
|
||
|
/// \brief Construct a PolynomialMod2 from big-endian byte array
|
||
|
PolynomialMod2(const byte *encodedPoly, size_t byteCount)
|
||
|
{Decode(encodedPoly, byteCount);}
|
||
|
|
||
|
/// \brief Construct a PolynomialMod2 from big-endian form stored in a BufferedTransformation
|
||
|
PolynomialMod2(BufferedTransformation &encodedPoly, size_t byteCount)
|
||
|
{Decode(encodedPoly, byteCount);}
|
||
|
|
||
|
/// \brief Create a uniformly distributed random polynomial
|
||
|
/// \details Create a random polynomial uniformly distributed over all polynomials with degree less than bitcount
|
||
|
PolynomialMod2(RandomNumberGenerator &rng, size_t bitcount)
|
||
|
{Randomize(rng, bitcount);}
|
||
|
|
||
|
/// \brief Provides x^i
|
||
|
/// \returns x^i
|
||
|
static PolynomialMod2 CRYPTOPP_API Monomial(size_t i);
|
||
|
/// \brief Provides x^t0 + x^t1 + x^t2
|
||
|
/// \returns x^t0 + x^t1 + x^t2
|
||
|
static PolynomialMod2 CRYPTOPP_API Trinomial(size_t t0, size_t t1, size_t t2);
|
||
|
/// \brief Provides x^t0 + x^t1 + x^t2 + x^t3 + x^t4
|
||
|
/// \returns 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);
|
||
|
/// \brief Provides x^(n-1) + ... + x + 1
|
||
|
/// \returns x^(n-1) + ... + x + 1
|
||
|
static PolynomialMod2 CRYPTOPP_API AllOnes(size_t n);
|
||
|
|
||
|
/// \brief The Zero polinomial
|
||
|
/// \returns the zero polynomial
|
||
|
static const PolynomialMod2 & CRYPTOPP_API Zero();
|
||
|
/// \brief The One polinomial
|
||
|
/// \returns the one polynomial
|
||
|
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
|
||
|
/// \details 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;
|
||
|
friend class GF2NT233;
|
||
|
|
||
|
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> >;
|
||
|
|
||
|
/// \brief 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); CRYPTOPP_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
|
||
|
{CRYPTOPP_ASSERT(a.Degree() < m_modulus.Degree() && b.Degree() < m_modulus.Degree()); return a.Equals(b);}
|
||
|
|
||
|
bool IsUnit(const Element &a) const
|
||
|
{CRYPTOPP_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;
|
||
|
};
|
||
|
|
||
|
/// \brief 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;
|
||
|
|
||
|
protected:
|
||
|
const Element& Reduced(const Element &a) const;
|
||
|
|
||
|
unsigned int t0, t1;
|
||
|
mutable PolynomialMod2 result;
|
||
|
};
|
||
|
|
||
|
/// \brief GF(2^n) for b233 and k233
|
||
|
/// \details GF2NT233 is a specialization of GF2NT that provides Multiply()
|
||
|
/// and Square() operations when carryless multiplies is available.
|
||
|
class CRYPTOPP_DLL GF2NT233 : public GF2NT
|
||
|
{
|
||
|
public:
|
||
|
// polynomial modulus = x^t0 + x^t1 + x^t2, t0 > t1 > t2
|
||
|
GF2NT233(unsigned int t0, unsigned int t1, unsigned int t2);
|
||
|
|
||
|
GF2NP * Clone() const {return new GF2NT233(*this);}
|
||
|
|
||
|
const Element& Multiply(const Element &a, const Element &b) const;
|
||
|
|
||
|
const Element& Square(const Element &a) const;
|
||
|
};
|
||
|
|
||
|
/// \brief 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)), t1(t1), t2(t2), t3(t3) {}
|
||
|
|
||
|
GF2NP * Clone() const {return new GF2NPP(*this);}
|
||
|
void DEREncode(BufferedTransformation &bt) const;
|
||
|
|
||
|
private:
|
||
|
unsigned int 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
|
||
|
|
||
|
#if CRYPTOPP_MSC_VERSION
|
||
|
# pragma warning(pop)
|
||
|
#endif
|
||
|
|
||
|
#endif
|