Atomic Read/Write Memory in Signature-free Byzantine Asynchronous   Message-passing Systems
  This article presents a signature-free distributed algorithm which builds an atomic read/write shared memory on top of an $n$-process asynchronous message-passing system in which up to $t<n/3$ processes may commit Byzantine failures. From a conceptual point of view, this algorithm is designed to be as close as possible to the algorithm proposed by Attiya, Bar-Noy and Dolev (JACM 1995), which builds an atomic register in an $n$-process asynchronous message-passing system where up to $t<n/2$ processes may crash. The proposed algorithm is particularly simple. It does not use cryptography to cope with Byzantine processes, and is optimal from a $t$-resilience point of view ($t<n/3$). A read operation requires $O(n)$ messages, and a write operation requires $O(n^2)$ messages. 
Achour Mosteafoui, Matoula Petrolia, Michel Raynal, and Claude Jard
cs.DC