Asymptotically Free Broadcast in Constant Expected Time via Packed VSS

Abraham, I and Asharov, G and Patil, S and Patra, A (2022) Asymptotically Free Broadcast in Constant Expected Time via Packed VSS. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7 - 10 November 2022, Chicago, pp. 384-414.

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Abstract

Broadcast is an essential primitive for secure computation. We focus in this paper on optimal resilience (i.e., when the number of corrupted parties t is less than a third of the computing parties n), and with no setup or cryptographic assumptions. While broadcast with worst case t rounds is impossible, it has been shown [Feldman and Micali STOC’88, Katz and Koo CRYPTO’06] how to construct protocols with expected constant number of rounds in the private channel model. However, those constructions have large communication complexity, specifically O(n2L+ n6log n) expected number of bits transmitted for broadcasting a message of length L. This leads to a significant communication blowup in secure computation protocols in this setting. In this paper, we substantially improve the communication complexity of broadcast in constant expected time. Specifically, the expected communication complexity of our protocol is O(nL+ n4log n). For messages of length L= Ω(n3log n), our broadcast has no asymptotic overhead (up to expectation), as each party has to send or receive O(n3log n) bits. We also consider parallel broadcast, where n parties wish to broadcast L bit messages in parallel. Our protocol has no asymptotic overhead for L= Ω(n2log n), which is a common communication pattern in perfectly secure MPC protocols. For instance, it is common that all parties share their inputs simultaneously at the same round, and verifiable secret sharing protocols require the dealer to broadcast a total of O(n2log n) bits. As an independent interest, our broadcast is achieved by a packed verifiable secret sharing, a new notion that we introduce. We show a protocol that verifies O(n) secrets simultaneously with the same cost of verifying just a single secret. This improves by a factor of n the state-of-the-art.

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; Security of data, Asymptotics; Broadcast; Byzantine Agreement; Communication complexity; Cryptographic assumptions; Expected time; MPC; Optimal resilience; Secure computation; Verifiable secret sharing, Computational complexity
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	10 Feb 2023 09:01
Last Modified:	10 Feb 2023 09:01
URI:	https://eprints.iisc.ac.in/id/eprint/80163

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