Hello all This is my first post on Haskell-beginner so i am not completely aware of protocols here . Pardon me for my ignorance . I am trying to implement elliptic curve prime factorisation and initially wrote function "addPoints" using let in clause. It works fine. When i converted the "addPoint" using where clause then its not working and not adding the points correctly . I run both functions from ghci and for same point " addPoints ( Conelliptic 1222 34 5678 ) ( Conpoint 123 42567 ) ( Conpoint 1234 4322222222222222) " addPoints function using where clause return Right 2 while let in clause return Left (Conpoint 4840 4122) . Could some one please help me to find out the bug . In case of indentation problem , source code on http://hpaste.org/49174 . Regards Mukesh Tiwari --y^2= x^3+ax+b mod n import Random import Control.Monad import Data.List import Data.Bits data Elliptic = Conelliptic Integer Integer Integer deriving ( Eq , Show ) data Point = Conpoint Integer Integer | Identity deriving ( Eq , Show ) powM :: Integer -> Integer -> Integer -> Integer powM a d n | d == 0 = 1 | d == 1 = mod a n | otherwise = mod q n where p = powM ( mod ( a^2 ) n ) ( shiftR d 1 ) n q = if (.&.) d 1 == 1 then mod ( a * p ) n else p calSd :: Integer -> IO ( Integer , Integer ) calSd n = return ( s , d ) where s = until ( \x -> testBit ( n - 1) ( fromIntegral x ) ) ( +1 ) 0 d = div ( n - 1 ) ( shiftL 1 ( fromIntegral s ) ) isProbable::Integer->IO Bool isProbable n | n <= 1 = return False | n == 2 = return True | even n = return False | otherwise = calSd n >>= (\( s , d ) -> rabinMiller 0 n s d ) rabinMiller::Integer->Integer->Integer->Integer->IO Bool rabinMiller cnt n s d | cnt>=5= return True | otherwise = randomRIO ( 2 , n - 2 ) >>= (\a -> case powM a d n == 1 of True -> rabinMiller ( cnt + 1 ) n s d _ -> if any ( == pred n ) . take ( fromIntegral s ) . iterate (\e -> mod ( e^2 ) n ) $ powM a d n then rabinMiller ( cnt + 1) n s d else return False ) {-- --add points of elliptic curve addPoints :: Elliptic -> Point -> Point -> Either Point Integer addPoints _ Identity p_2 = Left p_2 addPoints _ p_1 Identity = Left p_1 addPoints ( Conelliptic a b n ) ( Conpoint x_p y_p ) ( Conpoint x_q y_q ) | x_p /= x_q = case ( ( Conpoint x_r y_r ) , d ) of ( _ , 1 ) -> Left ( Conpoint x_r y_r ) ( _ , d' ) -> Right d' where [ u , v , d ] = extended_gcd ( x_p - x_q ) n s = mod ( ( y_p - y_q ) * u ) n x_r = mod ( s*s - x_p - x_q ) n y_r = mod ( -y_p - s * ( x_r - x_p ) ) n | otherwise = if mod ( y_p + y_q ) n == 0 then Left Identity else case ( ( Conpoint x_r y_r ) , d ) of ( _ , 1 ) -> Left ( Conpoint x_r y_r ) ( _ , d' ) -> Right d' where [ u , v , d ] = extended_gcd ( 2 * y_p ) n s = mod ( ( 3 * x_p * x_p + a ) * u ) n x_r = mod ( s * s - 2 * x_p ) n y_r = mod ( -y_p - s * ( x_r - x_p ) ) n --} --add points of elliptic curve addPoints::Elliptic->Point->Point-> Either Point Integer addPoints _ Identity p_2 = Left p_2 addPoints _ p_1 Identity = Left p_1 addPoints ( Conelliptic a b n ) ( Conpoint x_p y_p ) ( Conpoint x_q y_q ) | x_p /= x_q = let [ u , v , d ] = extended_gcd (x_p-x_q) n s = mod ( ( y_p - y_q ) * u ) n x_r = mod ( s * s - x_p - x_q ) n y_r= mod ( -y_p - s * ( x_r - x_p ) ) n in case ( ( Conpoint x_r y_r ) , d ) of ( _ , 1 ) -> Left ( Conpoint x_r y_r ) ( _ , d' ) -> Right d' | otherwise = if mod ( y_p + y_q ) n == 0 then Left Identity else let [ u , v , d ] = extended_gcd ( 2*y_p ) n s = mod ( ( 3 * x_p * x_p + a ) * u ) n x_r = mod ( s * s - 2 * x_p ) n y_r = mod ( -y_p - s * ( x_r - x_p ) ) n in case ( ( Conpoint x_r y_r ) , d ) of ( _ , 1 )-> Left (Conpoint x_r y_r) ( _ , d' ) -> Right d' extended_gcd::Integer->Integer->[Integer] extended_gcd u v= helpGcd u v 0 [ [ 1 , 0 ] , [ 0 , 1 ] ] where helpGcd u v n m @ ( [ [ a , b ] , [ c , d ] ] ) | v == 0 = if u<0 then [ - ( ( -1 ) ^ n ) * ( m !! 1 !! 1 ) , - ( ( -1 ) ^ ( n + 1 ) ) * ( m !! 0 !! 1 ) , -u ] else [ ( ( -1 ) ^ n ) * ( m !! 1 !! 1 ) , ( ( -1 ) ^ ( n + 1 ) ) * ( m !! 0 !! 1 ) , u ] | otherwise = helpGcd u' v' ( n + 1 ) m' where ( q , v' ) = quotRem u v t = [ [q , 1 ] , [ 1 , 0 ] ] m' = [ [ q * a + b , a ] , [ q * c + d , c ] ] --mult m t u' = v multiEC :: Elliptic -> Point -> Integer -> IO ( Either Point Integer ) multiEC _ _ 0 = return $ Left Identity multiEC ecurve point k | k>0 = return $ helpEC Identity point k where helpEC p _ 0 = Left p helpEC p q n = case (p',q') of ( Left p'' , Left q'' ) -> helpEC p'' q'' (div n 2) ( Right p'' , _ ) -> Right p'' ( _ , Right q'' ) -> Right q'' where p' =if odd n then addPoints ecurve p q else Left p q' = addPoints ecurve q q dscrmntEC a b = 4 * a * a * a + 27 * b * b randomCurve :: Integer -> IO [Integer] randomCurve n = randomRIO ( 1 , n ) >>= ( \a -> randomRIO ( 1 , n ) >>= ( \u -> randomRIO (1 , n) >>= (\v -> return [a , mod ( v*v - u*u*u - a*u ) n , n , u , v ] ) ) ) factor :: Integer -> Integer -> IO [Integer] factor 1 _ = return [] factor n m = isProbable n >>= (\x -> if x then return [n] else randomCurve n >>= (\[ a , b , n , u , v ] -> multiEC ( Conelliptic a b n ) ( Conpoint u v ) m >>= ( \p -> case p of Left p' -> factor n m Right p'-> factor ( div n p' ) m >>= ( \x -> factor p' m >>= (\y -> return $ x ++ y ) ) ) ) ) solve :: Integer -> IO [ Integer ] solve n = factor n ( foldl lcm 1 [1..10000] ) main = liftM read getLine >>=( \n -> solve n ) >>= print