Use crypto-bigint's reduction in ed448

Achieves feasible performance in the ed448 which makes it potentially viable
for real world usage.

Accordingly prepares a new release, updating the README.

Cargo.lock

@@ -5091,7 +5091,7 @@ checksum = "6877bb514081ee2a7ff5ef9de3281f14a4dd4bceac4c09388074a6b5df8a139a"
 
 [[package]]
 name = "minimal-ed448"
-version = "0.3.0"
+version = "0.3.1"
 dependencies = [
  "crypto-bigint 0.5.1",
  "ff 0.13.0",

crypto/ed448/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "minimal-ed448"
-version = "0.3.0"
+version = "0.3.1"
 description = "Unaudited, inefficient implementation of Ed448 in Rust"
 license = "MIT"
 repository = "https://github.com/serai-dex/serai/tree/develop/crypto/ed448"

crypto/ed448/README.md

@@ -1,9 +1,9 @@
 # Minimal Ed448
 
-Inefficient, barebones implementation of Ed448 bound to the ff/group API,
-rejecting torsion to achieve a PrimeGroup definition. This likely should not be
-used and was only done so another library under Serai could confirm its
-completion. It is minimally tested, yet should be correct for what it has. This
-has not undergone auditing.
+Barebones implementation of Ed448 bound to the ff/group API, rejecting torsion
+to achieve a PrimeGroup definition.
+
+This library has not been audited. While it is complete, and decently tested,
+any usage of it should be carefully considered.
 
 constant time and no_std.

crypto/ed448/src/backend.rs

@@ -69,6 +69,7 @@ macro_rules! field {
   (
     $FieldName: ident,
 
+    $MODULUS_PADDED_STR: ident,
     $MODULUS_STR: ident,
     $MODULUS: ident,
     $WIDE_MODULUS: ident,
@@ -89,12 +90,14 @@ macro_rules! field {
     use rand_core::RngCore;
 
     use generic_array::{typenum::U57, GenericArray};
-    use crypto_bigint::{Integer, NonZero, Encoding};
+    use crypto_bigint::{Integer, NonZero, Encoding, impl_modulus};
 
     use ff::{Field, PrimeField, FieldBits, PrimeFieldBits, helpers::sqrt_ratio_generic};
 
     use $crate::backend::u8_from_bool;
 
+    impl_modulus!(CryptoBigIntModulus, U512, $MODULUS_PADDED_STR);
+
     fn reduce(x: U1024) -> U512 {
       U512::from_le_slice(&x.rem(&NonZero::new($WIDE_MODULUS).unwrap()).to_le_bytes()[.. 64])
     }
@@ -121,9 +124,12 @@ macro_rules! field {
       &y,
       &$MODULUS.0
     ));
-    math_op!($FieldName, $FieldName, Mul, mul, MulAssign, mul_assign, |x, y| reduce(U1024::from(
-      U512::mul_wide(&x, &y)
-    )));
+    math_op!($FieldName, $FieldName, Mul, mul, MulAssign, mul_assign, |x, y| {
+      use crypto_bigint::modular::constant_mod::{ResidueParams, Residue};
+      Residue::<CryptoBigIntModulus, { CryptoBigIntModulus::LIMBS }>::new(&x)
+        .mul(&Residue::<CryptoBigIntModulus, { CryptoBigIntModulus::LIMBS }>::new(&y))
+        .retrieve()
+    });
 
     from_wrapper!($FieldName, U512, u8);
     from_wrapper!($FieldName, U512, u16);

crypto/ed448/src/field.rs

@@ -6,6 +6,13 @@ use crypto_bigint::{U512, U1024};
 #[derive(Clone, Copy, PartialEq, Eq, Default, Debug, Zeroize)]
 pub struct FieldElement(pub(crate) U512);
 
+const MODULUS_PADDED_STR: &str = concat!(
+  "00000000000000",
+  "00",
+  "fffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
+  "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+);
+
 const MODULUS_STR: &str = concat!(
   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
   "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
@@ -33,6 +40,7 @@ pub(crate) const Q_4: FieldElement =
 
 field!(
   FieldElement,
+  MODULUS_PADDED_STR,
   MODULUS_STR,
   MODULUS,
   WIDE_MODULUS,

crypto/ed448/src/scalar.rs

@@ -6,6 +6,13 @@ use crypto_bigint::{U512, U1024};
 #[derive(Clone, Copy, PartialEq, Eq, Default, Debug, Zeroize)]
 pub struct Scalar(pub(crate) U512);
 
+const MODULUS_PADDED_STR: &str = concat!(
+  "00000000000000",
+  "00",
+  "3fffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+  "7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3",
+);
+
 const MODULUS_STR: &str = concat!(
   "3fffffffffffffffffffffffffffffffffffffffffffffffffffffff",
   "7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3",
@@ -30,6 +37,7 @@ const WIDE_MODULUS: U1024 = U1024::from_be_hex(concat!(
 
 field!(
   Scalar,
+  MODULUS_PADDED_STR,
   MODULUS_STR,
   MODULUS,
   WIDE_MODULUS,