add mul to ModelParam traits

[zhenfeizhang]

Description

implement part of the solution suggested via
arkworks-rs/curves#66 (comment)

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[Pratyush]

@zhenfeizhang Thanks! do you mind adding undoing the formatting changes? (I think a git reset + git add of just the model parameters file should work)

Also, I think @alexander-zw was also looking into similar things.

[Pratyush]

What I had in mind was actually something even more aggressive: to move the actual mul code here, and call P::mul from GroupProjective::mul. That is, the impl of this method in GroupProjective changes to

fn mul(...) {
    P::mul(...)
}

Also, we might want to add both mul_projective and mul_affine methods here.

[zhenfeizhang]

I just tried your suggestion.

• we cannot add it directly to ModelParameter: we need to specify if it is TE or SW
• we also cannot directly invoke it from AffineCurve or ProjectiveCurve, the trait is bounded by ModelParameter that does not specify TE or SW

working on the rest of the changes now

[zhenfeizhang]

a workaround is to add an associated type for ModelParameters but it will be ugly and is a breaking change

[Pratyush]

Ah sorry, should have been clearer, I meant that in the current strategy, instead of calling base.mul(...) inside SWModelParameters, we should change the implementation as follows:

// inside SW/TEModelParameters:
pub trait SW/TEModelParameters {
	fn mul_projective(g: GroupProjective<Self>, scalar: ...) -> GroupProjective<Self> {
	    // default double-and-add impl
	} 
}

// inside `ProjectiveCurve`:
pub trait ProjectiveCurve {
	fn mul(...); // <- no default impl anymore
}

// inside sw/te::GroupProjective:
impl ProjectiveCurve for GroupProjective {
    ...
	
	fn mul() {
		P::mul_projective(...)
	}
}

[zhenfeizhang]

Got you. Should be fixed now.