# ignacio (jsign) - Update 3

Read material:

- [Group Law](https://en.wikipedia.org/wiki/Elliptic_curve#The_group_law) in elliptic curves
- Learned about affine vs projective coordinates in elliptic curves:
- [Elliptic curve point addition in projective coordinates](https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates)
- [Cryptography/Prime Curve/Standard Projective Coordinates](https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Standard_Projective_Coordinates), which mentions the interesting case of mixed additions, which I saw in [go-ipa](https://github.com/crate-crypto/go-ipa).

Published articles:

- I wrote and published [Verkle Tries exploration about Keccak vs Pedersen Commitments](https://hackmd.io/@jsign/verkle-tries-exploration-about-keccak-vs-pedersen-commitments).

Next steps:

- Kevaundray, Guillaume, and Dankrad have provided feedback about the above article and we have some roadmap about some next steps that align with current high priorities for the Stateless team.
- [ ] Benchmark: change Keccak benchmark to have sub-tests up to 256 non-zero bytes.
- [ ] Benchmark: cover the 128 non-zero entries in creating pedersen commitments.
- [ ] Benchmark: create a `results` folder and process to upload results there.
- [ ] Benchmark: rename `BenchmarkFullPedersen` to `BenchmarkFullCommit`
- [ ] Benchmark: add benchmark using `GetTreeKey` ”compare them against performing `keccak(addr)`, then `keccak(slot)` which represents the equivalent operation in the Ethereum MPT.”
- [ ] Benchmark: isolate `fp.Mul/fp.Inverse` and compare against blst verison (C and Go)
- [ ] Explore MPT depth for accounts and storage tries inside accounts.

I’ll be working on these things next.