Remove `crate::arithmetic::Group` trait

It was only present to enable an FFT implementation in `halo2_proofs`
that is generic over fields and groups, but we can replace it with an
equivalent trait in `halo2_proofs` that can have a blanket impl.

CHANGELOG.md

@@ -10,10 +10,10 @@ and this project adheres to Rust's notion of
 - Migrated to `ff 0.13`, `group 0.13`.
 
 ### Removed
-- `pasta_curves::arithmetic::SqrtRatio` (use `ff::Field::{sqrt_ratio, sqrt_alt}`
-  instead).
-- `pasta_curves::arithmetic::SqrtTables` (from public API, as it isn't suitable
-  for generic usage).
+- `pasta_curves::arithmetic`:
+  - `Group`
+  - `SqrtRatio` (use `ff::Field::{sqrt_ratio, sqrt_alt}` instead).
+  - `SqrtTables` (from public API, as it isn't suitable for generic usage).
 
 ## [0.4.1] - 2022-10-13
 ### Added

src/arithmetic.rs

@@ -9,24 +9,3 @@ mod fields;
 
 pub use curves::*;
 pub use fields::*;
-
-/// This represents an element of a group with basic operations that can be
-/// performed. This allows an FFT implementation (for example) to operate
-/// generically over either a field or elliptic curve group.
-pub trait Group: Copy + Clone + Send + Sync + 'static {
-    /// The group is assumed to be of prime order $p$. `Scalar` is the
-    /// associated scalar field of size $p$.
-    type Scalar: FieldExt;
-
-    /// Returns the additive identity of the group.
-    fn group_zero() -> Self;
-
-    /// Adds `rhs` to this group element.
-    fn group_add(&mut self, rhs: &Self);
-
-    /// Subtracts `rhs` from this group element.
-    fn group_sub(&mut self, rhs: &Self);
-
-    /// Scales this group element by a scalar.
-    fn group_scale(&mut self, by: &Self::Scalar);
-}

src/arithmetic/curves.rs

@@ -7,7 +7,7 @@ use group::prime::{PrimeCurve, PrimeCurveAffine};
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
 #[cfg(feature = "alloc")]
-use super::{FieldExt, Group};
+use super::FieldExt;
 
 #[cfg(feature = "alloc")]
 use alloc::boxed::Box;
@@ -28,7 +28,6 @@ pub trait CurveExt:
     + ConditionallySelectable
     + ConstantTimeEq
     + From<<Self as PrimeCurve>::Affine>
-    + Group<Scalar = <Self as group::Group>::Scalar>
 {
     /// The scalar field of this elliptic curve.
     type ScalarExt: FieldExt;

src/arithmetic/fields.rs

@@ -5,8 +5,6 @@ use core::mem::size_of;
 
 use static_assertions::const_assert;
 
-use super::Group;
-
 #[cfg(feature = "sqrt-table")]
 use alloc::{boxed::Box, vec::Vec};
 #[cfg(feature = "sqrt-table")]
@@ -32,7 +30,7 @@ pub(crate) trait SqrtTableHelpers: ff::PrimeField {
 
 /// This trait is a common interface for dealing with elements of a finite
 /// field.
-pub trait FieldExt: ff::PrimeField + Ord + Group<Scalar = Self> {
+pub trait FieldExt: ff::PrimeField + Ord {
     /// Modulus of the field written as a string for display purposes
     const MODULUS: &'static str;
 

src/curves.rs

@@ -19,7 +19,6 @@ use rand::RngCore;
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
 use super::{Fp, Fq};
-use crate::arithmetic::Group;
 
 #[cfg(feature = "alloc")]
 use crate::arithmetic::{Coordinates, CurveAffine, CurveExt, FieldExt};
@@ -783,23 +782,6 @@ macro_rules! new_curve_impl {
         impl_binops_multiplicative!($name, $scalar);
         impl_binops_multiplicative_mixed!($name_affine, $scalar, $name);
 
-        impl Group for $name {
-            type Scalar = $scalar;
-
-            fn group_zero() -> Self {
-                Self::identity()
-            }
-            fn group_add(&mut self, rhs: &Self) {
-                *self += *rhs;
-            }
-            fn group_sub(&mut self, rhs: &Self) {
-                *self -= *rhs;
-            }
-            fn group_scale(&mut self, by: &Self::Scalar) {
-                *self *= *by;
-            }
-        }
-
         #[cfg(feature = "gpu")]
         impl ec_gpu::GpuName for $name_affine {
             fn name() -> alloc::string::String {

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, Group, SqrtTableHelpers};
+use crate::arithmetic::{adc, mac, sbb, FieldExt, SqrtTableHelpers};
 
 #[cfg(feature = "sqrt-table")]
 use crate::arithmetic::SqrtTables;
@@ -475,23 +475,6 @@ impl<'a> From<&'a Fp> for [u8; 32] {
     }
 }
 
-impl Group for Fp {
-    type Scalar = Fp;
-
-    fn group_zero() -> Self {
-        Self::zero()
-    }
-    fn group_add(&mut self, rhs: &Self) {
-        *self += *rhs;
-    }
-    fn group_sub(&mut self, rhs: &Self) {
-        *self -= *rhs;
-    }
-    fn group_scale(&mut self, by: &Self::Scalar) {
-        *self *= *by;
-    }
-}
-
 impl ff::Field for Fp {
     const ZERO: Self = Self::zero();
     const ONE: Self = Self::one();

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, Group, SqrtTableHelpers};
+use crate::arithmetic::{adc, mac, sbb, FieldExt, SqrtTableHelpers};
 
 #[cfg(feature = "sqrt-table")]
 use crate::arithmetic::SqrtTables;
@@ -475,23 +475,6 @@ impl<'a> From<&'a Fq> for [u8; 32] {
     }
 }
 
-impl Group for Fq {
-    type Scalar = Fq;
-
-    fn group_zero() -> Self {
-        Self::zero()
-    }
-    fn group_add(&mut self, rhs: &Self) {
-        *self += *rhs;
-    }
-    fn group_sub(&mut self, rhs: &Self) {
-        *self -= *rhs;
-    }
-    fn group_scale(&mut self, by: &Self::Scalar) {
-        *self *= *by;
-    }
-}
-
 impl ff::Field for Fq {
     const ZERO: Self = Self::zero();
     const ONE: Self = Self::one();