At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPD2k that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integers modulo 2k, 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 Z/pkZ (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.

Philips Research
Lecture Notes in Computer Science
Theory of Cryptography Conference
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Abspoel, M.A, Cramer, R.J.F, Damgård, I.B, Escudero, D, & Yuan, C. (2019). Efficient information-theoretic Secure Multiparty Computation over Z/pkZ via Galois rings. In Proceedings of the Theory of Cryptography Conference (pp. 471–501). doi:10.1007/978-3-030-36030-6_19