Efficient Adaptively-Secure Byzantine Agreement for Long Messages

Amey Bhangale; Chen-Da Liu-Zhang; Julian Loss; Kartik Nayak

Paper 2021/1403

Efficient Adaptively-Secure Byzantine Agreement for Long Messages

Amey Bhangale, University of California, Riverside

Chen-Da Liu-Zhang

, Carnegie Mellon University

Julian Loss, Helmholtz Center for Information Security

Kartik Nayak, Duke University

Abstract

We investigate the communication complexity of Byzantine agreement protocols for long messages against an adaptive adversary. In this setting, prior results either achieved a communication complexity of $O(nl\cdot\poly(\kappa))$ or $O(nl + n^2 \cdot \poly(\kappa))$ for $l$-bit long messages. We improve the state of the art by presenting protocols with communication complexity $O(nl + n \cdot \poly(\kappa))$ in both the synchronous and asynchronous communication models. The synchronous protocol tolerates $t \le (1-\epsilon) \frac{n}{2}$ corruptions and assumes a VRF setup, while the asynchronous protocol tolerates $t \le (1-\epsilon) \frac{n}{3}$ corruptions under further cryptographic assumptions. Our protocols are very simple and combine subcommittee election with the recent approach of Nayak et al. (DISC `20). Surprisingly, the analysis of our protocols is 'all but simple' and involves an interesting new application of Mc Diarmid's inequality to obtain 'optimal' corruption thresholds.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Byzantine agreement blockchain communication complexity
Contact author(s): amey bhangale @ ucr edu
cliuzhan @ andrew cmu edu
lossjulian @ gmail com
kartik @ cs duke edu
History: 2022-06-06: revised; 2021-10-18: received; See all versions
Short URL: https://ia.cr/2021/1403
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1403,
      author = {Amey Bhangale and Chen-Da Liu-Zhang and Julian Loss and Kartik Nayak},
      title = {Efficient Adaptively-Secure Byzantine Agreement for Long Messages},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/1403},
      year = {2021},
      url = {https://eprint.iacr.org/2021/1403}
}