Remove `FieldExt` trait

One, two! One, two! And through and through
    The vorpal blade went snicker-snack!
He left it dead, and with its head
    He went galumphing back.

Closes zcash/pasta_curves#42.

CHANGELOG.md

@@ -11,6 +11,7 @@ and this project adheres to Rust's notion of
 
 ### Removed
 - `pasta_curves::arithmetic`:
+  - `FieldExt` (use `ff::PrimeField` or `ff::WithSmallOrderMulGroup` instead).
   - `Group`
   - `SqrtRatio` (use `ff::Field::{sqrt_ratio, sqrt_alt}` instead).
   - `SqrtTables` (from public API, as it isn't suitable for generic usage).

src/arithmetic.rs

@@ -8,4 +8,4 @@ mod curves;
 mod fields;
 
 pub use curves::*;
-pub use fields::*;
+pub(crate) use fields::*;

src/arithmetic/curves.rs

@@ -6,9 +6,6 @@ use group::prime::{PrimeCurve, PrimeCurveAffine};
 #[cfg(feature = "alloc")]
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
-#[cfg(feature = "alloc")]
-use super::FieldExt;
-
 #[cfg(feature = "alloc")]
 use alloc::boxed::Box;
 #[cfg(feature = "alloc")]
@@ -30,9 +27,9 @@ pub trait CurveExt:
     + From<<Self as PrimeCurve>::Affine>
 {
     /// The scalar field of this elliptic curve.
-    type ScalarExt: FieldExt;
+    type ScalarExt: ff::WithSmallOrderMulGroup<3>;
     /// The base field over which this elliptic curve is constructed.
-    type Base: FieldExt;
+    type Base: ff::WithSmallOrderMulGroup<3>;
     /// The affine version of the curve
     type AffineExt: CurveAffine<CurveExt = Self, ScalarExt = <Self as CurveExt>::ScalarExt>
         + Mul<Self::ScalarExt, Output = Self>
@@ -102,9 +99,9 @@ pub trait CurveAffine:
     + From<<Self as PrimeCurveAffine>::Curve>
 {
     /// The scalar field of this elliptic curve.
-    type ScalarExt: FieldExt + Ord;
+    type ScalarExt: ff::WithSmallOrderMulGroup<3> + Ord;
     /// The base field over which this elliptic curve is constructed.
-    type Base: FieldExt + Ord;
+    type Base: ff::WithSmallOrderMulGroup<3> + Ord;
     /// The projective form of the curve
     type CurveExt: CurveExt<AffineExt = Self, ScalarExt = <Self as CurveAffine>::ScalarExt>;
 

src/arithmetic/fields.rs

@@ -28,10 +28,6 @@ pub(crate) trait SqrtTableHelpers: ff::PrimeField {
     fn get_lower_32(&self) -> u32;
 }
 
-/// This trait is a common interface for dealing with elements of a finite
-/// field.
-pub trait FieldExt: ff::WithSmallOrderMulGroup<3> {}
-
 /// Parameters for a perfect hash function used in square root computation.
 #[cfg(feature = "sqrt-table")]
 #[cfg_attr(docsrs, doc(cfg(feature = "sqrt-table")))]

src/fields/fp.rs

@@ -11,7 +11,7 @@ use lazy_static::lazy_static;
 #[cfg(feature = "bits")]
 use ff::{FieldBits, PrimeFieldBits};
 
-use crate::arithmetic::{adc, mac, sbb, FieldExt, SqrtTableHelpers};
+use crate::arithmetic::{adc, mac, sbb, SqrtTableHelpers};
 
 #[cfg(feature = "sqrt-table")]
 use crate::arithmetic::SqrtTables;
@@ -728,8 +728,6 @@ impl SqrtTableHelpers for Fp {
     }
 }
 
-impl FieldExt for Fp {}
-
 impl WithSmallOrderMulGroup<3> for Fp {
     const ZETA: Self = Fp::from_raw([
         0x1dad5ebdfdfe4ab9,

src/fields/fq.rs

@@ -11,7 +11,7 @@ use lazy_static::lazy_static;
 #[cfg(feature = "bits")]
 use ff::{FieldBits, PrimeFieldBits};
 
-use crate::arithmetic::{adc, mac, sbb, FieldExt, SqrtTableHelpers};
+use crate::arithmetic::{adc, mac, sbb, SqrtTableHelpers};
 
 #[cfg(feature = "sqrt-table")]
 use crate::arithmetic::SqrtTables;
@@ -727,8 +727,6 @@ impl SqrtTableHelpers for Fq {
     }
 }
 
-impl FieldExt for Fq {}
-
 impl WithSmallOrderMulGroup<3> for Fq {
     const ZETA: Self = Fq::from_raw([
         0x2aa9d2e050aa0e4f,