Paper 2024/1004

Relaxed Vector Commitment for Shorter Signatures

Abstract

MPC-in-the-Head (MPCitH) has recently gained traction as a foundation for post-quantum signature schemes, offering robust security without trapdoors. Despite its strong security profile, MPCitH-based schemes suffer from high computational overhead and large signature sizes, limiting their practical application. This work addresses these inefficiencies by relaxing vector commitments within MPCitH-based schemes. We introduce the concept of vector semi-commitment, which relaxes the binding property of traditional vector commitment. Vector semi-commitment schemes may allow an adversary to find more than one preimage of a commitment. We instantiate vector semi-commitment schemes in both the random oracle model and the ideal cipher model, leveraging recent optimizations on GGM tree such as correlated GGM tree. We apply the ideal-cipher-based vector semi-commitment scheme to the BN++ signature scheme and prove it fully secure in the ideal cipher model. Implementing these improvements in the $\mathsf{AIMer}$ v2.0 signature scheme, we achieve up to 18% shorter signatures and up to 112% faster signing and verification speeds, setting new benchmarks for MPCitH-based schemes.