Asynchronous Agreement on a Core Set in Constant Expected Time and More Efficient Asynchronous VSS and MPC

Abraham, I and Ashsarov, G and Patra, A and Stern, G (2025) Asynchronous Agreement on a Core Set in Constant Expected Time and More Efficient Asynchronous VSS and MPC. In: 22nd Theory of Cryptography Conference, TCC 2024, 2 December 2024through 6 December 2024, Milan, pp. 451-482.

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Abstract

A major challenge of any asynchronous MPC protocol is the need to reach an agreement on the set of private inputs to be used as input for the MPC functionality. Ben-Or, Canetti and Goldreich STOC 93 call this problem Agreement on a Core Set (ACS) and solve it by running n parallel instances of asynchronous binary Byzantine agreements. To the best of our knowledge, all results in the perfect and statistical security setting used this same paradigm for solving ACS. Using all known asynchronous binary Byzantine agreement protocols, this type of ACS has Ω(logn) expected round complexity, which results in such a bound on the round complexity of MPC protocols as well (even for constant depth circuits). We provide a new solution for Agreement on a Core Set that runs in expected O(1) rounds. Our perfectly secure variant is optimally resilient (t<n/4) and requires just O(n4logn) expected communication complexity. We show a similar result with statistical security for t<n/3. Our ACS is based on a new notion of Asynchronously Validated Asynchronous Byzantine Agreement (AVABA) and new information-theoretic analogs to techniques used in the authenticated model. Along the way, we also construct a new perfectly secure packed asynchronous verifiable secret sharing (AVSS) protocol with just O(n3logn) communication complexity, improving the state of the art by a factor of O(n). This leads to a more efficient asynchronous MPC that matches the state-of-the-art synchronous MPC. © International Association for Cryptologic Research 2025.

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 publishers.
Keywords:	Network security, Byzantine Agreement; Communication complexity; Constant-depth circuits; Core set; Expected time; Perfect securities; Round complexity; Security settings; State of the art; Statistical securities, Authentication Protocol
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	30 Dec 2024 06:00
Last Modified:	30 Dec 2024 06:00
URI:	http://eprints.iisc.ac.in/id/eprint/87177

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