/usr/include/crypto++/gf2n.h is in libcrypto++-dev 5.6.1-6.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 | #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
|