Efficient Information-Theoretic Secure Multiparty Computation over $$\mathbb {Z}/p^k\mathbb {Z}$$ via Galois Rings

At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPD\(\mathbb {Z}_{2^k}\) that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integers modulo \(2^k\), thus solving a long-standing open question in MPC about secure computation over rings in this setting. In this paper we study this problem in the information-theoretic scenario. More specifically, we ask the following question: Can we obtain information-theoretic MPC protocols that work over rings with comparable efficiency to corresponding protocols over fields? We answer this question in the affirmative by presenting an efficient protocol for robust Secure Multiparty Computation over \(\mathbb {Z}/p^{k}\mathbb {Z}\) (for any prime p and positive integer k) that is perfectly secure against active adversaries corrupting a fraction of at most 1/3 players, and a robust protocol that is statistically secure against an active adversary corrupting a fraction of at most 1/2 players.