Add simple curve cycle trait for curve cycles

[drewstone]

Description

The purpose of this PR is to define a trait for standard (potentially non-pairing based) and pairing based curve cycles.

• Targeted PR against correct branch (master)
• Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work.
• Updated relevant documentation in the code
• Added a relevant changelog entry to the Pending section in CHANGELOG.md

No unit tests as this is just new trait def.

[drewstone]

Ngl I just wanna contribute to this awesome project. I am still wearing my training wheels when looking around. Let me know if this isn't the right place or implementation for something like this. I have yet to see a PCD or cycle engine defined for non-pairing based curves so I figured there ought to be one.

[daira]

Looks good. Can you impl this for Pallas and Vesta?

[Pratyush]

This makes me think we need to have a CurveCycle trait, like so:

pub trait CurveCycle 
where
    <Self::E1 as AffineCurve>::Projective: MulAssign<<Self::E2 as AffineCurve>::BaseField>,
    <Self::E2 as AffineCurve>::Projective: MulAssign<<Self::E1 as AffineCurve>::BaseField>,
{
	// Maybe these constraints are too tight and could cause rust's constraint solver
	// error out due to cycles (heh); we remove the
	// bounds on the associated types if that's the case.
	type E1: AffineCurve<
		BaseField = <Self::E2 as AffineCurve>::ScalarField,
		ScalarField = <Self::E2 as AffineCurve>::BaseField,
	>;
	type E2: AffineCurve<
		BaseField = <Self::E1 as AffineCurve>::ScalarField,
		ScalarField = <Self::E1 as AffineCurve>::BaseField,
	>;
}

pub trait PairingFriendlyCycle: CurveCycle {
	// add whatever extra bounds are necessary.
	type Engine1: PairingEngine<
		G1Affine = Self::E1,
		G1Projective = <Self::E1 as AffineCurve>::Projective,
		Fq = <Self::E1 as AffineCurve>::BaseField,
		Fr = <Self::E1 as AffineCurve>::ScalarField,
	>;
	
	type Engine2: PairingEngine<
		G2Affine = Self::E2,
		G2Projective = <Self::E2 as AffineCurve>::Projective,
		Fq = <Self::E2 as AffineCurve>::BaseField,
		Fr = <Self::E2 as AffineCurve>::ScalarField,
	>;
}

[drewstone]

@daira where's the right place to implement that.. should be as simple as this right?

impl SimpleCycleEngine for PastaCycle {
    type E1 = Pallas;
    type E2 = Vesta;
}

And that seems more robust @Pratyush, happy to add that. Ideally any change is backwards compatible but otherwise would require updating the downstream dependencies.

[drewstone]

I've updated the trait with your feedback @Pratyush. Getting rid of the strict def on E2 managed to get it to compile without issues. Let me know your thoughts!

[Pratyush]

Thanks for the PR! could you add a relevant entry in CHANGELOG.md under Improvements? Oh and a final format.

[drewstone]

All set @Pratyush