/usr/include/crypto++/nbtheory.h is in libcrypto++-dev 5.6.1-6+deb8u3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 | // 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
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