110 lines
4.6 KiB
C++
110 lines
4.6 KiB
C++
// nbtheory.h - written and placed in the public domain by Wei Dai
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#ifndef CRYPTOPP_NBTHEORY_H
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#define CRYPTOPP_NBTHEORY_H
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#include "integer.h"
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#include "algparam.h"
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namespace CryptoPP {
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// export a table of small primes
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extern const unsigned int maxPrimeTableSize;
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extern const word lastSmallPrime;
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extern unsigned int primeTableSize;
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extern word primeTable[];
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// build up the table to maxPrimeTableSize
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void BuildPrimeTable();
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// ************ primality testing ****************
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bool IsSmallPrime(const Integer &p);
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// returns true if p is divisible by some prime less than bound
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// bound not be greater than the largest entry in the prime table
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bool TrialDivision(const Integer &p, unsigned bound);
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// returns true if p is NOT divisible by small primes
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bool SmallDivisorsTest(const Integer &p);
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bool IsStrongProbablePrime(const Integer &n, const Integer &b);
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bool IsStrongLucasProbablePrime(const Integer &n);
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// Rabin-Miller primality test, i.e. repeating the strong probable prime test
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// for several rounds with random bases
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bool RabinMillerTest(RandomNumberGenerator &rng, const Integer &w, unsigned int rounds);
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// primality test, used to generate primes
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bool IsPrime(const Integer &p);
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// more reliable than IsPrime(), used to verify primes generated by others
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bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level = 1);
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class PrimeSelector
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{
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public:
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virtual ~PrimeSelector() {}
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const PrimeSelector *GetSelectorPointer() const {return this;}
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virtual bool IsAcceptable(const Integer &candidate) const =0;
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};
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// use a fast sieve to find the first probable prime in {x | p<=x<=max and x%mod==equiv}
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// returns true iff successful, value of p is undefined if no such prime exists
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bool FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod, const PrimeSelector *pSelector);
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unsigned int PrimeSearchInterval(const Integer &max);
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AlgorithmParameters<AlgorithmParameters<AlgorithmParameters<NullNameValuePairs, Integer::RandomNumberType>, Integer>, Integer>
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MakeParametersForTwoPrimesOfEqualSize(unsigned int productBitLength);
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// ********** other number theoretic functions ************
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inline Integer GCD(const Integer &a, const Integer &b)
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{return Integer::Gcd(a,b);}
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inline bool RelativelyPrime(const Integer &a, const Integer &b)
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{return Integer::Gcd(a,b) == Integer::One();}
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inline Integer LCM(const Integer &a, const Integer &b)
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{return a/Integer::Gcd(a,b)*b;}
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inline Integer EuclideanMultiplicativeInverse(const Integer &a, const Integer &b)
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{return a.InverseMod(b);}
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// use Chinese Remainder Theorem to calculate x given x mod p and x mod q
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Integer CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q);
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// use this one if u = inverse of p mod q has been precalculated
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Integer CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q, const Integer &u);
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// if b is prime, then Jacobi(a, b) returns 0 if a%b==0, 1 if a is quadratic residue mod b, -1 otherwise
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// check a number theory book for what Jacobi symbol means when b is not prime
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int Jacobi(const Integer &a, const Integer &b);
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// calculates the Lucas function V_e(p, 1) mod n
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Integer Lucas(const Integer &e, const Integer &p, const Integer &n);
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// calculates x such that m==Lucas(e, x, p*q), p q primes
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Integer InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q);
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// use this one if u=inverse of p mod q has been precalculated
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Integer InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q, const Integer &u);
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inline Integer ModularExponentiation(const Integer &a, const Integer &e, const Integer &m)
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{return a_exp_b_mod_c(a, e, m);}
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// returns x such that x*x%p == a, p prime
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Integer ModularSquareRoot(const Integer &a, const Integer &p);
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// returns x such that a==ModularExponentiation(x, e, p*q), p q primes,
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// and e relatively prime to (p-1)*(q-1)
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Integer ModularRoot(const Integer &a, const Integer &e, const Integer &p, const Integer &q);
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// use this one if dp=d%(p-1), dq=d%(q-1), (d is inverse of e mod (p-1)*(q-1))
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// and u=inverse of p mod q have been precalculated
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Integer ModularRoot(const Integer &a, const Integer &dp, const Integer &dq, const Integer &p, const Integer &q, const Integer &u);
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// find r1 and r2 such that ax^2 + bx + c == 0 (mod p) for x in {r1, r2}, p prime
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// returns true if solutions exist
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bool SolveModularQuadraticEquation(Integer &r1, Integer &r2, const Integer &a, const Integer &b, const Integer &c, const Integer &p);
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// returns log base 2 of estimated number of operations to calculate discrete log or factor a number
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unsigned int DiscreteLogWorkFactor(unsigned int bitlength);
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unsigned int FactoringWorkFactor(unsigned int bitlength);
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}
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#endif
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