ff 0.13 (#269)

* Partial move to ff 0.13

It turns out the newly released k256 0.12 isn't on ff 0.13, preventing further
work at this time.

* Update all crates to work on ff 0.13

The provided curves still need to be expanded to fit the new API.

* Finish adding dalek-ff-group ff 0.13 constants

* Correct FieldElement::product definition

Also stops exporting macros.

* Test most new parts of ff 0.13

* Additionally test ff-group-tests with BLS12-381 and the pasta curves

We only tested curves from RustCrypto. Now we test a curve offered by zk-crypto,
the group behind ff/group, and the pasta curves, which is by Zcash (though
Zcash developers are also behind zk-crypto).

* Finish Ed448

Fully specifies all constants, passes all tests in ff-group-tests, and finishes moving to ff-0.13.

* Add RustCrypto/elliptic-curves to allowed git repos

Needed due to k256/p256 incorrectly defining product.

* Finish writing ff 0.13 tests

* Add additional comments to dalek

* Further comments

* Update ethereum-serai to ff 0.13

crypto/ed448/src/scalar.rs

@@ -2,12 +2,15 @@ use zeroize::Zeroize;
 
 use crypto_bigint::{U512, U1024};
 
-use crate::field;
-
 /// Ed448 Scalar field element.
 #[derive(Clone, Copy, PartialEq, Eq, Default, Debug, Zeroize)]
 pub struct Scalar(pub(crate) U512);
 
+const MODULUS_STR: &str = concat!(
+  "3fffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+  "7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3",
+);
+
 // 2**446 - 13818066809895115352007386748515426880336692474882178609894547503885
 pub(crate) const MODULUS: Scalar = Scalar(U512::from_be_hex(concat!(
   "00000000000000",
@@ -25,7 +28,26 @@ const WIDE_MODULUS: U1024 = U1024::from_be_hex(concat!(
   "7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3",
 ));
 
-field!(Scalar, MODULUS, WIDE_MODULUS, 446);
+field!(
+  Scalar,
+  MODULUS_STR,
+  MODULUS,
+  WIDE_MODULUS,
+  446,
+  concat!(
+    "7a22ac554961bc91aac7e2463961b610481b6bd7a46d27e2f41165beffffffff",
+    "ffffffffffffffffffffffffffffffffffffffffffffff1f0000000000000000",
+  ),
+  2,
+  concat!(
+    "f24458ab92c27823558fc58d72c26c219036d6ae49db4ec4e923ca7cffffffff",
+    "ffffffffffffffffffffffffffffffffffffffffffffff3f0000000000000000",
+  ),
+  concat!(
+    "0400000000000000000000000000000000000000000000000000000000000000",
+    "0000000000000000000000000000000000000000000000000000000000000000",
+  ),
+);
 
 impl Scalar {
   /// Perform a wide reduction to obtain a non-biased Scalar.
@@ -35,7 +57,6 @@ impl Scalar {
 }
 
 #[test]
-fn test_scalar_field() {
-  // TODO: Move to test_prime_field_bits once the impl is finished
-  ff_group_tests::prime_field::test_prime_field::<_, Scalar>(&mut rand_core::OsRng);
+fn test_scalar() {
+  ff_group_tests::prime_field::test_prime_field_bits::<_, Scalar>(&mut rand_core::OsRng);
 }