arithmic/on-chain

[arithmic-ASHISH]

The objective of this PR is to have the Jolt proof verified on-chain. To achieve this, we proceed with the following steps:

Porting the Jolt Verifier:

Split the Jolt Verifier into two parts Jolt1(ops over BN254 Scalar field) and Jolt2 (ops over BN254 Base field)

Compute a Rank-1 Constraint System (R1CS) for the Jolt1 Verifier over the BN254 scalar field(1).

Compute an R1CS for the Jolt2 Verifier over the BN254 base field(2).

The above R1CS (1) will be verified using Spartan, with Polynomial Commitment Scheme (PCS) Hyperkzg.

Linking Jolt1 and Jolt2:

Jolt1 and Jolt2 share some data like commitments, combiners etc. Check this via Linking.

Compute an R1CS for Linking over the BN254 base field(3)

Porting the Spartan Verifier(Hyperkzg):

Port the Spartan Verifier(Hyperkzg) from the BN254 scalar field to the BN254 base field.

Compute an R1CS for the Spartan Verifier over the BN254 base field(4).

Combined R1CS

Combine the R1CS (2), (3) and (4) as a single R1CS(5)

The above R1CS will be verified using Spartan, with PCS via Surge.

Porting the Spartan Verifier(Surge):

Port the Spartan Verifier(Surge) from the BN254 base field to the BN254 scalar field.

Compute an R1CS for the Spartan Verifier over the BN254 base field(4).

This R1CS will be proved using Groth-16, with the resulting proof being verified on-chain via a Groth-16 verifier.