A standalone Plonky2 verifier
-----------------------------

This is a (WIP) implementation of a Plonky2 verifier in Haskell.

[Plonky2](https://github.com/0xPolygonZero/plonky2/) is a zero-knowledge proof
system developed by Polygon Zero, optimized for recursive proofs.

The goal here is to provide an executable specification (along a with less precise,
but still detailed human language description) of the Plonky2 verification 
algorithm. 

Another goal is to be a basis for further tooling (for example:
estimating verifier costs, helping the design of recursive circuits, generating 
Plonky2 verifier circuits for other proof systems, etc)

Note: It's deliberately no a goal for this verifier to be efficient; instead we 
try to focus on simplicity.


### Implementation status

- [x] Parsing the proof and verification key from JSON
- [ ] Parsing from Plonky's custom binary serialization
- [x] Generating verifier challenges
- [ ] Recursive circuit subtle details (like [this](https://github.com/0xPolygonZero/plonky2/blob/356aefb6863ac881fb71f9bf851582c915428458/plonky2/src/fri/challenges.rs#L55-L64]))
- [ ] Constraints check
- [ ] FRI check
- [ ] Documenting Plonky2 internals and the verifier algorithm

Supported gates:

- [x] ArithmeticGate
- [x] ArithmeticExtensionGate
- [x] BaseSumGate
- [ ] CosetInterpolationGate
- [x] ConstantGate
- [x] ExponentiationGate
- [ ] LookupGate
- [ ] LookupTableGate
- [x] MulExtensionGate
- [x] NoopGate
- [x] PublicInputGate
- [ ] PoseidonGate
- [ ] PoseidonMdsGate
- [ ] RandomAccessGate
- [ ] ReducingGate
- [ ] ReducingExtensionGate

Optional features:

- [ ] Field extensions with degree higher than 2
- [ ] Being parametric over the field choice
- [ ] Supporting different hash function choices