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-rw-r--r--CryptoPP/nbtheory.h131
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diff --git a/CryptoPP/nbtheory.h b/CryptoPP/nbtheory.h
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-// nbtheory.h - written and placed in the public domain by Wei Dai
-
-#ifndef CRYPTOPP_NBTHEORY_H
-#define CRYPTOPP_NBTHEORY_H
-
-#include "integer.h"
-#include "algparam.h"
-
-NAMESPACE_BEGIN(CryptoPP)
-
-// obtain pointer to small prime table and get its size
-CRYPTOPP_DLL const word16 * CRYPTOPP_API GetPrimeTable(unsigned int &size);
-
-// ************ primality testing ****************
-
-// generate a provable prime
-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);
-
-// returns true if p is divisible by some prime less than bound
-// bound not be greater than the largest entry in the prime table
-CRYPTOPP_DLL bool CRYPTOPP_API TrialDivision(const Integer &p, unsigned bound);
-
-// returns true if p is NOT divisible by small primes
-CRYPTOPP_DLL bool CRYPTOPP_API SmallDivisorsTest(const Integer &p);
-
-// These is no reason to use these two, use the ones below instead
-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);
-
-// Rabin-Miller primality test, i.e. repeating the strong probable prime test
-// for several rounds with random bases
-CRYPTOPP_DLL bool CRYPTOPP_API RabinMillerTest(RandomNumberGenerator &rng, const Integer &w, unsigned int rounds);
-
-// primality test, used to generate primes
-CRYPTOPP_DLL bool CRYPTOPP_API IsPrime(const Integer &p);
-
-// more reliable than IsPrime(), used to verify primes generated by others
-CRYPTOPP_DLL bool CRYPTOPP_API VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level = 1);
-
-class CRYPTOPP_DLL PrimeSelector
-{
-public:
- const PrimeSelector *GetSelectorPointer() const {return this;}
- virtual bool IsAcceptable(const Integer &candidate) const =0;
-};
-
-// use a fast sieve to find the first probable prime in {x | p<=x<=max and x%mod==equiv}
-// returns true iff successful, value of p is undefined if no such prime exists
-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);}
-
-// use Chinese Remainder Theorem to calculate x given x mod p and x mod q, and u = inverse of p mod q
-CRYPTOPP_DLL Integer CRYPTOPP_API CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q, const Integer &u);
-
-// if b is prime, then Jacobi(a, b) returns 0 if a%b==0, 1 if a is quadratic residue mod b, -1 otherwise
-// check a number theory book for what Jacobi symbol means when b is not prime
-CRYPTOPP_DLL int CRYPTOPP_API Jacobi(const Integer &a, const Integer &b);
-
-// calculates the Lucas function V_e(p, 1) mod n
-CRYPTOPP_DLL Integer CRYPTOPP_API Lucas(const Integer &e, const Integer &p, const Integer &n);
-// calculates x such that m==Lucas(e, x, p*q), p q primes, u=inverse of p mod q
-CRYPTOPP_DLL Integer CRYPTOPP_API InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q, const Integer &u);
-
-inline Integer ModularExponentiation(const Integer &a, const Integer &e, const Integer &m)
- {return a_exp_b_mod_c(a, e, m);}
-// returns x such that x*x%p == a, p prime
-CRYPTOPP_DLL Integer CRYPTOPP_API ModularSquareRoot(const Integer &a, const Integer &p);
-// returns x such that a==ModularExponentiation(x, e, p*q), p q primes,
-// and e relatively prime to (p-1)*(q-1)
-// dp=d%(p-1), dq=d%(q-1), (d is inverse of e mod (p-1)*(q-1))
-// and u=inverse of p mod q
-CRYPTOPP_DLL Integer CRYPTOPP_API ModularRoot(const Integer &a, const Integer &dp, const Integer &dq, const Integer &p, const Integer &q, const Integer &u);
-
-// find r1 and r2 such that ax^2 + bx + c == 0 (mod p) for x in {r1, r2}, p prime
-// returns true if solutions exist
-CRYPTOPP_DLL bool CRYPTOPP_API SolveModularQuadraticEquation(Integer &r1, Integer &r2, const Integer &a, const Integer &b, const Integer &c, const Integer &p);
-
-// returns log base 2 of estimated number of operations to calculate discrete log or factor a number
-CRYPTOPP_DLL unsigned int CRYPTOPP_API DiscreteLogWorkFactor(unsigned int bitlength);
-CRYPTOPP_DLL unsigned int CRYPTOPP_API FactoringWorkFactor(unsigned int bitlength);
-
-// ********************************************************
-
-//! generator of prime numbers of special forms
-class CRYPTOPP_DLL PrimeAndGenerator
-{
-public:
- PrimeAndGenerator() {}
- // generate a random prime p of the form 2*q+delta, where delta is 1 or -1 and q is also prime
- // Precondition: pbits > 5
- // warning: this is slow, because primes of this form are harder to find
- PrimeAndGenerator(signed int delta, RandomNumberGenerator &rng, unsigned int pbits)
- {Generate(delta, rng, pbits, pbits-1);}
- // generate a random prime p of the form 2*r*q+delta, where q is also prime
- // Precondition: qbits > 4 && pbits > qbits
- 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