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authorAlexander Harkness <bearbin@gmail.com>2013-11-24 15:21:13 +0100
committerAlexander Harkness <bearbin@gmail.com>2013-11-24 15:21:13 +0100
commit3438e5d3ddf8444f0e31009ffbe8237ef3752c22 (patch)
tree7c2f76d5e9281c130e60fb932c4dda89a49863b6 /CryptoPP/gf2n.h
parentMoved source to src (diff)
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Diffstat (limited to 'CryptoPP/gf2n.h')
-rw-r--r--CryptoPP/gf2n.h369
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diff --git a/CryptoPP/gf2n.h b/CryptoPP/gf2n.h
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--- a/CryptoPP/gf2n.h
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-#ifndef CRYPTOPP_GF2N_H
-#define CRYPTOPP_GF2N_H
-
-/*! \file */
-
-#include "cryptlib.h"
-#include "secblock.h"
-#include "misc.h"
-#include "algebra.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 BitCount()-1;}
- //! 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
- {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