Move common fields into ModelParameters

[alexander-zw]

Description

In addition to some simple changes to move COFACTOR, COFACTOR_INV, and is_in_correct_subgroup_assuming_on_curve(), a new trait MultipliablePoint had to be created because each type of curve has its own GroupAffine and GroupProjective. As a result, is_in_correct_subgroup_assuming_on_curve() now has more generic types, but fortunately if the corresponding GroupAffine struct has an identically named function, that one does not require any generics. Because of this change, some duplicate code in ec/src/models/twisted_edwards_extended.rs was removed.

closes: #326

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[Pratyush]

Hm I think you don't need to introduce a new trait; just add Affine and Projective types into the ModelParameters trait.

[alexander-zw]

Hm I think you don't need to introduce a new trait; just add Affine and Projective types into the ModelParameters trait.

Ah I see, still getting used to Rust

Wait, wouldn't I still need to define a trait to bound Affine so it has the mul_bits function?

[alexander-zw]

Well I used the AffineCurve trait, but now I get the compile error

expected associated type, found struct `models::short_weierstrass_jacobian::GroupAffine`

note: expected reference `&<P as models::ModelParameters>::Affine`
         found reference `&models::short_weierstrass_jacobian::GroupAffine<P>`
help: consider constraining the associated type `<P as models::ModelParameters>::Affine` to `models::short_weierstrass_jacobian::GroupAffine<P>` or calling a method that returns `<P as models::ModelParameters>::Affine`

On the line

P::is_in_correct_subgroup_assuming_on_curve(self)

[Pratyush]

Suggested change

	self.mul_bits(BitIteratorBE::new(by.into()))
	self.mul_bits(BitIteratorBE::without_leading_zeros(by.into()))

[alexander-zw]

Is this more efficient? Why isn't it the default new implementation?

[alexander-zw]

It doesn't seem that this does anything in this case, because mul_bits() calls skip_while() anyway

[Pratyush]

Well I used the AffineCurve trait, but now I get the compile error

expected associated type, found struct `models::short_weierstrass_jacobian::GroupAffine`

note: expected reference `&<P as models::ModelParameters>::Affine`
         found reference `&models::short_weierstrass_jacobian::GroupAffine<P>`
help: consider constraining the associated type `<P as models::ModelParameters>::Affine` to `models::short_weierstrass_jacobian::GroupAffine<P>` or calling a method that returns `<P as models::ModelParameters>::Affine`

On the line

P::is_in_correct_subgroup_assuming_on_curve(self)

You have to constrain the Parameters associated type to match the respective Affine struct. You can do that by changing the definition of TEParameters to trait TEParameters: ModelParameters<Affine = twisted_edwards::GroupAffine<Self>>, and similarly for SWParameters (i.e., see the suggestions below).

[alexander-zw]

Well I used the AffineCurve trait, but now I get the compile error

expected associated type, found struct `models::short_weierstrass_jacobian::GroupAffine`

note: expected reference `&<P as models::ModelParameters>::Affine`
         found reference `&models::short_weierstrass_jacobian::GroupAffine<P>`
help: consider constraining the associated type `<P as models::ModelParameters>::Affine` to `models::short_weierstrass_jacobian::GroupAffine<P>` or calling a method that returns `<P as models::ModelParameters>::Affine`

On the line

P::is_in_correct_subgroup_assuming_on_curve(self)

You have to constrain the Parameters associated type to match the respective Affine struct. You can do that by changing the definition of TEParameters to trait TEParameters: ModelParameters<Affine = twisted_edwards::GroupAffine<Self>>, and similarly for SWParameters (i.e., see the suggestions below).

Oh I was going to change every instance of Parameters into Parameters<Affine = Self>, your suggestion is much easier

[alexander-zw]

Why do they have both mul_by_cofactor_to_projective and scale_by_cofactor if they do the exact same thing?

[alexander-zw]

Update: I removed scale_by_cofactor