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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)
+
+// export a table of small primes
+extern const unsigned int maxPrimeTableSize;
+extern const word lastSmallPrime;
+extern unsigned int primeTableSize;
+extern word primeTable[];
+
+// build up the table to maxPrimeTableSize
+void BuildPrimeTable();
+
+// ************ primality testing ****************
+
+// generate a provable prime
+Integer MaurerProvablePrime(RandomNumberGenerator &rng, unsigned int bits);
+Integer MihailescuProvablePrime(RandomNumberGenerator &rng, unsigned int bits);
+
+bool 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
+bool TrialDivision(const Integer &p, unsigned bound);
+
+// returns true if p is NOT divisible by small primes
+bool SmallDivisorsTest(const Integer &p);
+
+// These is no reason to use these two, use the ones below instead
+bool IsFermatProbablePrime(const Integer &n, const Integer &b);
+bool IsLucasProbablePrime(const Integer &n);
+
+bool IsStrongProbablePrime(const Integer &n, const Integer &b);
+bool IsStrongLucasProbablePrime(const Integer &n);
+
+// Rabin-Miller primality test, i.e. repeating the strong probable prime test 
+// for several rounds with random bases
+bool RabinMillerTest(RandomNumberGenerator &rng, const Integer &w, unsigned int rounds);
+
+// primality test, used to generate primes
+bool IsPrime(const Integer &p);
+
+// more reliable than IsPrime(), used to verify primes generated by others
+bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level = 1);
+
+class 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
+bool FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod, const PrimeSelector *pSelector);
+
+unsigned int PrimeSearchInterval(const Integer &max);
+
+AlgorithmParameters<AlgorithmParameters<AlgorithmParameters<NullNameValuePairs, Integer::RandomNumberType>, Integer>, Integer>
+	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
+Integer CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q);
+// use this one if u = inverse of p mod q has been precalculated
+Integer 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
+int Jacobi(const Integer &a, const Integer &b);
+
+// calculates the Lucas function V_e(p, 1) mod n
+Integer Lucas(const Integer &e, const Integer &p, const Integer &n);
+// calculates x such that m==Lucas(e, x, p*q), p q primes
+Integer InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q);
+// use this one if u=inverse of p mod q has been precalculated
+Integer 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
+Integer 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)
+Integer ModularRoot(const Integer &a, const Integer &e, const Integer &p, const Integer &q);
+// use this one if 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 have been precalculated
+Integer 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
+bool 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
+unsigned int DiscreteLogWorkFactor(unsigned int bitlength);
+unsigned int FactoringWorkFactor(unsigned int bitlength);
+
+// ********************************************************
+
+//! generator of prime numbers of special forms
+class 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