|Maintainer||Vincent Hanquez <firstname.lastname@example.org>|
- generatePrime :: CPRG g => g -> Int -> (Integer, g)
- generateSafePrime :: CPRG g => g -> Int -> (Integer, g)
- isProbablyPrime :: CPRG g => g -> Integer -> (Bool, g)
- findPrimeFrom :: CPRG g => g -> Integer -> (Integer, g)
- findPrimeFromWith :: CPRG g => g -> (g -> Integer -> (Bool, g)) -> Integer -> (Integer, g)
- primalityTestNaive :: Integer -> Bool
- primalityTestMillerRabin :: CPRG g => g -> Int -> Integer -> (Bool, g)
- primalityTestFermat :: Int -> Integer -> Integer -> Bool
- isCoprime :: Integer -> Integer -> Bool
generate a prime number of the required bitsize
generate a prime number of the form 2p+1 where p is also prime. it is also knowed as a Sophie Germaine prime or safe prime.
The number of safe prime is significantly smaller to the number of prime, as such it shouldn't be used if this number is supposed to be kept safe.
returns if the number is probably prime. first a list of small primes are implicitely tested for divisibility, then a fermat primality test is used with arbitrary numbers and then the Miller Rabin algorithm is used with an accuracy of 30 recursions
find a prime from a starting point with no specific property.
find a prime from a starting point where the property hold.
Test naively is integer is prime. while naive, we skip even number and stop iteration at i > sqrt(n)
Miller Rabin algorithm return if the number is probably prime or composite. the tries parameter is the number of recursion, that determines the accuracy of the test.
number of iterations of the algorithm
number to test for primality
Probabilitic Test using Fermat primility test. Beware of Carmichael numbers that are Fermat liars, i.e. this test is useless for them. always combines with some other test.