group: Move uncompressed encodings to an UncompressedEncoding trait

Specifications of deployed elliptic curves fall into one of two
categories:
- They specify both compressed and uncompressed encodings, allowing
  implementations to use either depending on performance vs data size
  considerations.
- They specify a single point encoding format using point compression.

I am unaware of any elliptic curve specification that explicitly forbids
compressed encodings.

To support both categories of elliptic curves, we provide the
CurveAffine::Compressed associated type which all curves must define,
and then curves that additionally specify an uncompressed encoding may
implement the UncompressedEncoding trait and its Uncompressed associated
type.

pairing::PairingCurveAffine continues to require that its groups provide
uncompressed encodings, because this is relied upon by bellman::groth16.
We can revisit this restriction when that module is refactored as a
separate crate.

src/groth16/mod.rs

@@ -2,7 +2,7 @@
 //!
 //! [Groth16]: https://eprint.iacr.org/2016/260
 
-use group::CurveAffine;
+use group::{CurveAffine, UncompressedEncoding};
 use pairing::{Engine, MultiMillerLoop};
 
 use crate::SynthesisError;
@@ -158,7 +158,7 @@ impl<E: Engine> VerifyingKey<E> {
 
     pub fn read<R: Read>(mut reader: R) -> io::Result<Self> {
         let read_g1 = |reader: &mut R| -> io::Result<E::G1Affine> {
-            let mut g1_repr = <E::G1Affine as CurveAffine>::Uncompressed::default();
+            let mut g1_repr = <E::G1Affine as UncompressedEncoding>::Uncompressed::default();
             reader.read_exact(g1_repr.as_mut())?;
 
             let affine = E::G1Affine::from_uncompressed(&g1_repr);
@@ -170,7 +170,7 @@ impl<E: Engine> VerifyingKey<E> {
         };
 
         let read_g2 = |reader: &mut R| -> io::Result<E::G2Affine> {
-            let mut g2_repr = <E::G2Affine as CurveAffine>::Uncompressed::default();
+            let mut g2_repr = <E::G2Affine as UncompressedEncoding>::Uncompressed::default();
             reader.read_exact(g2_repr.as_mut())?;
 
             let affine = E::G2Affine::from_uncompressed(&g2_repr);
@@ -289,7 +289,7 @@ impl<E: Engine> Parameters<E> {
 
     pub fn read<R: Read>(mut reader: R, checked: bool) -> io::Result<Self> {
         let read_g1 = |reader: &mut R| -> io::Result<E::G1Affine> {
-            let mut repr = <E::G1Affine as CurveAffine>::Uncompressed::default();
+            let mut repr = <E::G1Affine as UncompressedEncoding>::Uncompressed::default();
             reader.read_exact(repr.as_mut())?;
 
             let affine = if checked {
@@ -317,7 +317,7 @@ impl<E: Engine> Parameters<E> {
         };
 
         let read_g2 = |reader: &mut R| -> io::Result<E::G2Affine> {
-            let mut repr = <E::G2Affine as CurveAffine>::Uncompressed::default();
+            let mut repr = <E::G2Affine as UncompressedEncoding>::Uncompressed::default();
             reader.read_exact(repr.as_mut())?;
 
             let affine = if checked {

src/groth16/tests/dummy_engine.rs

@@ -1,5 +1,5 @@
 use ff::{Field, PrimeField};
-use group::{CurveAffine, CurveProjective, Group, PrimeGroup};
+use group::{CurveAffine, CurveProjective, Group, PrimeGroup, UncompressedEncoding};
 use pairing::{Engine, MillerLoopResult, MultiMillerLoop, PairingCurveAffine};
 
 use rand_core::RngCore;
@@ -434,7 +434,6 @@ impl AsRef<[u8]> for FakePoint {
 
 impl CurveAffine for Fr {
     type Compressed = FakePoint;
-    type Uncompressed = FakePoint;
     type Projective = Fr;
     type Scalar = Fr;
 
@@ -465,6 +464,10 @@ impl CurveAffine for Fr {
     fn to_compressed(&self) -> Self::Compressed {
         unimplemented!()
     }
+}
+
+impl UncompressedEncoding for Fr {
+    type Uncompressed = FakePoint;
 
     fn from_uncompressed(_bytes: &Self::Uncompressed) -> CtOption<Self> {
         unimplemented!()