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/field.rs

@@ -2,12 +2,15 @@ use zeroize::Zeroize;
 
 use crypto_bigint::{U512, U1024};
 
-use crate::field;
-
 /// Ed448 field element.
 #[derive(Clone, Copy, PartialEq, Eq, Default, Debug, Zeroize)]
 pub struct FieldElement(pub(crate) U512);
 
+const MODULUS_STR: &str = concat!(
+  "fffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
+  "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+);
+
 // 2**448 - 2**224 - 1
 pub(crate) const MODULUS: FieldElement = FieldElement(U512::from_be_hex(concat!(
   "00000000000000",
@@ -22,16 +25,34 @@ const WIDE_MODULUS: U1024 = U1024::from_be_hex(concat!(
   "00000000000000",
   "00",
   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
-  "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+  "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
 ));
 
 pub(crate) const Q_4: FieldElement =
   FieldElement(MODULUS.0.saturating_add(&U512::ONE).wrapping_div(&U512::from_u8(4)));
 
-field!(FieldElement, MODULUS, WIDE_MODULUS, 448);
+field!(
+  FieldElement,
+  MODULUS_STR,
+  MODULUS,
+  WIDE_MODULUS,
+  448,
+  concat!(
+    "00000000000000000000000000000000000000000000000000000080ffffffff",
+    "ffffffffffffffffffffffffffffffffffffffffffffff7f0000000000000000",
+  ),
+  7,
+  concat!(
+    "fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffff",
+    "ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000",
+  ),
+  concat!(
+    "3100000000000000000000000000000000000000000000000000000000000000",
+    "0000000000000000000000000000000000000000000000000000000000000000",
+  ),
+);
 
 #[test]
 fn test_field() {
-  // TODO: Move to test_prime_field_bits once the impl is finished
-  ff_group_tests::prime_field::test_prime_field::<_, FieldElement>(&mut rand_core::OsRng);
+  ff_group_tests::prime_field::test_prime_field_bits::<_, FieldElement>(&mut rand_core::OsRng);
 }