370 lines
12 KiB
C++
370 lines
12 KiB
C++
#ifndef CRYPTOPP_GF2N_H
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#define CRYPTOPP_GF2N_H
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/*! \file */
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#include "cryptlib.h"
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#include "secblock.h"
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#include "misc.h"
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#include "algebra.h"
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#include <iosfwd>
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NAMESPACE_BEGIN(CryptoPP)
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//! Polynomial with Coefficients in GF(2)
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/*! \nosubgrouping */
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class CRYPTOPP_DLL PolynomialMod2
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{
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public:
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//! \name ENUMS, EXCEPTIONS, and TYPEDEFS
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//@{
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//! divide by zero exception
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class DivideByZero : public Exception
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{
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public:
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DivideByZero() : Exception(OTHER_ERROR, "PolynomialMod2: division by zero") {}
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};
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typedef unsigned int RandomizationParameter;
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//@}
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//! \name CREATORS
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//@{
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//! creates the zero polynomial
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PolynomialMod2();
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//! copy constructor
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PolynomialMod2(const PolynomialMod2& t);
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//! convert from word
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/*! value should be encoded with the least significant bit as coefficient to x^0
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and most significant bit as coefficient to x^(WORD_BITS-1)
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bitLength denotes how much memory to allocate initially
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*/
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PolynomialMod2(word value, size_t bitLength=WORD_BITS);
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//! convert from big-endian byte array
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PolynomialMod2(const byte *encodedPoly, size_t byteCount)
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{Decode(encodedPoly, byteCount);}
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//! convert from big-endian form stored in a BufferedTransformation
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PolynomialMod2(BufferedTransformation &encodedPoly, size_t byteCount)
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{Decode(encodedPoly, byteCount);}
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//! create a random polynomial uniformly distributed over all polynomials with degree less than bitcount
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PolynomialMod2(RandomNumberGenerator &rng, size_t bitcount)
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{Randomize(rng, bitcount);}
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//! return x^i
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static PolynomialMod2 CRYPTOPP_API Monomial(size_t i);
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//! return x^t0 + x^t1 + x^t2
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static PolynomialMod2 CRYPTOPP_API Trinomial(size_t t0, size_t t1, size_t t2);
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//! return x^t0 + x^t1 + x^t2 + x^t3 + x^t4
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static PolynomialMod2 CRYPTOPP_API Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4);
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//! return x^(n-1) + ... + x + 1
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static PolynomialMod2 CRYPTOPP_API AllOnes(size_t n);
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//!
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static const PolynomialMod2 & CRYPTOPP_API Zero();
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//!
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static const PolynomialMod2 & CRYPTOPP_API One();
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//@}
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//! \name ENCODE/DECODE
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//@{
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//! minimum number of bytes to encode this polynomial
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/*! MinEncodedSize of 0 is 1 */
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unsigned int MinEncodedSize() const {return STDMAX(1U, ByteCount());}
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//! encode in big-endian format
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/*! if outputLen < MinEncodedSize, the most significant bytes will be dropped
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if outputLen > MinEncodedSize, the most significant bytes will be padded
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*/
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void Encode(byte *output, size_t outputLen) const;
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//!
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void Encode(BufferedTransformation &bt, size_t outputLen) const;
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//!
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void Decode(const byte *input, size_t inputLen);
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//!
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//* Precondition: bt.MaxRetrievable() >= inputLen
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void Decode(BufferedTransformation &bt, size_t inputLen);
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//! encode value as big-endian octet string
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void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const;
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//! decode value as big-endian octet string
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void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length);
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//@}
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//! \name ACCESSORS
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//@{
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//! number of significant bits = Degree() + 1
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unsigned int BitCount() const;
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//! number of significant bytes = ceiling(BitCount()/8)
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unsigned int ByteCount() const;
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//! number of significant words = ceiling(ByteCount()/sizeof(word))
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unsigned int WordCount() const;
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//! return the n-th bit, n=0 being the least significant bit
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bool GetBit(size_t n) const {return GetCoefficient(n)!=0;}
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//! return the n-th byte
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byte GetByte(size_t n) const;
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//! the zero polynomial will return a degree of -1
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signed int Degree() const {return BitCount()-1;}
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//! degree + 1
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unsigned int CoefficientCount() const {return BitCount();}
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//! return coefficient for x^i
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int GetCoefficient(size_t i) const
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{return (i/WORD_BITS < reg.size()) ? int(reg[i/WORD_BITS] >> (i % WORD_BITS)) & 1 : 0;}
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//! return coefficient for x^i
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int operator[](unsigned int i) const {return GetCoefficient(i);}
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//!
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bool IsZero() const {return !*this;}
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//!
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bool Equals(const PolynomialMod2 &rhs) const;
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//@}
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//! \name MANIPULATORS
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//@{
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//!
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PolynomialMod2& operator=(const PolynomialMod2& t);
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//!
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PolynomialMod2& operator&=(const PolynomialMod2& t);
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//!
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PolynomialMod2& operator^=(const PolynomialMod2& t);
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//!
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PolynomialMod2& operator+=(const PolynomialMod2& t) {return *this ^= t;}
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//!
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PolynomialMod2& operator-=(const PolynomialMod2& t) {return *this ^= t;}
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//!
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PolynomialMod2& operator*=(const PolynomialMod2& t);
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//!
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PolynomialMod2& operator/=(const PolynomialMod2& t);
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//!
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PolynomialMod2& operator%=(const PolynomialMod2& t);
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//!
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PolynomialMod2& operator<<=(unsigned int);
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//!
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PolynomialMod2& operator>>=(unsigned int);
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//!
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void Randomize(RandomNumberGenerator &rng, size_t bitcount);
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//!
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void SetBit(size_t i, int value = 1);
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//! set the n-th byte to value
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void SetByte(size_t n, byte value);
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//!
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void SetCoefficient(size_t i, int value) {SetBit(i, value);}
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//!
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void swap(PolynomialMod2 &a) {reg.swap(a.reg);}
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//@}
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//! \name UNARY OPERATORS
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//@{
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//!
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bool operator!() const;
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//!
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PolynomialMod2 operator+() const {return *this;}
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//!
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PolynomialMod2 operator-() const {return *this;}
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//@}
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//! \name BINARY OPERATORS
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//@{
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//!
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PolynomialMod2 And(const PolynomialMod2 &b) const;
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//!
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PolynomialMod2 Xor(const PolynomialMod2 &b) const;
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//!
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PolynomialMod2 Plus(const PolynomialMod2 &b) const {return Xor(b);}
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//!
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PolynomialMod2 Minus(const PolynomialMod2 &b) const {return Xor(b);}
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//!
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PolynomialMod2 Times(const PolynomialMod2 &b) const;
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//!
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PolynomialMod2 DividedBy(const PolynomialMod2 &b) const;
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//!
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PolynomialMod2 Modulo(const PolynomialMod2 &b) const;
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//!
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PolynomialMod2 operator>>(unsigned int n) const;
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//!
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PolynomialMod2 operator<<(unsigned int n) const;
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//@}
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//! \name OTHER ARITHMETIC FUNCTIONS
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//@{
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//! sum modulo 2 of all coefficients
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unsigned int Parity() const;
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//! check for irreducibility
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bool IsIrreducible() const;
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//! is always zero since we're working modulo 2
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PolynomialMod2 Doubled() const {return Zero();}
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//!
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PolynomialMod2 Squared() const;
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//! only 1 is a unit
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bool IsUnit() const {return Equals(One());}
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//! return inverse if *this is a unit, otherwise return 0
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PolynomialMod2 MultiplicativeInverse() const {return IsUnit() ? One() : Zero();}
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//! greatest common divisor
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static PolynomialMod2 CRYPTOPP_API Gcd(const PolynomialMod2 &a, const PolynomialMod2 &n);
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//! calculate multiplicative inverse of *this mod n
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PolynomialMod2 InverseMod(const PolynomialMod2 &) const;
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//! calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))
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static void CRYPTOPP_API Divide(PolynomialMod2 &r, PolynomialMod2 &q, const PolynomialMod2 &a, const PolynomialMod2 &d);
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//@}
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//! \name INPUT/OUTPUT
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//@{
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//!
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friend std::ostream& operator<<(std::ostream& out, const PolynomialMod2 &a);
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//@}
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private:
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friend class GF2NT;
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SecWordBlock reg;
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};
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//!
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inline bool operator==(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
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{return a.Equals(b);}
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//!
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inline bool operator!=(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
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{return !(a==b);}
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//! compares degree
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inline bool operator> (const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
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{return a.Degree() > b.Degree();}
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//! compares degree
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inline bool operator>=(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
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{return a.Degree() >= b.Degree();}
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//! compares degree
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inline bool operator< (const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
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{return a.Degree() < b.Degree();}
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//! compares degree
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inline bool operator<=(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b)
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{return a.Degree() <= b.Degree();}
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//!
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inline CryptoPP::PolynomialMod2 operator&(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.And(b);}
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//!
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inline CryptoPP::PolynomialMod2 operator^(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Xor(b);}
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//!
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inline CryptoPP::PolynomialMod2 operator+(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Plus(b);}
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//!
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inline CryptoPP::PolynomialMod2 operator-(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Minus(b);}
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//!
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inline CryptoPP::PolynomialMod2 operator*(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Times(b);}
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//!
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inline CryptoPP::PolynomialMod2 operator/(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.DividedBy(b);}
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//!
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inline CryptoPP::PolynomialMod2 operator%(const CryptoPP::PolynomialMod2 &a, const CryptoPP::PolynomialMod2 &b) {return a.Modulo(b);}
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// CodeWarrior 8 workaround: put these template instantiations after overloaded operator declarations,
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// but before the use of QuotientRing<EuclideanDomainOf<PolynomialMod2> > for VC .NET 2003
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CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<PolynomialMod2>;
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CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<PolynomialMod2>;
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CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<PolynomialMod2>;
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CRYPTOPP_DLL_TEMPLATE_CLASS EuclideanDomainOf<PolynomialMod2>;
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CRYPTOPP_DLL_TEMPLATE_CLASS QuotientRing<EuclideanDomainOf<PolynomialMod2> >;
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//! GF(2^n) with Polynomial Basis
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class CRYPTOPP_DLL GF2NP : public QuotientRing<EuclideanDomainOf<PolynomialMod2> >
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{
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public:
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GF2NP(const PolynomialMod2 &modulus);
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virtual GF2NP * Clone() const {return new GF2NP(*this);}
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virtual void DEREncode(BufferedTransformation &bt) const
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{assert(false);} // no ASN.1 syntax yet for general polynomial basis
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void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
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void BERDecodeElement(BufferedTransformation &in, Element &a) const;
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bool Equal(const Element &a, const Element &b) const
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{assert(a.Degree() < m_modulus.Degree() && b.Degree() < m_modulus.Degree()); return a.Equals(b);}
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bool IsUnit(const Element &a) const
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{assert(a.Degree() < m_modulus.Degree()); return !!a;}
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unsigned int MaxElementBitLength() const
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{return m;}
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unsigned int MaxElementByteLength() const
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{return (unsigned int)BitsToBytes(MaxElementBitLength());}
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Element SquareRoot(const Element &a) const;
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Element HalfTrace(const Element &a) const;
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// returns z such that z^2 + z == a
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Element SolveQuadraticEquation(const Element &a) const;
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protected:
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unsigned int m;
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};
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//! GF(2^n) with Trinomial Basis
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class CRYPTOPP_DLL GF2NT : public GF2NP
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{
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public:
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// polynomial modulus = x^t0 + x^t1 + x^t2, t0 > t1 > t2
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GF2NT(unsigned int t0, unsigned int t1, unsigned int t2);
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GF2NP * Clone() const {return new GF2NT(*this);}
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void DEREncode(BufferedTransformation &bt) const;
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const Element& Multiply(const Element &a, const Element &b) const;
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const Element& Square(const Element &a) const
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{return Reduced(a.Squared());}
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const Element& MultiplicativeInverse(const Element &a) const;
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private:
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const Element& Reduced(const Element &a) const;
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unsigned int t0, t1;
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mutable PolynomialMod2 result;
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};
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//! GF(2^n) with Pentanomial Basis
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class CRYPTOPP_DLL GF2NPP : public GF2NP
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{
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public:
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// polynomial modulus = x^t0 + x^t1 + x^t2 + x^t3 + x^t4, t0 > t1 > t2 > t3 > t4
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GF2NPP(unsigned int t0, unsigned int t1, unsigned int t2, unsigned int t3, unsigned int t4)
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: GF2NP(PolynomialMod2::Pentanomial(t0, t1, t2, t3, t4)), t0(t0), t1(t1), t2(t2), t3(t3) {}
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GF2NP * Clone() const {return new GF2NPP(*this);}
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void DEREncode(BufferedTransformation &bt) const;
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private:
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unsigned int t0, t1, t2, t3;
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};
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// construct new GF2NP from the ASN.1 sequence Characteristic-two
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CRYPTOPP_DLL GF2NP * CRYPTOPP_API BERDecodeGF2NP(BufferedTransformation &bt);
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NAMESPACE_END
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#ifndef __BORLANDC__
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NAMESPACE_BEGIN(std)
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template<> inline void swap(CryptoPP::PolynomialMod2 &a, CryptoPP::PolynomialMod2 &b)
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{
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a.swap(b);
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}
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NAMESPACE_END
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#endif
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#endif
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