Paper 2018/829

Information-Theoretic Broadcast with Dishonest Majority for Long Messages

Wutichai Chongchitmate and Rafail Ostrovsky

Abstract

Byzantine broadcast is a fundamental primitive for secure computation. In a setting with $n$ parties in the presence of an adversary controlling at most $t$ parties, while a lot of progress in optimizing communication complexity has been made for $t < n/2$, little progress has been made for the general case $t<n$, especially for information-theoretic security. In particular, all information-theoretic secure broadcast protocols for $\ell$-bit messages and $t<n$ and optimal round complexity $\mathcal{O}(n)$ have, so far, required a communication complexity of $\mathcal{O}(\ell n^2)$. A broadcast extension protocol allows a long message to be broadcast more efficiently using a small number of single-bit broadcasts. Through broadcast extension, so far, the best achievable round complexity for $t<n$ setting with the optimal communication complexity of $\mathcal{O}(\ell n)$ is $\mathcal{O}(n^4)$ rounds. In this work, we construct a new broadcast extension protocol for $t<n$ with information-theoretic security. Our protocol improves the round complexity to $\mathcal{O}(n^3)$ while maintaining the optimal communication complexity for long messages. Our result shortens the gap between the information-theoretic setting and the computational setting, and between the optimal communication protocol and the optimal round protocol in the information-theoretic setting for $t<n$.