Paper 2025/177
On the Power of Sumcheck in Secure Multiparty Computation
Abstract
Lund et al. (JACM 1992) invented the powerful Sumcheck protocol that has been extensively used in complexity theory and in designing concretely efficient (zero-knowledge) arguments. In this work, we systematically study Sumcheck in the context of secure multi-party computation (MPC). Our main result is a new generic framework for lifting semi-honest MPC protocols to maliciously secure ones, with a {\em constant} multiplicative overhead in {\em both} computation and communication, and in the best case, only an additional logarithmic communication cost. In general, our approach applies to any semi-honest linear secret-sharing based MPC secure up to additive attacks, where linear secret-sharing can be enhanced with an authentication mechanism. At a high-level, our approach has a highly distributive flavor, where the parties jointly emulate a Sumcheck prover to prove the correctness of MPC semi-honest evaluations in zero-knowledge, while simultaneously emulating a Sumcheck verifier to verify the proof themselves. Along the way, we provide a new perspective on the {\em fully linear interactive oracle proof} (FLIOP) systems proposed by Boneh et al. (CRYPTO 2019). That is, essentially distributed Sumcheck on proving a batch of multiplications can be viewed as an optimized concrete instantiation of the FLIOP-based approach.
As a concrete application of our techniques, we first consider semi-honest MPC protocols based on Shamir secret sharing in the honest majority setting. Given
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- MPCDistributed Zero-Knowledge ProofsSumcheck
- Contact author(s)
-
lizh0048 @ e ntu edu sg
xingcp @ sjtu edu cn
yaoyizhou0620 @ sjtu edu cn
chen_yuan @ sjtu edu cn - History
- 2025-02-16: revised
- 2025-02-06: received
- See all versions
- Short URL
- https://ia.cr/2025/177
- License
-
CC BY-NC
BibTeX
@misc{cryptoeprint:2025/177, author = {Zhe Li and Chaoping Xing and Yizhou Yao and Chen Yuan}, title = {On the Power of Sumcheck in Secure Multiparty Computation}, howpublished = {Cryptology {ePrint} Archive, Paper 2025/177}, year = {2025}, url = {https://eprint.iacr.org/2025/177} }