From b21162cf8e06f40baa1f58be6a8c17435cebc34d Mon Sep 17 00:00:00 2001 From: weidai Date: Fri, 4 Oct 2002 17:31:41 +0000 Subject: Initial revision git-svn-id: svn://svn.code.sf.net/p/cryptopp/code/trunk/c5@2 57ff6487-cd31-0410-9ec3-f628ee90f5f0 --- nbtheory.h | 143 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 143 insertions(+) create mode 100644 nbtheory.h (limited to 'nbtheory.h') diff --git a/nbtheory.h b/nbtheory.h new file mode 100644 index 0000000..685dc41 --- /dev/null +++ b/nbtheory.h @@ -0,0 +1,143 @@ +// 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, 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 -- cgit v1.2.1