implement Tonelli Shanks

ModularArithmeticUtils.hs

@@ -0,0 +1,19 @@
+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