Add `Absorb` trait bound on `PCCommitment`

[mmagician]

Summary

Using the PCS in a wider context will require absorbing the commitment for Fiat Shamir.

The current challenge is that Absorb is not implemented for AffineRepr, and the current pairing-based schemes in this repo have commitments of the form:

pub struct Commitment<E: Pairing>(
    /// The commitment is a group element.
    pub E::G1Affine,
);

We unfortunately can't add a blanket impl like:

impl<T> Absorb for T
where
    T: AffineRepr,
{
    fn to_sponge_bytes(&self, dest: &mut Vec<u8>) {
        todo!()
    }

    fn to_sponge_field_elements<F: PrimeField>(&self, dest: &mut Vec<F>) {
        todo!()
    }
}

Rust complains "conflicting implementations of trait absorb::Absorb for type u8".

Option 1

We could add Absorb on AffineRepr in the ec crate. However, aside from creating a cyclic dependency from ec to crypto-primitives, I think this is not the best design.

Option 2

One solution is to further restrict G: AffineRepr + Absorb. This propagates into a lot of trait bounds in the poly-commit repo, though. The upside is that it doesn't require any upstream changes, and the two current implementors of AffineRepr which are the structs short_weierstrass::Affine and twisted_edwards::Affine already have Absorb implemented.

Option 3

Larger breaking refactor that makes use of the fact that most pairing computations (and certainly our implementations in ec::models) only ever support SW. The proposal is then to rip out the associated type G1Affine from Pairing, and restrict the class of pairings that can be done to SW-curves, so that we can have:

pub struct Commitment<P: SWCurveConfig>(
    /// The commitment is a group element.
    pub Affine<P>,
);

This almost works, as we still have IPA Commitment struct here in poly-commit which uses the trait AffineRepr (i.e. not an associated type from Pairing):

pub struct Commitment<G: AffineRepr> {
    /// A Pedersen commitment to the polynomial.
    pub comm: G,
    ...
}

And so mixing in Option 2 would need to happen anyway, but limited to one PCS.

Option 4

Any other ideas?

[Pratyush]

Hm I don't quite see the problem. Presumably, we want PCCommitment: Absorb only because we want to use PC generically, right?

If so, then the only place the P::G1Affine: Absorb requirement will appear is in

• impl PCCommitment for Commitment<P>, and
• impl PolyCommit for KZG/IPA/etc

Does it appear anywhere else?

[mmagician]

@Pratyush see #144

[mahmudsudo]

can i take on this ?