Crypto.Number.Prime

cryptonite-0.13: Cryptography Primitives sink

License | BSD-style
Maintainer | Vincent Hanquez <vincent@snarc.org>
Stability | experimental
Portability | Good
Safe Haskell | None
Language | Haskell2010

Crypto.Number.Prime

Description

Synopsis

- generatePrime :: MonadRandom m => Int -> m Integer
- generateSafePrime :: MonadRandom m => Int -> m Integer
- isProbablyPrime :: Integer -> Bool
- findPrimeFrom :: Integer -> Integer
- findPrimeFromWith :: (Integer -> Bool) -> Integer -> Integer
- primalityTestMillerRabin :: Int -> Integer -> Bool
- primalityTestNaive :: Integer -> Bool
- primalityTestFermat :: Int -> Integer -> Integer -> Bool
- isCoprime :: Integer -> Integer -> Bool

# Documentation

generatePrime :: MonadRandom m => Int -> m Integer

generate a prime number of the required bitsize

generateSafePrime :: MonadRandom m => Int -> m Integer

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.

isProbablyPrime :: Integer -> Bool

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

findPrimeFrom :: Integer -> Integer

find a prime from a starting point with no specific property.

findPrimeFromWith :: (Integer -> Bool) -> Integer -> Integer

find a prime from a starting point where the property hold.

primalityTestMillerRabin :: Int -> Integer -> Bool

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.

primalityTestNaive :: Integer -> Bool

Test naively is integer is prime. while naive, we skip even number and stop iteration at i > sqrt(n)

primalityTestFermat

Arguments

:: Int | number of iterations of the algorithm
-> Integer | starting a
-> Integer | number to test for primality
-> Bool |

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.

isCoprime :: Integer -> Integer -> Bool

Test is two integer are coprime to each other