### Efficient Adaptively-Secure Byzantine Agreement for Long Messages

Amey Bhangale, Chen-Da Liu-Zhang, Julian Loss, and Kartik Nayak

##### 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 \emph{all but simple} and involves an interesting new application of Mc Diarmid's inequality to obtain {\em optimal} corruption thresholds.

##### Metadata
Available format(s)
Category
Cryptographic protocols
Publication info
Preprint. Minor revision.
Keywords
Byzantine agreementblockchaincommunication complexity
Contact author(s)
cliuzhan @ andrew cmu edu
kartik @ cs duke edu
lossjulian @ gmail com
amey bhangale @ ucr edu
History
2021-10-18: received
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},
note = {\url{https://eprint.iacr.org/2021/1403}},
url = {https://eprint.iacr.org/2021/1403}
}
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