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Synchronous Byzantine Lattice Agreement in O(log(f )) Rounds

Abstract : 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.
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https://hal-cnrs.archives-ouvertes.fr/hal-02473843
Contributor : Emmanuelle Anceaume <>
Submitted on : Tuesday, February 11, 2020 - 8:29:31 AM
Last modification on : Thursday, September 3, 2020 - 11:58:02 AM
Long-term archiving on: : Tuesday, May 12, 2020 - 12:32:05 PM

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  • HAL Id : hal-02473843, version 1

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Giuseppe Di Luna, Emmanuelle Anceaume, Silvia Bonomi, Leonardo Querzoni. Synchronous Byzantine Lattice Agreement in O(log(f )) Rounds. ICDCS 2020 - 40th IEEE International Conference on Distributed Computing Systems, IEEE, Nov 2020, Singapore, Singapore. pp.1-11. ⟨hal-02473843⟩

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