%0 Conference Proceedings %T Synchronous Byzantine Lattice Agreement in O(log(f )) Rounds %+ Dipartimento di Ingegneria informatica automatica e gestionale [Roma] (DIAG UNIROMA) %+ Confidentialité, Intégrité, Disponibilité et Répartition (CIDRE) %+ Middleware Laboratory (MIDLAB) %A Di Luna, Giuseppe, Antonio %A Anceaume, Emmanuelle %A Bonomi, Silvia %A Querzoni, Leonardo %Z Emmanuelle Anceaume was partially funded by the "Sapienza Visiting Professor Programme" %< avec comité de lecture %B ICDCS 2020 - 40th IEEE International Conference on Distributed Computing Systems %C Singapore, Singapore %I IEEE %P 1-11 %8 2020-11-29 %D 2020 %K Fault-tolerance %K Byzantine faults %K Byzantine Agreement %Z Computer Science [cs] %Z Computer Science [cs]/Data Structures and Algorithms [cs.DS] %Z Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]Conference papers %X In the Lattice Agreement (LA) problem, originally proposed by Attiya et al. [1], a set of processes has to decide on a chain of a lattice. More precisely, each correct process proposes an element e of a certain join-semi lattice L and it has to decide on a value that contains e. Moreover, any pair pi, pj of correct processes has to decide two values deci and decj that are comparable (e.g., deci ≤ decj or decj < deci). In this paper we present new contributions for the synchronous case. We investigate the problem in the usual message passing model for a system of n processes with distinct unique IDs. We first prove that, when only authenticated channels are available, the problem cannot be solved if f = n/3 or more processes are Byzantine. We then propose a novel algorithm that works in a synchronous system model with signatures (i.e., the authenticated message model), tolerates up to f byzantine failures (where f < n/3) and that terminates in O(log f) rounds. We discuss how to remove authenticated messages at the price of algorithm resiliency (f < n/4). Finally, we present a transformer that converts any synchronous LA algorithm to an algorithm for synchronous Generalised Lattice Agreement. %G English %2 https://cnrs.hal.science/hal-02473843/document %2 https://cnrs.hal.science/hal-02473843/file/main.pdf %L hal-02473843 %U https://cnrs.hal.science/hal-02473843 %~ UNIV-RENNES1 %~ CNRS %~ INRIA %~ UNIV-UBS %~ INSA-RENNES %~ INRIA-RENNES %~ IRISA %~ IRISA_SET %~ INRIA_TEST %~ SUP_CIDRE %~ TESTALAIN1 %~ CENTRALESUPELEC %~ INRIA2 %~ UR1-HAL %~ UR1-MATH-STIC %~ UR1-UFR-ISTIC %~ TEST-UR-CSS %~ CENTRALESUPELEC-SACLAY-VP %~ UNIV-RENNES %~ INRIA-RENGRE %~ UR1-MATH-NUM %~ CYBERSCHOOL