Implement `inverse` operation for FieldElement.

[CPerezz]

As seen on the code of field.rs, inverse() FieldElement function implementation remains unimplemented.

On https://github.com/dusk-network/dusk-corretto/pull/12 we've just implemented the Kalinski's Montgomery Modular Inverse algorithm for the Doppio's FieldElement mod 2^252 + 27742317777372353535851937790883648493 (prime of the field).

So maybe I can make a PR with the implementation of the Inverse operation and the proper tests and doc comments if it's useful.

References:

• B. S. Kaliski Jr. - The Montgomery inverse and its applica-tions. IEEE Transactions on Computers, 44(8):1064–1065, August-1995.

• Montgomery inversion - Erkay Sava ̧s & Çetin Kaya Koç J Cryptogr Eng (2018) 8:201–210 https://doi.org/10.1007/s13389-017-0161-x

[hdevalence]

Hi!

The curve25519-dalek source code the field.rs implementation is copied from has an implementation of inversion using a hardcoded addition chain; we were planning to use that implementation, but we didn't get to it yet since we're still working on curve selection (the curve Sean found may not be optimal).

[CPerezz]

I saw what I think you're referring to on https://github.com/dalek-cryptography/curve25519-dalek/blob/f630041af28e9a405255f98a8a93adca18e4315b/src/field.rs#L175 I was, however, unsure as to whether this method will allow for a different prime of the field value ( and if this could be done by just changing some limb values).

@Bounce23 and I plan to create set inclusion proofs using Doppio - with respect to the search for optimal curves, is that in relation to the optimization for those addition chains? Or for a larger goal of the project?