Fully-Secure MPC with Minimal Trust

Ishai, Y and Patra, A and Patranabis, S and Ravi, D and Srinivasan, A (2022) Fully-Secure MPC with Minimal Trust. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7 - 10 November 2022, Chicago, pp. 470-501.

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Abstract

The task of achieving full security (with guaranteed output delivery) in secure multiparty computation (MPC) is a long-studied problem. Known impossibility results (Cleve, STOC 86) rule out general solutions in the dishonest majority setting. In this work, we consider solutions that use an external trusted party (TP) to bypass the impossibility results, and study the minimal requirements needed from this trusted party. In particular, we restrict ourselves to the extreme setting where the size of the TP is independent of the size of the functionality to be computed (called “small" TP) and this TP is invoked only once during the protocol execution. We present several positive and negative results for fully-secure MPC in this setting. For a natural class of protocols, specifically, those with a universal output decoder, we show that the size of the TP must necessarily be exponential in the number of parties. This result holds irrespective of the computational assumptions used in the protocol. The class of protocols to which our lower bound applies is broad enough to capture prior results in the area, implying that the prior techniques necessitate the use of an exponential-sized TP. We additionally rule out the possibility of achieving information-theoretic full security (without the restriction of using a universal output decoder) using a “small" TP in the plain model (i.e., without any setup).In order to get around the above negative result, we consider protocols without a universal output decoder. The main positive result in our work is a construction of such a fully-secure MPC protocol assuming the existence of a succinct Functional Encryption scheme. We also give evidence that such an assumption is likely to be necessary for fully-secure MPC in certain restricted settings.Finally, we explore the possibility of achieving full-security with a semi-honest TP that could collude with other malicious parties (which form a dishonest majority). In this setting, we show that even fairness is impossible to achieve regardless of the “small TP” requirement. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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, Computational assumptions; Exponentials; Fully secure; General solutions; Impossibility results; Low bound; Multi-party computation protocols; Protocol execution; Secure multi-party computation; Trusted party, Decoding
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	10 Feb 2023 08:46
Last Modified:	10 Feb 2023 08:46
URI:	https://eprints.iisc.ac.in/id/eprint/80158

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