On Perfectly Secure Two-Party Computation for Symmetric Functionalities with Correlated Randomness

Alon, B and Nissenbaum, O and Omri, E and Paskin-Cherniavsky, A and Patra, A (2022) On Perfectly Secure Two-Party Computation for Symmetric Functionalities with Correlated Randomness. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7 - 10 November 2022, Chicago, pp. 532-561.

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Abstract

A multiparty computation protocol is perfectly secure for some function f if it perfectly emulates an ideal computation of f. Thus, perfect security is the strongest and most desirable notion of security, as it guarantees security in the face of any adversary and eliminates the dependency on any security parameter. Ben-Or et al. [2] [STOC ’88] and Chaum et al. [5] [STOC ’88] showed that any function can be computed with perfect security if strictly less than one-third of the parties can be corrupted. For two-party sender-receiver functionalities (where only one party receives an output), Ishai et al. [9] [TCC ’13] showed that any function can be computed with perfect security in the correlated randomness model. Unfortunately, they also showed that perfect security cannot be achieved in general for two-party functions that give outputs to both parties (even in the correlated randomness model). We study the feasibility of obtaining perfect security for deterministic symmetric two-party functionalities (i.e., where both parties obtain the same output) in the face of malicious adversaries. We explore both the plain model as well as the correlated randomness model. We provide positive results in the plain model, and negative results in the correlated randomness model. As a corollary, we obtain the following results. 1.We provide a characterization of symmetric functionalities with (up to) four possible outputs that can be computed with perfect security. The characterization is further refined when restricted to three possible outputs and to Boolean functions. All characterizations are the same for both the plain model and the correlated randomness model.2.We show that if a functionality contains an embedded XOR or an embedded AND, then it cannot be computed with perfect security (even in the correlated randomness model).

Item Type:	Conference Paper
Publication:	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher:	Springer Science and Business Media Deutschland GmbH
Additional Information:	The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH.
Keywords:	Cryptography, Correlated randomness; Deterministics; Malicious adversaries; Multi-party computation protocols; Perfect securities; Secure two-party computations; Security parameters; Symmetrics; Two-party computation, Random processes
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	10 Feb 2023 08:49
Last Modified:	10 Feb 2023 08:49
URI:	https://eprints.iisc.ac.in/id/eprint/80161

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