Pollard p-1

PollardPminus1.hs

@@ -0,0 +1,59 @@
+import Text.Read (readMaybe)
+import System.Exit (exitSuccess)
+import Data.Bits
+
+main :: IO ()
+main = do
+    n <- askNumber "Enter an integer n>1 to factor:"
+    b <- askNumber "Enter the bound B:"
+    putStrLn ("n = " ++ show n)
+
+    case pollardP1 n b of
+        Just factor -> do
+            putStrLn ("Found factor: " ++ show factor)
+            let otherFactor = n `div` factor
+            putStrLn ("Other factor: " ++ show otherFactor)
+        Nothing -> do
+            putStrLn "Failed to find a factor using Pollard p-1 method. n could be prime or different parameters needed."
+
+askNumber :: String -> IO Integer
+askNumber s = do
+    putStrLn s
+    input <- getLine
+    case readMaybe input of
+        Just n | n > 1 -> return n
+        _ -> do
+            putStrLn "Not a valid integer"
+            exitSuccess
+
+-- Pollard p-1 factorization algorithm
+pollardP1 :: Integer -> Integer -> Maybe Integer
+pollardP1 n b = tryBases [2..5]
+  where
+    tryBases [] = Nothing
+    tryBases (a:as) =
+        case pollardP1WithParams n a b of
+            Just factor -> Just factor
+            Nothing     -> tryBases as
+
+-- Pollard p-1 with configurable parameters
+pollardP1WithParams :: Integer -> Integer -> Integer -> Maybe Integer
+pollardP1WithParams n a b = go a 2
+  where
+    go currentA k
+        | k > b = Nothing  -- Bound exceeded, failed to find factor
+        | otherwise =
+            let newA = modExp currentA k n
+                d = gcd (newA - 1) n
+            in if d > 1 && d < n
+               then Just d  -- Found a non-trivial factor
+               else if d == n
+               then Nothing -- Found n itself, try with different parameters
+               else go newA (k + 1)
+
+-- 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
+