Start experimenting with full generation of all of the numeric types.

Previously, we used a little bit of generation to drive a lot of Rust
macros. This works, but it's a little confusing to read and write. In
addition, we used a lot of implementations with variable timings based
on their input, which isn't great for crypto. This is the start of an
attempt to just generate all of the relevant Rust code directly, and to
use timing-channel resistant implementations for most of the routines.

old/unsigned/modexp.rs

@@ -0,0 +1,116 @@
+/// Modular exponentiation for a value.
+pub trait ModExp<T> {
+    /// Modular exponentiation using the given modulus type. If it's possible,
+    /// we suggest using Barrett values, which are much faster than doing
+    /// modulo with the number types.
+    fn modexp(&self, e: &Self, m: &T) -> Self;
+}
+
+macro_rules! modexp_impls {
+    ($name: ident, $other: ident) => {
+        impl ModExp<$other> for $name {
+            fn modexp(&self, ine: &$name, m: &$other) -> $name {
+                // S <- g
+                let mut s = self.clone();
+                // A <- 1
+                let mut a = $name::from(1u64);
+                // We do a quick skim through and find the highest index that
+                // actually has a value in it.
+                let mut e = ine.clone();
+                // While e != 0 do the following:
+                while e.value.iter().any(|x| *x != 0) {
+                    // If e is odd then A <- A * S
+                    if e.value[0] & 1 != 0 {
+                        a = a.modmul(&s, m);
+                    }
+                    // e <- floor(e / 2)
+                    let mut carry = 0;
+                    e.value.iter_mut().rev().for_each(|x| {
+                        let new_carry = *x & 1;
+                        *x = (*x >> 1) | (carry << 63);
+                        carry = new_carry;
+                    });
+                    // If e != 0 then S <- S * S
+                    s = s.modsq(m);
+                }
+                // Return A
+                a
+            }
+        }
+    };
+}
+
+#[cfg(test)]
+macro_rules! generate_modexp_tests {
+    ($name: ident, $lname: ident) => {
+        #[test]
+        fn $lname() {
+            generate_modexp_tests!(body $name, $lname);
+        }
+    };
+    (ignore $name: ident, $lname: ident) => {
+        #[test]
+        #[ignore]
+        fn $lname() {
+            generate_modexp_tests!(body $name, $lname);
+        }
+    };
+    (body $name: ident, $lname: ident) => {
+        let fname = build_test_path("modexp", stringify!($name));
+        run_test(fname.to_string(), 6, |case| {
+            let (neg0, bbytes) = case.get("b").unwrap();
+            let (neg1, ebytes) = case.get("e").unwrap();
+            let (neg2, mbytes) = case.get("m").unwrap();
+            let (neg3, rbytes) = case.get("r").unwrap();
+            assert!(!neg0 && !neg1 && !neg2 && !neg3);
+
+            let b = $name::from_bytes(bbytes);
+            let e = $name::from_bytes(ebytes);
+            let m = $name::from_bytes(mbytes);
+            let r = $name::from_bytes(rbytes);
+            assert_eq!(r, b.modexp(&e, &m));
+        });
+    };
+}
+
+#[cfg(test)]
+macro_rules! generate_barrett_modexp_tests {
+    (ignore $name: ident, $lname: ident, $bname: ident) => {
+        #[test]
+        #[ignore]
+        fn $lname() {
+            generate_barrett_modexp_tests!(body $name, $lname, $bname);
+        }
+    };
+    ($name: ident, $lname: ident, $bname: ident) => {
+        #[test]
+        fn $lname() {
+            generate_barrett_modexp_tests!(body $name, $lname, $bname);
+        }
+    };
+    (body $name: ident, $lname: ident, $bname: ident) => {
+        let fname = build_test_path("modexp", stringify!($name));
+        run_test(fname.to_string(), 6, |case| {
+            let (neg0, bbytes) = case.get("b").unwrap();
+            let (neg1, ebytes) = case.get("e").unwrap();
+            let (neg2, mbytes) = case.get("m").unwrap();
+            let (neg3, rbytes) = case.get("r").unwrap();
+            let (neg4, kbytes) = case.get("k").unwrap();
+            let (neg5, ubytes) = case.get("u").unwrap();
+            assert!(!neg0 && !neg1 && !neg2 && !neg3 && !neg4 && !neg5);
+
+            let b    = $name::from_bytes(bbytes);
+            let e    = $name::from_bytes(ebytes);
+            let m    = $name::from_bytes(mbytes);
+            let r    = $name::from_bytes(rbytes);
+            let kbig = $name::from_bytes(kbytes);
+            let k    = usize::from(kbig);
+            let mu   = $bname::from_bytes(ubytes);
+            let bar  = $name::new_barrett(k, $bname::from(m), mu);
+
+            if k == b.value.len() {
+                assert_eq!(r, b.modexp(&e, &bar));
+            }
+        });
+    };
+}