Overview
Previously, VOLE ZK was a designed verifier; VOLE in the Head follows MPC in the Head and makes it Public Verifiable.
This would theoretically enable Onchain Verification on Ethereum, but VOLE ZK is difficult to implement at a realistic cost due to the larger Proof size compared to SNARK and others.
Scholl et al. propose FAEST as a quantum-tolerant signature scheme in their VOLE itH paper.
The zkTLS project zkPass has also adopted VOLE itH.
Building Blocks
VLE itH is based on the VOLE ZK protocol called QuickSilver and the Oblivious Transfer protocol called SoftSpoken. With SoftSpoken+GGM Construction, Single Point VOLE (SPVOLE) is achieved. This reduces the Communication Cost from O(N) to O(log N).
Reference
https://eprint.iacr.org/2023/996 https://youtu.be/tbsy9Jik3IQ?feature=shared https://csrc.nist.gov/csrc/media/Projects/post-quantum-cryptography/documents/pqc-seminars/presentations/15-vole-in-the-head-06182024.pdf