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We study information-theoretic multiparty computation (MPC) protocols over rings Z/ pkZ that have good asymptotic communication complexity for a large number of players. An important ingredient for such protocols is arithmetic secret sharing, i.e., linear secret-sharing schemes with multiplicative properties. The standard way to obtain these over fields is with a family of linear codes C, such that C, C⊥ and C2 are asymptotically good (strongly multiplicative). For our purposes here it suffices if the square code C2 is not the whole space, i.e., has codimension at least 1 (multiplicative). Our approach is to lift such a family of codes defined over a finite field F to a Galois ring, which is a local ring that has F as its residue field and that contains Z/ pkZ as a subring, and thus enables arithmetic that is compatible with both structures. Although arbitrary lifts preserve the distance and dual distance of a code, as we demonstrate with a counterexample, the multiplicative property is not preserved. We work around this issue by showing a dedicated lift that preserves self-orthogonality (as well as distance and dual distance), for p≥ 3. Self-orthogonal codes are multiplicative, therefore we can use existing results of asymptotically good self-dual codes over fields to obtain arithmetic secret sharing over Galois rings. For p= 2 we obtain multiplicativity by using existing techniques of secret-sharing using both C and C⊥, incurring a constant overhead. As a result, we obtain asymptotically good arithmetic secret-sharing schemes over Galois rings. With these schemes in hand, we extend existing field-based MPC protocols to obtain MPC over Z/ pkZ, in the setting of a submaximal adversary corrupting less than a fraction 1 / 2 - ε of the players, where ε> 0 is arbitrarily small. We consider 3 different corruption models. For passive and active security with abort, our protocols communicate O(n) bits per multiplication. For full security with guaranteed output delivery we use a preprocessing model and get O(n) bits per multiplication in the online phase and O(nlog n) bits per multiplication in the offline phase. Thus, we obtain true linear bit complexities, without the common assumption that the ring size depends on the number of players.

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.

At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPDZ2k 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 Z/p^k 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.

Background HIV treatment prescription is a complex process. Clinical decision support systems (CDSS) are a category of health information technologies that can assist clinicians to choose optimal treatments based on clinical trials and expert knowledge. The usability of some CDSSs for HIV treatment would be significantly improved by using the knowledge obtained by treating other patients. This knowledge, however, is mainly contained in patient records, whose usage is restricted due to privacy and confidentiality constraints. Methods A treatment effectiveness measure, containing valuable information for HIV treatment prescription, was defined and a method to extract this measure from patient records was developed. This method uses an advanced cryptographic technology, known as secure Multiparty Computation (henceforth referred to as MPC), to preserve the privacy of the patient records and the confidentiality of the clinicians’ decisions. Findings Our solution enables to compute an effectiveness measure of an HIV treatment, the average time-to-treatment-failure, while preserving privacy. Experimental results show that our solution, although at proof-of-concept stage, has good efficiency and provides a result to a query within 24 min for a dataset of realistic size. Interpretation This paper presents a novel and efficient approach HIV clinical decision support systems, that harnesses the potential and insights acquired from treatment data, while preserving the privacy of patient records and the confidentiality of clinician decisions.