Unsigned modular operations.

generation/Test.hs

@@ -1,4 +1,47 @@
+import Data.Bits hiding (bit)
+import Debug.Trace
+import GHC.Integer.GMP.Internals
 import qualified Karatsuba
+import Numeric
+import Test.QuickCheck
+
+modular_exponentiation :: Integer -> Integer -> Integer -> Integer
+modular_exponentiation x y m = m_e_loop x y 1
+ where
+  m_e_loop _ 0 result = result
+  m_e_loop b e result = m_e_loop b' e' result'
+   where
+    b'      = (b * b) `mod` m
+    e'      = e `shiftR` 1
+    result' = if testBit e 0 then (result * b) `mod` m else result
+
+prop_modExpSane :: Integer -> Integer -> Integer -> Property
+prop_modExpSane b e m = (m' > 1) ==> modular_exponentiation b' e' m' == powModInteger b' e' m'
+ where
+  b' = abs b
+  e' = abs e
+  m' = abs m
+
+modexpLR :: Int -> Integer -> Integer -> Integer -> Integer
+modexpLR bitsize b e m = go (bitsize - 1) 1
+ where
+   go bit r0
+     | bit < 0       = r0
+     | testBit e bit = trace ("1: r = " ++ showHex r2 "") $ go (bit - 1) r2
+     | otherwise     = trace ("0: r = " ++ showHex r1 "") $ go (bit - 1) r1
+    where
+     r1 = (r0 * r0) `mod` m
+     r2 = (r1 * b)  `mod` m
+
+prop_modExpLR192 :: Integer -> Integer -> Integer -> Property
+prop_modExpLR192 b e m = (m' > 1) ==> modexpLR 192 b' e' m' == powModInteger b' e' m'
+ where
+  b' = abs b `mod` (2 ^ (192 :: Integer))
+  e' = abs e `mod` (2 ^ (192 :: Integer))
+  m' = abs m `mod` (2 ^ (192 :: Integer))
 
 main :: IO ()
-main = Karatsuba.runChecks
+main =
+  do Karatsuba.runChecks 
+     Karatsuba.runQuickCheck "Modular exponentiation sanity check" prop_modExpSane
+     Karatsuba.runQuickCheck "ModExp LR 192 works" prop_modExpLR192