Reduce duplicate code across different curve cycle providers

[ashWhiteHat]

I reduced test and transcript trait code across curve cycle by macros.

improvement
curve cycle group methods difference is only vartime_multiscalar_mul.
https://github.com/microsoft/Nova/blob/main/src/provider/mod.rs#L159
If we call msm method through such that Self::msm(), we can use same trait between pasta and other cycle pair.

question
Is there any reason not to use complete addition for ecc gadget?
https://github.com/microsoft/Nova/blob/main/src/gadgets/ecc.rs#L135
We can skip condition branch constraint.

typo
the duplication

https://eprint.iacr.org/2023/1192.pdf#page=4&zoom=100,100,250

I would appreciate it if you could confirm.
Thank you.

[srinathsetty]

close #202

I reduced test and transcript trait code across curve cycle by macros.

Does it actually close the issue? There is still impl_traits that is duplicated between mod.rs and pasta.rs, right?

[srinathsetty]

question
Is there any reason not to use complete addition for ecc gadget?
https://github.com/microsoft/Nova/blob/main/src/gadgets/ecc.rs#L135
We can skip condition branch constraint.

I don't fully understand this question. Can you please elaborate?

[ashWhiteHat]

Does it actually close the issue? There is still impl_traits that is duplicated between mod.rs and pasta.rs, right?

Exactly.
I unlinked the issue.

I don't fully understand this question. Can you please elaborate?

Sorry for confusing.
This seems my mistake.
I thought that the curve complete addition law can save the number of constraints because it can skip condition branch (identity and doubling case).
but it can save the number of constraints because it can perform affine coordinate arithmetic by using the feature that the inversion cost is as cheap as multiplication as following article says.
https://bitzecbzc.github.io/technology/jubjub/index.html#introducing-jubjub

It seems we can't save the number of constraints, because the Weierstrass affine coordinate still needs condition branch.