Introduce CurveAffine trait

This unifies the methods previously exposed by the `PrimeCurveAffine`
and `CofactorCurveAffine` traits. The prime-order and cofactor traits
are now all marker traits, and their affine-specific traits are
automatically derived.

CHANGELOG.md

@@ -6,6 +6,24 @@ and this library adheres to Rust's notion of
 [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
 ## [Unreleased]
+### Added
+- `group::CurveAffine`
+
+### Changed
+- The curve-related traits have been refactored around the new `CurveAffine`
+  trait:
+  - `group::Curve::AffineRepr` has been renamed to `Curve::Affine`.
+  - All of the trait methods and associated types on the following traits have
+    been removed (use `group::Curve::Affine` or the `group::CurveAffine` trait
+    instead; trait implementors must implement `group::CurveAffine` instead
+    using the same logic):
+    - `group::cofactor::CofactorCurve`
+    - `group::cofactor::CofactorCurveAffine`
+    - `group::prime::PrimeCurve`
+    - `group::prime::PrimeCurveAffine`
+  - `group::cofactor::CofactorCurveAffine` and `group::prime::PrimeCurveAffine`
+    now have blanket implementations for all types `C: group::CurveAffine` where
+    `C::Curve` implements `CofactorCurve` or `PrimeCurve` respectively.
 
 ## [0.13.0] - 2022-12-06
 ### Changed

src/cofactor.rs

@@ -1,9 +1,6 @@
-use core::fmt;
-use core::ops::{Mul, Neg};
-use ff::PrimeField;
 use subtle::{Choice, CtOption};
 
-use crate::{prime::PrimeGroup, Curve, Group, GroupEncoding, GroupOps, GroupOpsOwned};
+use crate::{prime::PrimeGroup, Curve, CurveAffine, Group, GroupEncoding, GroupOps, GroupOpsOwned};
 
 /// This trait represents an element of a cryptographic group with a large prime-order
 /// subgroup and a comparatively-small cofactor.
@@ -54,47 +51,10 @@ pub trait CofactorGroup:
 
 /// Efficient representation of an elliptic curve point guaranteed to be
 /// in the correct prime order subgroup.
-pub trait CofactorCurve:
-    Curve<AffineRepr = <Self as CofactorCurve>::Affine> + CofactorGroup
-{
-    type Affine: CofactorCurveAffine<Curve = Self, Scalar = Self::Scalar>
-        + Mul<Self::Scalar, Output = Self>
-        + for<'r> Mul<&'r Self::Scalar, Output = Self>;
-}
+pub trait CofactorCurve: Curve + CofactorGroup {}
 
 /// Affine representation of an elliptic curve point guaranteed to be
 /// in the correct prime order subgroup.
-pub trait CofactorCurveAffine:
-    GroupEncoding
-    + Copy
-    + Clone
-    + Sized
-    + Send
-    + Sync
-    + fmt::Debug
-    + PartialEq
-    + Eq
-    + 'static
-    + Neg<Output = Self>
-    + Mul<<Self as CofactorCurveAffine>::Scalar, Output = <Self as CofactorCurveAffine>::Curve>
-    + for<'r> Mul<
-        &'r <Self as CofactorCurveAffine>::Scalar,
-        Output = <Self as CofactorCurveAffine>::Curve,
-    >
-{
-    type Scalar: PrimeField;
-    type Curve: CofactorCurve<Affine = Self, Scalar = Self::Scalar>;
-
-    /// Returns the additive identity.
-    fn identity() -> Self;
+pub trait CofactorCurveAffine: CurveAffine {}
 
-    /// Returns a fixed generator of unknown exponent.
-    fn generator() -> Self;
-
-    /// Determines if this point represents the point at infinity; the
-    /// additive identity.
-    fn is_identity(&self) -> Choice;
-
-    /// Converts this element to its curve representation.
-    fn to_curve(&self) -> Self::Curve;
-}
+impl<C: CurveAffine> CofactorCurveAffine for C where C::Curve: CofactorCurve {}

src/lib.rs

@@ -92,16 +92,16 @@ pub trait Group:
     fn double(&self) -> Self;
 }
 
-/// Efficient representation of an elliptic curve point guaranteed.
-pub trait Curve:
-    Group + GroupOps<<Self as Curve>::AffineRepr> + GroupOpsOwned<<Self as Curve>::AffineRepr>
-{
+/// Efficient representation of an elliptic curve point.
+pub trait Curve: Group + GroupOps<Self::Affine> + GroupOpsOwned<Self::Affine> {
     /// The affine representation for this elliptic curve.
-    type AffineRepr;
+    type Affine: CurveAffine<Curve = Self, Scalar = Self::Scalar>
+        + Mul<Self::Scalar, Output = Self>
+        + for<'r> Mul<&'r Self::Scalar, Output = Self>;
 
     /// Converts a batch of projective elements into affine elements. This function will
     /// panic if `p.len() != q.len()`.
-    fn batch_normalize(p: &[Self], q: &mut [Self::AffineRepr]) {
+    fn batch_normalize(p: &[Self], q: &mut [Self::Affine]) {
         assert_eq!(p.len(), q.len());
 
         for (p, q) in p.iter().zip(q.iter_mut()) {
@@ -110,7 +110,45 @@ pub trait Curve:
     }
 
     /// Converts this element into its affine representation.
-    fn to_affine(&self) -> Self::AffineRepr;
+    fn to_affine(&self) -> Self::Affine;
+}
+
+/// Affine representation of an elliptic curve point.
+pub trait CurveAffine:
+    GroupEncoding
+    + Copy
+    + Clone
+    + Sized
+    + Send
+    + Sync
+    + fmt::Debug
+    + PartialEq
+    + Eq
+    + 'static
+    + Neg<Output = Self>
+    + Mul<<Self::Curve as Group>::Scalar, Output = Self::Curve>
+    + for<'r> Mul<&'r <Self::Curve as Group>::Scalar, Output = Self::Curve>
+{
+    /// The efficient representation for this elliptic curve.
+    type Curve: Curve<Affine = Self, Scalar = Self::Scalar>;
+
+    /// Scalars modulo the order of this group's scalar field.
+    ///
+    /// This associated type is temporary, and will be removed once downstream users have
+    /// migrated to using `Curve` as the primary generic bound.
+    type Scalar: PrimeField;
+
+    /// Returns the additive identity.
+    fn identity() -> Self;
+
+    /// Returns a fixed generator of unknown exponent.
+    fn generator() -> Self;
+
+    /// Determines if this point represents the additive identity.
+    fn is_identity(&self) -> Choice;
+
+    /// Converts this affine point to its efficient representation.
+    fn to_curve(&self) -> Self::Curve;
 }
 
 pub trait GroupEncoding: Sized {

src/prime.rs

@@ -1,50 +1,14 @@
-use core::fmt;
-use core::ops::{Mul, Neg};
-use ff::PrimeField;
-use subtle::Choice;
-
-use crate::{Curve, Group, GroupEncoding};
+use crate::{Curve, CurveAffine, Group, GroupEncoding};
 
 /// This trait represents an element of a prime-order cryptographic group.
 pub trait PrimeGroup: Group + GroupEncoding {}
 
 /// Efficient representation of an elliptic curve point guaranteed to be
 /// in the correct prime order subgroup.
-pub trait PrimeCurve: Curve<AffineRepr = <Self as PrimeCurve>::Affine> + PrimeGroup {
-    type Affine: PrimeCurveAffine<Curve = Self, Scalar = Self::Scalar>
-        + Mul<Self::Scalar, Output = Self>
-        + for<'r> Mul<&'r Self::Scalar, Output = Self>;
-}
+pub trait PrimeCurve: Curve + PrimeGroup {}
 
 /// Affine representation of an elliptic curve point guaranteed to be
 /// in the correct prime order subgroup.
-pub trait PrimeCurveAffine: GroupEncoding
-    + Copy
-    + Clone
-    + Sized
-    + Send
-    + Sync
-    + fmt::Debug
-    + PartialEq
-    + Eq
-    + 'static
-    + Neg<Output = Self>
-    + Mul<<Self as PrimeCurveAffine>::Scalar, Output = <Self as PrimeCurveAffine>::Curve>
-    + for<'r> Mul<&'r <Self as PrimeCurveAffine>::Scalar, Output = <Self as PrimeCurveAffine>::Curve>
-{
-    type Scalar: PrimeField;
-    type Curve: PrimeCurve<Affine = Self, Scalar = Self::Scalar>;
-
-    /// Returns the additive identity.
-    fn identity() -> Self;
-
-    /// Returns a fixed generator of unknown exponent.
-    fn generator() -> Self;
-
-    /// Determines if this point represents the point at infinity; the
-    /// additive identity.
-    fn is_identity(&self) -> Choice;
+pub trait PrimeCurveAffine: CurveAffine {}
 
-    /// Converts this element to its curve representation.
-    fn to_curve(&self) -> Self::Curve;
-}
+impl<C: CurveAffine> PrimeCurveAffine for C where C::Curve: PrimeCurve {}

src/tests/mod.rs

@@ -4,11 +4,7 @@ use ff::{Field, PrimeField};
 use rand::SeedableRng;
 use rand_xorshift::XorShiftRng;
 
-use crate::{
-    prime::{PrimeCurve, PrimeCurveAffine},
-    wnaf::WnafGroup,
-    GroupEncoding, UncompressedEncoding,
-};
+use crate::{prime::PrimeCurve, wnaf::WnafGroup, CurveAffine, GroupEncoding, UncompressedEncoding};
 
 pub fn curve_tests<G: PrimeCurve>() {
     let mut rng = XorShiftRng::from_seed([
@@ -426,7 +422,7 @@ fn random_compressed_encoding_tests<G: PrimeCurve>() {
 
 pub fn random_uncompressed_encoding_tests<G: PrimeCurve>()
 where
-    <G as PrimeCurve>::Affine: UncompressedEncoding,
+    G::Affine: UncompressedEncoding,
 {
     let mut rng = XorShiftRng::from_seed([
         0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,