module ModularArithmeticUtils (modExp, modMul, legendre) where

import Data.Bits (testBit, shiftR)

-- Modular exponentiation: compute a^b mod m
modExp :: Integer -> Integer -> Integer -> Integer
modExp b 0 m = 1
modExp b e m = t * modExp ((b * b) `mod` m) (shiftR e 1) m `mod` m
            where t = if testBit e 0 then b `mod` m else 1

-- Compute (a * b) mod m
modMul :: Integer -> Integer -> Integer -> Integer
modMul a b m = (a * b) `mod` m

-- Compute the Legendre symbol (a/p)
-- (a/p) = a^((p-1)/2) mod p
-- (a/p) in {-1, 0, 1}
legendre :: Integer -> Integer -> Integer
legendre a p = modExp a ((p - 1) `div` 2) p