Error-Free Multi-Valued Consensus with Byzantine Failures
  In this paper, we present an efficient deterministic algorithm for consensus in presence of Byzantine failures. Our algorithm achieves consensus on an $L$-bit value with communication complexity $O(nL + n^4 L^{0.5} + n^6)$ bits, in a network consisting of $n$ processors with up to $t$ Byzantine failures, such that $t<n/3$. For large enough $L$, communication complexity of the proposed algorithm approaches $O(nL)$ bits. In other words, for large $L$, the communication complexity is linear in the number of processors in the network. This is an improvement over the work of Fitzi and Hirt (from PODC 2006), who proposed a probabilistically correct multi-valued Byzantine consensus algorithm with a similar complexity for large $L$. In contrast to the algorithm by Fitzi and Hirt, our algorithm is guaranteed to be always error-free. Our algorithm require no cryptographic technique, such as authentication, nor any secret sharing mechanism. To the best of our knowledge, we are the first to show that, for large $L$, error-free multi-valued Byzantine consensus on an $L$-bit value is achievable with $O(nL)$ bits of communication. 
Guanfeng Liang and Nitin Vaidya
cs.DC cs.CR