Interchangeability of NonNativeFieldVar and FpVar for FieldVar

[weikengchen]

Summary

This issue is to discuss how to make NonNativeFieldVar a drop-in replacement for FieldVar in curve operations.

Problem Definition

One of the reasons that we implemented FieldVar for NonNativeFieldVar is to allow it to be a drop-in replacement of FpVar, so that one doesn't need to build a hierarchy of nonnative primitives.

This, however, is not covered by the current implementation, see:
https://github.com/arkworks-rs/r1cs-std/blob/master/src/groups/curves/short_weierstrass/mod.rs#L44

#[derive(Derivative)]
#[derivative(Debug, Clone)]
#[must_use]
pub struct ProjectiveVar<
    P: SWModelParameters,
    F: FieldVar<P::BaseField, <P::BaseField as Field>::BasePrimeField>,
> where
    for<'a> &'a F: FieldOpsBounds<'a, P::BaseField, F>,
{
    ...
}

It would be ideal, though, to lift this restriction. However, we want to make sure that we don't change the existing writing system---it would be highly inconvenient to use

pub struct ProjectiveVar<
    P: SWModelParameters,
    F: FieldVar<P::BaseField, CF>,
    CF: PrimeField,
> 

because it introduces one more param CF.

A possible workaround, though not favorable, is to define GeneralizedProjectVar<P, F, CF> and let Projective<P, F> = GeneralizedProjectVar<P, F, <P::BaseField as Field>::BasePrimeField>. This is not favored since nonnative field is not important to this level.

Proposal

We need to think about what would be the best way to do this.

---

For Admin Use

• Not duplicate issue
• Appropriate labels applied
• Appropriate contributors tagged
• Contributor assigned/self-assigned

[rubdos]

What about:

pub struct ProjectiveVar<
    P: SWModelParameters,
    F: FieldVar<P::BaseField, CF>,
    CF: PrimeField = <P::BaseField as Field>::BasePrimeField,
>  {
}

... would that not suffice here? I suppose that too will sit in the way quite often though.