# GKR Seoul stay - PSE
## Goal:
See if GKR can be the next big thing and whether it will only be useful to make some protocols better or can actually mean a change in paradigm in the ecosystem.

The expected outcome of the stay would be to have answers to the questions & topics below:

## Things to explore:
- GKR aggregation perf/complexity
- Lev
- Soowon(GKR full recursion impl using circom / observed that proof size linear to the recursions)
- I think it is because of an overhead of compilation of circom circuit (R1CS) to layered arithmetic circuit. So it can be improved by implementation of native layered arithmetic circuit - Soowon
- GKR verification inside of a KZG Proof
- reducing the sumcheck verification cost can be beneficial for the proving time for the final wrapper circuit
- Possible components to check GKR MVP:
- BigInt arithmetic
- LogUp Improved with GKR for multi-column lookups
- Layer complexity for circuits in GKR
- How to merge to intermediate steps?
- How to encode a VM trace into a GKR circuit?
- Which arithmetisation should we use? CCS, Plonkish, R1CS, AIR?
- Alternatives to non-determinism in witness for ZKEVM?
- Interaction between circuit layers. Is it needed?
- Start from ZKEVM project to see where it can be useful there.
- ZKML would benefit from that?
- Is the SIMD paradigm the only one that we can extract from GKR? Where else is GKR useful in the design?
- Any GKR-ways to improve the state of the art of folding schemes?
- Can we map GKR to any real use-case thing (tangible) so that we can see how they solve their biggest counterparts?

:::info
Please, Feel free to add anything that you think would be interesting to check during the stay in Seoul down below.
:::

- Better GKR style polynomial identity between layers.
- What about having mult-only GKR layers and compute Grandproduct?
- Primitive GKR circuit will depend on VM design
- Should we start with EVM or?
- Should we try to design a new VM?
- Should we try to use another existing VM?
- Or generally LLVM?
- Or should we try to design an 'algebra'-friendly VM?
- What should be the instructions for the benchmark?
- How much GPU acceleration can improve MSM?
- LogUp's fractional circuit idea can be used for GKR circuit for ML

# Application ideas

See note for details https://hackmd.io/uF9thzLvR-qGDWuDEAAMFA?both:
- sha256 with lookups
- keccak with lookups
- floating point with lookups
- DSL for "static computation" with focus on lookups
- RISC-U implementation using Lasso + halo2 based Jolt design
- WIP Lasso + hyperplonk: https://github.com/DoHoonKim8/plonkish
- WIP RISC-U with Lasso simulation: https://github.com/ed255/riscu-jolt
- Design of a CPU circuit with co-processors / extensions with lookups