ZK-for-Z2K: MPC-in-the-Head Zero-Knowledge Proofs for Z₂^k

In this work, we extend the MPC-in-the-Head framework, used in recent efficient zero-knowledge protocols, to work over the ring Z 2k, which is the primary operating domain for modern CPUs. The proposed schemes are compatible with any threshold linear secret sharing scheme and draw inspiration from MPC protocols adapted for ring operations. Additionally, we explore various batching methodologies, leveraging Shamir's secret sharing schemes and Galois ring extensions, and show the applicability of our approach in RAM program verification. Finally, we analyse different options for instantiating the resulting ZK scheme over rings and compare their communication costs.