EPF4: Week 3 -> Standalone Verkle Trie Libraries

Hi, Agnish here. I finally decided upon a couple of things. But let's talk about what I learnt the previous week. Sorry for delaying this so much, I was really overwhelmed with school and my day job.

What I learnt / did

I dived deeper into Ignacio's notes, learnt more about Affine and Projective Coordinates and how to double Multiplicative and Inverse operations on them. Studied the different forms in which curves like BLS12_381 and Bandersnatch can be represented, namely the Twisted Edwards, Weistrass and Montgomery form.

Again there's a Montgomery trick which often works for BLS12_381 but not Bandersnatch, you can read it from Ignacio's blog, and find my comment on Montgomery trick to read about how our goal should be maximise mult ops and minimize inv ops as inv ops are ~100x costlier than mult.

Learnt ways to effectively benchmark MKTs and VKTs. Spoke to the Only Dust team from Quadratic Labs to proceed further with development of Java libraries of VKT for Besu. Asked Karim Taam to be my mentor for the same, someone who actively contributed in creating Bonsai Tries for Hyperledger Besu. Had 1 meeting with them to understand the proper workflow of how to proceed with dev and integration.

Also had a chat with Zahary from Nimbus, and had a call with the Nimbus Team where I decided to work on the Nim library for Inner Product Arguments and Multiproofs for the Verkle Trie library for Nim Lang, for the Nimbus client.