Paper 2024/1004

Relaxed Vector Commitment for Shorter Signatures

Abstract

The MPC-in-the-Head (MPCitH) paradigm has recently gained traction as a foundation for post-quantum signature schemes, offering robust security without the need for 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 enhancing vector commitments within MPCitH-based schemes. We introduce the concept of vector semi-commitment, which relaxes traditional vector commitment requirements without compromising security, thus reducing signature size while maintaining performance. We instantiate vector semi-commitment schemes in both the random oracle model and the ideal cipher model, leveraging recent optimizations such as the Half-tree technique. Additionally, we propose a key injection technique that further minimizes signature size by embedding the secret key into the Half-GGM tree. We apply these improvements 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.