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Update documentation

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Jeffrey Walton 2018-03-26 17:41:06 -04:00
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commit 780a2b8c82
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1 changed files with 27 additions and 5 deletions
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nbtheory.h
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@ -165,16 +165,38 @@ inline Integer LCM(const Integer &a, const Integer &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
/// \brief Chinese Remainder Theorem
/// \param xp the first number, mod p
/// \param p the first prime modulus
/// \param xq the second number, mod q
/// \param q the second prime modulus
/// \param u inverse of p mod q
/// \returns the CRT value of the parameters
/// \details CRT uses the Chinese Remainder Theorem to calculate <tt>x</tt> given
/// <tt>x mod p</tt> and <tt>x mod q</tt>, and <tt>u</tt> the inverse of <tt>p mod q</tt>.
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
/// \brief Calculate the Jacobi symbol
/// \param a the first term
/// \param b the second term
/// \returns the the Jacobi symbol.
/// \details Jacobi symbols are calculated using the following rules:
/// -# if <tt>b</tt> is prime, then <tt>Jacobi(a, b)</tt>, then return 0
/// -# if <tt>a%b</tt>==0 AND <tt>a</tt> is quadratic residue <tt>mod b</tt>, then return 1
/// -# return -1 otherwise
/// \details Refer to a number theory book for what Jacobi symbol means when <tt>b</tt> 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
/// \brief Calculate the Lucas value
/// \returns the Lucas value
/// \details Lucas() calculates the Lucas function <tt>V_e(p, 1) mod n</tt>.
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
/// \brief Calculate the inverse Lucas value
/// \returns the inverse Lucas value
/// \details InverseLucas() calculates <tt>x</tt> such that <tt>m==Lucas(e, x, p*q)</tt>,
/// <tt>p q</tt> primes, <tt>u</tt> is inverse of <tt>p mod q</tt>.
CRYPTOPP_DLL Integer CRYPTOPP_API InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q, const Integer &u);
/// \brief Modular multiplication