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

Gilad Asharov; Anirudh Chandramouli

doi:10.1007/978-3-031-58740-5_11

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

Gilad Asharov, Anirudh Chandramouli

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

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 language	English
Title of host publication	Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings
Editors	Marc Joye, Gregor Leander
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	310-339
Number of pages	30
ISBN (Print)	9783031587399
DOIs	https://doi.org/10.1007/978-3-031-58740-5_11
State	Published - 2024
Event	43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024 - Zurich, Switzerland Duration: 26 May 2024 → 30 May 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14655 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024
Country/Territory	Switzerland
City	Zurich
Period	26/05/24 → 30/05/24

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2024.

Keywords

Broadcast
Byzantine Agreement
Perfect Secure Computation
Verifiable Secret Sharing

Access to Document

10.1007/978-3-031-58740-5_11

Cite this

Asharov, G., & Chandramouli, A. (2024). Perfect (Parallel) Broadcast in Constant Expected Rounds via Statistical VSS. In M. Joye, & G. Leander (Eds.), Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings (pp. 310-339). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14655 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-58740-5_11

Asharov, Gilad ; Chandramouli, Anirudh. / Perfect (Parallel) Broadcast in Constant Expected Rounds via Statistical VSS. Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. editor / Marc Joye ; Gregor Leander. Springer Science and Business Media Deutschland GmbH, 2024. pp. 310-339 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Asharov, G & Chandramouli, A 2024, Perfect (Parallel) Broadcast in Constant Expected Rounds via Statistical VSS. in M Joye & G Leander (eds), Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14655 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 310-339, 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024, Zurich, Switzerland, 26/05/24. https://doi.org/10.1007/978-3-031-58740-5_11

Perfect (Parallel) Broadcast in Constant Expected Rounds via Statistical VSS. / Asharov, Gilad; Chandramouli, Anirudh.
Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. ed. / Marc Joye; Gregor Leander. Springer Science and Business Media Deutschland GmbH, 2024. p. 310-339 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14655 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Asharov G, Chandramouli A. Perfect (Parallel) Broadcast in Constant Expected Rounds via Statistical VSS. In Joye M, Leander G, editors, Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2024, Proceedings. Springer Science and Business Media Deutschland GmbH. 2024. p. 310-339. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-58740-5_11