Implement Secp256k1 about curves HOT 7 CLOSED

I'm in favor of wrapping k256 (https://github.com/RustCrypto/elliptic-curves/tree/master/k256). See Tony's blog post on it: https://iqlusion.blog/k256-crate-pure-rust-projective-secp256k1-library.

from curves.

I think it would make sense to only wrap their field code, and use our existing Short Weierstrass Jacobian type for curve arithmetic. This is so that we can easily reuse the existing gadget infrastructure in the future (which works only with our existing Twisted Edwards and Short Weierstrass structs).

from curves.

Would Ed25519 make sense? Ristretto maybe less so

from curves.

We can just move this one? https://github.com/FindoraNetwork/ark-bulletproofs-secq256k1/tree/main/src/curve/secp256k1

With the recent algebra library upgrade, this should be pretty easy. I just need a yes or no.

from curves.

I think with the new infrastructure we can avoid the extra limb; I would be in favour of that.

from curves.

Let me double check---I suspect that 256 can fit curve25519 but not secp256k1.

from curves.

By "new infrastructure" I mean the new trait design, not the existing arithmetic routines. We would need to introduce a separate impl of montgomery reductions and multiplication to avoid the extra limb.

from curves.