Perfect (Parallel) Broadcast in Constant Expected Rounds via Statistical VSS

Gilad Asharov, Anirudh Chandramouli

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study broadcast protocols in the information-theoretic model under optimal conditions, where the number of corruptions t is at most one-third of the parties, n. While worst-case Ω(n) round broadcast protocols are known to be impossible to achieve, protocols with an expected constant number of rounds have been demonstrated since the seminal work of Feldman and Micali [STOC’88]. Communication complexity for such protocols has gradually improved over the years, reaching O(nL) plus expected O(n4logn) for broadcasting a message of size L bits. This paper presents a perfectly secure broadcast protocol with expected constant rounds and communication complexity of O(nL) plus expected O(n3log2n) bits. In addition, we consider the problem of parallel broadcast, where n senders, each wish to broadcast a message of size L. We show a parallel broadcast protocol with expected constant rounds and communication complexity of O(n2L) plus expected O(n3log2n) bits. Our protocol is optimal (up to expectation) for messages of length L∈Ω(nlog2n). Our main contribution is a framework for obtaining perfectly secure broadcast with an expected constant number of rounds from a statistically secure verifiable secret sharing. Moreover, we provide a new statistically secure verifiable secret sharing where the broadcast cost per participant is reduced from O(nlogn) bits to only O(polylogn) bits. All our protocols are adaptively secure.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings
EditorsMarc Joye, Gregor Leander
PublisherSpringer Science and Business Media Deutschland GmbH
Pages310-339
Number of pages30
ISBN (Print)9783031587399
DOIs
StatePublished - 2024
Event43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024 - Zurich, Switzerland
Duration: 26 May 202430 May 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14655 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024
Country/TerritorySwitzerland
CityZurich
Period26/05/2430/05/24

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2024.

Keywords

  • Broadcast
  • Byzantine Agreement
  • Perfect Secure Computation
  • Verifiable Secret Sharing

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