primeorder: support curves with any a

[survived]

Closes #726

[tarcieri]

@survived can you rebase now that I landed #728?

I'd suggest getting rid of the inherent methods for ProjectivePoint::add and use overlapping Add impls for the different EquationAProperties ZSTs, similar to what was done for Double.

[survived]

Sure! I just wanted to finish algorithms implementation first and see they it work fine. I'll mark PR as ready for review when I'm done :)

[tarcieri]

FWIW you should be able to use the implementations @newpavlov mentioned in #726, e.g. https://github.com/RustCrypto/elliptic-curves/pull/218/files#diff-cf2092dccb9b015c6defd5f649e6449e52e4cef9b10c77e2a96d6201033c8232R170

[survived]

If I'm not missing anything, all algos are already implemented, so I only left to rebase it now and use trait approach. But I'll keep in mind that there's another implementation, thanks!

[tarcieri]

@survived yeah, rebase on master and copy-and-paste the implementations into impls for the respective traits (Add and Double)

Should be fairly straightforward

[survived]

@tarcieri unfortunately, compiler doesn't allow me to implement the same trait twice for ProjectivePoint. Here's minimal example that reproduces this behavior.

[tarcieri]

Aah, unfortunate.

Another option is moving the implementation to methods on the ZSTs and having e.g. Double call that.

[survived]

Indeed that should work! Let me try it

[survived]

@tarcieri I came up with similar ZST-based approach, check it out. I added type PointArithmetic: PointArithmetic<C> associated type to the PrimeCurveParams trait, and new PointArithmetic<C> trait which basically defines double, add, and add_mixed functions. Then we don't actually need to change interface of ProjectivePoint, ProjectivePoint::{double, add, add_mixed} would just use PointArithmetic::{double, add, add_mixed}. What do you think?

[tarcieri]

Looks good overall! That's more or less what I had in mind.

[survived]

Do you want to keep Double trait, or shall I revert this change?

[tarcieri]

I already added it to elliptic-curve, so seems OK to keep. I'll switch to that trait in #730

[survived]

@tarcieri PR is ready for review!