This paper proposes a hierarchy of three Byzantine-resistant protocols aimed to be used in practical distributed systems: multi-valued consensus, vector consensus and atomic broadcast. These protocols are designed as successive transformations from one to another. The first protocol, multi-valued consensus, is implemented on top of a randomized binary consensus. The protocols share a set of important structural properties. Firstly, they do not use signatures obtained with public-key cryptography, a well-known performance bottleneck in this kind of protocols. Secondly, they are time-free, i.e., they make no synchrony assumptions, since these assumptions are often vulnerable to subtle but effective attacks. Thirdly, they have no leaders, thus avoiding the cost of detecting corrupt processes. Fourthly, they have optimal resilience, i.e., they tolerate f = n−1 3 out of a total of n processes. The multi-valued consensus protocol terminates in a constant expected number of rounds, while the vector consensus and atomic broadcast protocols have time complexities O(f ).
All of the aforementioned protocols are binary consensus protocols, i.e., the agreed upon value is v ∈ {0, 1}. In the multi-valued consensus protocol of Correia et al. REF , the set of values V is of arbitrary size.
From Consensus to Atomic Broadcast: Time-Free Byzantine-Resistant Protocols without Signatures
Comput. J.
Computer Science