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We study the Byzantine lattice agreement (BLA) problem in asynchronousdistributed message passing systems. In the BLA problem, each process proposesa value from a join semi-lattice and needs to output a value also in thelattice such that all output values of correct processes lie on a chain despitethe presence of Byzantine processes. We present an algorithm for this problemwith round complexity of $O(\log f)$ which tolerates $f < \frac{n}{5}$Byzantine failures in the asynchronous setting without digital signatures,where $n$ is the number of processes. We also show how this algorithm can bemodified to work in the authenticated setting (i.e., with digital signatures)to tolerate $f < \frac{n}{3}$ Byzantine failures.

Byzantine Lattice Agreement in Asynchronous Systems