SolaveyStrassen

ModularArithmeticUtils.hs

@@ -1,4 +1,4 @@
-module ModularArithmeticUtils (modExp, modMul, legendre, factorOutTwos) where
+module ModularArithmeticUtils (modExp, modMul, legendre, factorOutTwos, jacobi) where
 
 import Data.Bits (testBit, shiftR)
 

SolaveyStrassen.hs

@@ -0,0 +1,28 @@
+module SolaveyStrassen (solaveyStrassen) where
+
+import ModularArithmeticUtils (modExp, jacobi)
+import System.Random (randomRIO)
+
+
+solaveyStrassen :: Integer -> Integer -> IO Bool
+solaveyStrassen n k
+  | n < 2     = return False
+  | n == 2    = return True
+  | even n    = return False
+  | otherwise = go k
+    where
+    expHalf = (n - 1) `div` 2
+
+    go 0 = return True
+    go i = do
+      a <- randomRIO (2, n - 2)
+      if gcd a n /= 1
+        then return False
+        else do
+          let x = modExp a expHalf n
+              j = jacobi a n `mod` n
+
+          if x /= j
+            then return False
+            else go (i - 1)
+