Encapsulate isogeny mapping in a new struct

[drskalman]

Description

This PR moves the definition of the coefficients of the isogeny map of WB hashing to a separate struct rather than defining it in the WBParams itself. This is done to declutter the definition of the curve and make it explicit that the four polynomials are related and defining a single map according to these suggestions from @mmagician
and @Pratyush

---

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[drskalman]

@mmagician @Pratyush I moved the definition of the coefficient to g1_swu_iso.rs instead of making a new file. I thought is less visited compared to g1.rs so it is not so critical if it is filled with the coefficients of the isogeny map (perhaps we can rename it as g1_iso.rs as it now that it contains both the definitions of the isogenous curve and of the isogeny map). If you still think it should be rather a separate file containing only the const struct instantiation, I could do so as well..

[Pratyush]

This looks great to me, modulo some small changes.

[Pratyush]

Suggested change

	pub struct IsogenyMap<
	'a,
	DOMAINE: SWCurveConfig,
	CODOMAINE: SWCurveConfig<BaseField = BaseField<DOMAINE>>,
	> {
	pub x_map_numerator: &'a [BaseField<CODOMAINE>],
	pub x_map_denominator: &'a [BaseField<CODOMAINE>],
	pub y_map_numerator: &'a [BaseField<CODOMAINE>],
	pub y_map_denominator: &'a [BaseField<CODOMAINE>],
	pub _phantom_domain: PhantomData<DOMAINE>,
	}
	pub struct IsogenyMap<
	'a,
	DOMAIN: SWCurveConfig,
	CODOMAIN: SWCurveConfig<BaseField = BaseField<DOMAIN>>,
	> {
	pub x_map_numerator: &'a [BaseField<CODOMAIN>],
	pub x_map_denominator: &'a [BaseField<CODOMAIN>],
	pub y_map_numerator: &'a [BaseField<CODOMAIN>],
	pub y_map_denominator: &'a [BaseField<CODOMAIN>],
	}

[drskalman]

@Pratyush: As you see, it says:

error[E0392]: parameter `DOMAIN` is never used                                                                                                                                                                                                                                            
  --> ec/src/hashing/curve_maps/wb/mod.rs:28:5                                                                                                                                                                                                                                            
   |                                                                                                                                                                                                                                                                                      
28 |     DOMAIN: SWCurveConfig,                                                                                                                                                                                                                                                           
   |     ^^^^^^ unused parameter                                                                                                                                                                                                                                                          
   |                                                                                                                                                                                                                                                                                      
   = help: consider removing `DOMAIN`, referring to it in a field, or using a marker such as `PhantomData`                                                                                                                                                                                

What should we do beside using PhantomData?

[Pratyush]

Ah, sorry, didn't realize that we we weren't using DOMAIN. There's two options:

• Reinstate the PhantomData<CODOMAIN> field, but make it private. To enable constructing an IsogenyMap, let's add a new method which does the construction.
• Change the *_map_denominator type signatures to be &'a [BaseField<DOMAIN>]. Admittedly this is a bit of a hack, but this avoids adding back the field.

[drskalman]

• To enable constructing an IsogenyMap, let's add a new method which does the construction.

Hmm, then new need to be a const function which means the arguments to new should be const. so I have to define constants PHI_X_NOM, PHI_X_DEN,..., before calling new. Then we should put them in a struct so we know they are related perhaps. Then the IsogenyMap struct will have some existential crisis. (because it is just there now to hold the apply function).

[Pratyush]

That should be possible, since it's a simple method, no?

[drskalman]

hmm but they need to have static lifetime no? perhaps I don't know the syntax of sending an argument on the fly witth static lifetime. IsogenyMap::new(&[1,23]) complains about lifetime and it doesn't let me do IsogenyMap::new(&'static[1,23]) where my creativing reachs its limit.

[drskalman]

I try sending them as array instead of refrences...

[drskalman]

I can't because they don't have the same size across the curves.

[drskalman]

@Pratyush here is the code with new constructor. If you tell me how to send the slices with static lifetime to new function so it compiles, then I'll update this PR accordingly.

[Pratyush]

I think the following should work:

impl</* bounds */> IsogenyMap<'a, DOMAIN, CODOMAIN> {
	const fn new(
	    x_numerator: &'a [BaseField<CODOMAIN>],
	    x_denominator: &'a [BaseField<CODOMAIN>],
	    ...
	) → Self {
	    Self {
	        x_numerator,
	        x_denominator,
	        ...
	    }
	}
}