Introduce NonIdentityPoint

[daxpedda]

This is similar to NonZeroScalar.

I often found myself handrolling custom serde implementations to make sure that a ProjectivePoint is not an identity element.

Additionally it could be useful to allow arithmetic that can guarantee some outputs without having to constantly check for identity elements. For example multiplying a NonIdentityElement with a NonZeroScalar should yield a NonIdentityElement without having to do any checks or returning an (Ct)Option.

Interactions with PublicKey could be similar to whats done between NonZeroScalar and SecretKey, enabling non-fallible conversions.

Happy to make a PR of course.

[tarcieri]

Seems fine to me.

Wonder if it should be NonIdentity<T> so you can have NonIdentity<AffinePoint<C>> and NonIdentity<ProjectivePoint<C>>

[daxpedda]

Personally I don't have a use-case for it, but it's a great idea.
The API might look a bit convoluted though, because there is no common trait.

Alternatively we could also do NonProjectiveIdentity and NonAffineIdentity.

I will start on an implementation with NonIdentity<T> as you suggested and we can go from there, feel free to suggest otherwise anytime.

[daxpedda]

So somehow I have to implement the same functions over NonIdentity<ProjectivePoint<C>> and NonIdentity<AffinePoint<C>>.

As they don't share traits I thought I could do something like this: impl<C> NonIdentity<ProjectivePoint<C>> { ... }, which I quickly found out isn't allowed.

I could solve this issue by making a NonIdentityExt trait, which would maybe allow something like impl<C> NonIdentityExt for NonIdentity<ProjectivePoint<C>> and impl<C> NonIdentityExt for NonIdentity<AffinePoint<C>> with the same function names.

So currently I'm leaning towards just making them two separate types, as proposed above.
Any different suggestions?

[tarcieri]

So somehow I have to implement the same functions over NonIdentity<ProjectivePoint> and NonIdentity<AffinePoint>.

As they don't share traits...

It seems like quite a few of them should be able to be generic. They do share traits, namely the core::ops ones.

[daxpedda]

Yeah, so the problem was how to make a new function, there is no commonly shared trait between AffinePoint and ProjectivePoint to get the identity point. We could add one?

Alternatively I will just make new_projective() and new_affine().

[daxpedda]

Cc zkcrypto/group#41.

[tarcieri]

there is no commonly shared trait between AffinePoint and ProjectivePoint to get the identity point.

Default ?