nbtheory.h

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// nbtheory.h - originally written and placed in the public domain by Wei Dai
 
 
#ifndef CRYPTOPP_NBTHEORY_H
#define CRYPTOPP_NBTHEORY_H
 
#include "cryptlib.h"
#include "integer.h"
#include "algparam.h"
 
NAMESPACE_BEGIN(CryptoPP)
 
 
CRYPTOPP_DLL const word16 * CRYPTOPP_API GetPrimeTable(unsigned int &size);
 
// ************ primality testing ****************
 
CRYPTOPP_DLL Integer CRYPTOPP_API MaurerProvablePrime(RandomNumberGenerator &rng, unsigned int bits);
 
CRYPTOPP_DLL Integer CRYPTOPP_API MihailescuProvablePrime(RandomNumberGenerator &rng, unsigned int bits);
 
CRYPTOPP_DLL bool CRYPTOPP_API IsSmallPrime(const Integer &p);
 
CRYPTOPP_DLL bool CRYPTOPP_API TrialDivision(const Integer &p, unsigned bound);
 
CRYPTOPP_DLL bool CRYPTOPP_API SmallDivisorsTest(const Integer &p);
 
CRYPTOPP_DLL bool CRYPTOPP_API IsFermatProbablePrime(const Integer &n, const Integer &b);
 
CRYPTOPP_DLL bool CRYPTOPP_API IsLucasProbablePrime(const Integer &n);
 
CRYPTOPP_DLL bool CRYPTOPP_API IsStrongProbablePrime(const Integer &n, const Integer &b);
 
CRYPTOPP_DLL bool CRYPTOPP_API IsStrongLucasProbablePrime(const Integer &n);
 
CRYPTOPP_DLL bool CRYPTOPP_API RabinMillerTest(RandomNumberGenerator &rng, const Integer &n, unsigned int rounds);
 
CRYPTOPP_DLL bool CRYPTOPP_API IsPrime(const Integer &p);
 
CRYPTOPP_DLL bool CRYPTOPP_API VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level = 1);
 
class CRYPTOPP_DLL PrimeSelector
{
public:
        virtual ~PrimeSelector() {}
        const PrimeSelector *GetSelectorPointer() const {return this;}
        virtual bool IsAcceptable(const Integer &candidate) const =0;
};
 
CRYPTOPP_DLL bool CRYPTOPP_API FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod, const PrimeSelector *pSelector);
 
CRYPTOPP_DLL unsigned int CRYPTOPP_API PrimeSearchInterval(const Integer &max);
 
CRYPTOPP_DLL AlgorithmParameters CRYPTOPP_API MakeParametersForTwoPrimesOfEqualSize(unsigned int productBitLength);
 
// ********** other number theoretic functions ************
 
inline Integer GCD(const Integer &a, const Integer &b)
        {return Integer::Gcd(a,b);}
 
inline bool RelativelyPrime(const Integer &a, const Integer &b)
        {return Integer::Gcd(a,b) == Integer::One();}
 
inline Integer LCM(const Integer &a, const Integer &b)
        {return a/Integer::Gcd(a,b)*b;}
 
inline Integer EuclideanMultiplicativeInverse(const Integer &a, const Integer &b)
        {return a.InverseMod(b);}
 
 
CRYPTOPP_DLL Integer CRYPTOPP_API CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q, const Integer &u);
 
CRYPTOPP_DLL int CRYPTOPP_API Jacobi(const Integer &a, const Integer &b);
 
CRYPTOPP_DLL Integer CRYPTOPP_API Lucas(const Integer &e, const Integer &p, const Integer &n);
 
CRYPTOPP_DLL Integer CRYPTOPP_API InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q, const Integer &u);
 
inline Integer ModularMultiplication(const Integer &x, const Integer &y, const Integer &m)
        {return a_times_b_mod_c(x, y, m);}
 
inline Integer ModularExponentiation(const Integer &x, const Integer &e, const Integer &m)
        {return a_exp_b_mod_c(x, e, m);}
 
CRYPTOPP_DLL Integer CRYPTOPP_API ModularSquareRoot(const Integer &a, const Integer &p);
 
CRYPTOPP_DLL Integer CRYPTOPP_API ModularRoot(const Integer &a, const Integer &dp, const Integer &dq, const Integer &p, const Integer &q, const Integer &u);
 
CRYPTOPP_DLL bool CRYPTOPP_API SolveModularQuadraticEquation(Integer &r1, Integer &r2, const Integer &a, const Integer &b, const Integer &c, const Integer &p);
 
CRYPTOPP_DLL unsigned int CRYPTOPP_API DiscreteLogWorkFactor(unsigned int bitlength);
 
CRYPTOPP_DLL unsigned int CRYPTOPP_API FactoringWorkFactor(unsigned int bitlength);
 
// ********************************************************
 
class CRYPTOPP_DLL PrimeAndGenerator
{
public:
        PrimeAndGenerator() {}
 
        PrimeAndGenerator(signed int delta, RandomNumberGenerator &rng, unsigned int pbits)
                {Generate(delta, rng, pbits, pbits-1);}
 
        PrimeAndGenerator(signed int delta, RandomNumberGenerator &rng, unsigned int pbits, unsigned qbits)
                {Generate(delta, rng, pbits, qbits);}
 
        void Generate(signed int delta, RandomNumberGenerator &rng, unsigned int pbits, unsigned qbits);
 
        const Integer& Prime() const {return p;}
 
        const Integer& SubPrime() const {return q;}
 
        const Integer& Generator() const {return g;}
 
private:
        Integer p, q, g;
};
 
NAMESPACE_END
 
#endif