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

generation/generation.cabal

@@ -58,4 +58,4 @@ test-suite test-generation
   default-language:    Haskell2010
   main-is:             Test.hs
   ghc-options:         -Wall
-  build-depends:       base, generation
+  build-depends:       base, generation, integer-gmp, QuickCheck

generation/src/ModOps.hs

@@ -5,7 +5,6 @@ module ModOps(modulusOps)
 import Data.Map.Strict(Map)
 import qualified Data.Map.Strict as Map
 import File
-import Gen(toLit)
 import Generators
 import GHC.Integer.GMP.Internals(powModInteger)
 import Language.Rust.Data.Ident
@@ -15,7 +14,7 @@ import Language.Rust.Syntax
 import System.Random(RandomGen)
 
 numTestCases :: Int
-numTestCases = 3000
+numTestCases = 1000
 
 modulusOps :: File
 modulusOps = File {
@@ -30,9 +29,15 @@ declareModOps :: Word -> [Word] -> SourceFile Span
 declareModOps bitsize _ =
     let sname = mkIdent ("U" ++ show bitsize)
         bname = mkIdent ("U" ++ show (bitsize * 2))
-    in [sourceFile| 
+        testFileLit = Lit [] (Str (testFile bitsize) Cooked Unsuffixed mempty) mempty
-        use crate::unsigned::$$sname;
+    in [sourceFile|
+        use core::convert::TryFrom; 
+        use crate::unsigned::{$$sname, $$bname};
         use crate::{DivMod, ModularOperations};
+        #[cfg(test)]
+        use crate::CryptoNum;
+        #[cfg(test)]
+        use crate::testing::{build_test_path,run_test};
 
         impl ModularOperations for $$sname {
             fn reduce(&self, m: &$$sname) -> $$sname {
@@ -41,18 +46,69 @@ declareModOps bitsize _ =
             }
 
             fn modmul(&self, y: &$$sname, m: &$$sname) -> $$sname {
-                panic!("modmul")
+                let r = self * y;
+                let bigm = $$bname::from(m);
+                let bigres = r % bigm;
+                $$sname::try_from(bigres)
+                        .expect("Mathematics is broken?! (mod returned too big result")
             }
 
             fn modsq(&self, m: &$$sname) -> $$sname {
-                panic!("reduce")
+                let r = self * self;
+                let bigm = $$bname::from(m);
+                let bigres = r % bigm;
+                $$sname::try_from(bigres)
+                        .expect("Mathematics is broken?! (mod returned too big result")
             }
 
             fn modexp(&self, e: &$$sname, m: &$$sname) -> $$sname {
-                panic!("reduce")
+                let mut r    = $$sname::from(1u64);
+                let     bigm = $$bname::from(m);
+
+                for digit in e.value.iter().rev() {
+                    for bit in (0..64).rev() {
+                        r = r.modsq(&m);
+                        let big_possible_r = (&r * self) % &bigm;
+                        let possible_r = $$sname::try_from(big_possible_r)
+                                                 .expect("Math is broken (again)");
+                        let bit = (*digit >> bit) & 1;
+                        r = if bit == 1 { possible_r } else { r };
+                    }
+                }
+
+                r
             }
         }
-    |]
+
+        #[cfg(test)]
+        #[allow(non_snake_case)]
+        #[test]
+        fn KATs() {
+            run_test(build_test_path("modops", $$(testFileLit)), 7, |case| {
+                let (neg0, xbytes) = case.get("x").unwrap();
+                let (neg1, ybytes) = case.get("y").unwrap();
+                let (neg2, mbytes) = case.get("m").unwrap();
+                let (neg3, rbytes) = case.get("r").unwrap();
+                let (neg4, tbytes) = case.get("t").unwrap();
+                let (neg5, sbytes) = case.get("s").unwrap();
+                let (neg6, ebytes) = case.get("e").unwrap();
+
+                assert!(!neg0 && !neg1 && !neg2 && !neg3 && !neg4 && !neg5 && !neg6);
+                let x = $$sname::from_bytes(&xbytes);
+                let y = $$sname::from_bytes(&ybytes);
+                let m = $$sname::from_bytes(&mbytes);
+                let r = $$sname::from_bytes(&rbytes);
+                let t = $$sname::from_bytes(&tbytes);
+                let s = $$sname::from_bytes(&sbytes);
+                let e = $$sname::from_bytes(&ebytes);
+
+                assert_eq!(r, x.reduce(&m));
+                assert_eq!(t, x.modmul(&y, &m));
+                assert_eq!(s, x.modsq(&m));
+                assert_eq!(e, x.modexp(&y, &m));
+            });
+        }
+     |]
 
 generateModulusTests :: RandomGen g => Word -> g -> [Map String String]
 generateModulusTests size g = go g numTestCases

src/testing.rs

@@ -63,7 +63,6 @@ fn next_test_case(contents: &mut Lines, lines: usize) ->
 pub fn run_test<F>(fname: PathBuf, i: usize, f: F)
  where F: Fn(HashMap<String,(bool,Vec<u8>)>)
 {
-    println!("fname: {:?}", fname);
     let mut file = File::open(fname).unwrap();
     let mut contents = String::new();
     file.read_to_string(&mut contents).unwrap();