Remove FieldExt::ROOT_OF_UNITY

We can use the `ff::PrimeField::root_of_unity` method everywhere we
currently use this associated constant. If there is a more general
need for accessing this as an associated constant, we should consider
that for `ff::PrimeField`.

CHANGELOG.md

@@ -6,6 +6,9 @@ and this project adheres to Rust's notion of
 [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
 ## [Unreleased]
+### Removed
+- `pasta_curves::arithmetic`:
+  - `FieldExt::ROOT_OF_UNITY` (use `ff::PrimeField::root_of_unity` instead).
 
 ## [0.2.1] - 2021-09-17
 ### Changed

src/arithmetic/fields.rs

@@ -28,10 +28,7 @@ pub trait FieldExt: ff::PrimeField + From<bool> + Ord + Group<Scalar = Self> {
     /// Modulus of the field written as a string for display purposes
     const MODULUS: &'static str;
 
-    /// Generator of the $2^S$ multiplicative subgroup
+    /// Inverse of `PrimeField::root_of_unity()`
-    const ROOT_OF_UNITY: Self;
-
-    /// Inverse of `ROOT_OF_UNITY`
     const ROOT_OF_UNITY_INV: Self;
 
     /// The value $(T-1)/2$ such that $2^S \cdot T = p - 1$ with $T$ odd.
@@ -233,7 +230,7 @@ impl<F: FieldExt> SqrtTables<F> {
             marker: PhantomData,
         };
 
-        let mut gtab = (0..4).scan(F::ROOT_OF_UNITY, |gi, _| {
+        let mut gtab = (0..4).scan(F::root_of_unity(), |gi, _| {
             // gi == ROOT_OF_UNITY^(256^i)
             let gtab_i: Vec<F> = (0..256)
                 .scan(F::one(), |acc, _| {
@@ -331,7 +328,7 @@ impl<F: FieldExt> SqrtTables<F> {
 
         let sqdiv = res.square() * div;
         let is_square = (sqdiv - num).is_zero();
-        let is_nonsquare = (sqdiv - F::ROOT_OF_UNITY * num).is_zero();
+        let is_nonsquare = (sqdiv - F::root_of_unity() * num).is_zero();
         assert!(bool::from(
             num.is_zero() | div.is_zero() | (is_square ^ is_nonsquare)
         ));
@@ -348,7 +345,7 @@ impl<F: FieldExt> SqrtTables<F> {
 
         let sq = res.square();
         let is_square = (sq - u).is_zero();
-        let is_nonsquare = (sq - F::ROOT_OF_UNITY * u).is_zero();
+        let is_nonsquare = (sq - F::root_of_unity() * u).is_zero();
         assert!(bool::from(u.is_zero() | (is_square ^ is_nonsquare)));
 
         (is_square, res)

src/curves.rs

@@ -1100,7 +1100,7 @@ impl Ep {
         0x4000000000000000,
     ]);
 
-    /// `(F::ROOT_OF_UNITY.invert().unwrap() * z).sqrt().unwrap()`
+    /// `(F::root_of_unity().invert().unwrap() * z).sqrt().unwrap()`
     pub const THETA: Fp = Fp::from_raw([
         0xca330bcc09ac318e,
         0x51f64fc4dc888857,
@@ -1200,7 +1200,7 @@ impl Eq {
         0x4000000000000000,
     ]);
 
-    /// `(F::ROOT_OF_UNITY.invert().unwrap() * z).sqrt().unwrap()`
+    /// `(F::root_of_unity().invert().unwrap() * z).sqrt().unwrap()`
     pub const THETA: Fq = Fq::from_raw([
         0x632cae9872df1b5d,
         0x38578ccadf03ac27,

src/fields/fp.rs

@@ -673,7 +673,6 @@ lazy_static! {
 impl FieldExt for Fp {
     const MODULUS: &'static str =
         "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001";
-    const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;
     const ROOT_OF_UNITY_INV: Self = Fp::from_raw([
         0xf0b87c7db2ce91f6,
         0x84a0a1d8859f066f,
@@ -854,8 +853,8 @@ fn test_sqrt_ratio_and_alt() {
     assert!(v_alt == v);
 
     // (false, sqrt(ROOT_OF_UNITY * num/div)), if num and div are nonzero and num/div is a nonsquare in the field
-    let num = num * Fp::ROOT_OF_UNITY;
+    let num = num * Fp::root_of_unity();
-    let expected = Fp::TWO_INV * Fp::ROOT_OF_UNITY * Fp::from_u64(5).invert().unwrap();
+    let expected = Fp::TWO_INV * Fp::root_of_unity() * Fp::from_u64(5).invert().unwrap();
     let (is_square, v) = Fp::sqrt_ratio(&num, &div);
     assert!(!bool::from(is_square));
     assert!(v == expected || (-v) == expected);
@@ -904,7 +903,7 @@ fn test_zeta() {
 #[test]
 fn test_root_of_unity() {
     assert_eq!(
-        Fp::ROOT_OF_UNITY.pow_vartime(&[1 << Fp::S, 0, 0, 0]),
+        Fp::root_of_unity().pow_vartime(&[1 << Fp::S, 0, 0, 0]),
         Fp::one()
     );
 }
@@ -912,7 +911,7 @@ fn test_root_of_unity() {
 #[cfg(feature = "std")]
 #[test]
 fn test_inv_root_of_unity() {
-    assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::ROOT_OF_UNITY.invert().unwrap());
+    assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::root_of_unity().invert().unwrap());
 }
 
 #[cfg(feature = "std")]

src/fields/fq.rs

@@ -673,7 +673,6 @@ lazy_static! {
 impl FieldExt for Fq {
     const MODULUS: &'static str =
         "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001";
-    const ROOT_OF_UNITY: Self = ROOT_OF_UNITY;
     const ROOT_OF_UNITY_INV: Self = Fq::from_raw([
         0x57eecda0a84b6836,
         0x4ad38b9084b8a80c,
@@ -854,8 +853,8 @@ fn test_sqrt_ratio_and_alt() {
     assert!(v_alt == v);
 
     // (false, sqrt(ROOT_OF_UNITY * num/div)), if num and div are nonzero and num/div is a nonsquare in the field
-    let num = num * Fq::ROOT_OF_UNITY;
+    let num = num * Fq::root_of_unity();
-    let expected = Fq::TWO_INV * Fq::ROOT_OF_UNITY * Fq::from_u64(5).invert().unwrap();
+    let expected = Fq::TWO_INV * Fq::root_of_unity() * Fq::from_u64(5).invert().unwrap();
     let (is_square, v) = Fq::sqrt_ratio(&num, &div);
     assert!(!bool::from(is_square));
     assert!(v == expected || (-v) == expected);
@@ -903,7 +902,7 @@ fn test_zeta() {
 #[test]
 fn test_root_of_unity() {
     assert_eq!(
-        Fq::ROOT_OF_UNITY.pow_vartime(&[1 << Fq::S, 0, 0, 0]),
+        Fq::root_of_unity().pow_vartime(&[1 << Fq::S, 0, 0, 0]),
         Fq::one()
     );
 }
@@ -911,7 +910,7 @@ fn test_root_of_unity() {
 #[cfg(feature = "std")]
 #[test]
 fn test_inv_root_of_unity() {
-    assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::ROOT_OF_UNITY.invert().unwrap());
+    assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::root_of_unity().invert().unwrap());
 }
 
 #[cfg(feature = "std")]