Signature-free asynchronous Byzantine systems: from multivalued to binary consensus with $$t<n/3$$ t < n / 3 , $$O(n^2)$$ O ( n 2 ) messages, and constant time

Abstract

This paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asynchronous message-passing system made up of n processes where up to t may commit Byzantine failures. This algorithm has the following noteworthy properties: it assumes t < n/3 (and is consequently optimal from a resilience point of view), uses $$O(n^2)$$O(n2) messages, has a constant time complexity, and uses neither signatures nor additional computational power (such as random numbers, failure detectors, additional scheduling assumption, or additional synchrony assumption). The design of this reduction algorithm relies on two new all-to-all communication abstractions. The first one allows the non-faulty processes to reduce the number of proposed values to c, where c is a small constant. The second communication abstraction allows each non-faulty process to compute a set of (proposed) values satisfying the following property: if the set of a non-faulty process is a singleton containing value v, the set of any non-faulty process contains v. Both communication abstractions have an $$O(n^2)$$O(n2) message complexity and a constant time complexity. The reduction of multivalued Byzantine consensus to binary Byzantine consensus is then a simple sequential use of these communication abstractions. To the best of our knowledge, this is the first asynchronous message-passing algorithm that reduces multivalued consensus to binary consensus with $$O(n^2)$$O(n2) messages and constant time complexity (measured with the longest causal chain of messages) in the presence of up to t < n/3 Byzantine processes, and without using cryptography techniques. Moreover, this reduction algorithm uses a single instance of the underlying binary consensus, and tolerates message re-ordering by Byzantine processes.