ChainSafe / ChainSafe/ProtoBanshee

Starky verifier in Halo2

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Description

Implement a verifier chip for Starky proofs for Halo2. The goal is to check if composing Starky (or another AIR+FRI system) verifier would be cheaper than just doing SHA in Halo2 and for what number of hashes this becomes viable optimization.

> Note that AIR-based proofs, such as STARKs or Starky, haven't been composed into PLONK circuits yet. Implementing such a circuit isn't trivial and since the usefulness of this optimization is at question, the implementation should be seen as a research prototype. The use of approximation and abstraction is advised.

### [Spec](https://hackmd.io/@timofey/Syhx6DqIn#Halo2-StarkyVerifier-circuit)

### References:
- FRI gadget for Halo2 https://github.com/maxgillett/halo2-fri-gadget
- Plonky2Verifier for Halo2 https://github.com/DoHoonKim8/stark-verifier/tree/main/semaphore_aggregation/src/snark/chip
- STARK verifier in Circom https://github.com/0xPolygonHermez/pil-stark/blob/main/circuits.bn128/stark_verifier.circom.ejs
- Winterfell STARK verifier in Circom https://github.com/VictorColomb/stark-snark-recursive-proofs

### Points of contact (potential)
- https://github.com/DoHoonKim8
- https://twitter.com/jbaylina
- https://twitter.com/maxgillett

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