Abstract
A fundamental primitive in distributed computing is Reliable Message Transmission (RMT), which refers to the task of correctly sending a message from a party to another, despite the presence of Byzantine corruptions. We explicitly consider the initial knowledge possessed by the parties-players by employing the recently introduced Partial Knowledge Model [13], where a player has knowledge over an arbitrary subgraph of the network, and the general adversary model of Hirt and Maurer [5]. Our main contribution is a tight condition for the feasibility of RMT in the setting resulting from the combination of these two quite general models; this settles the central open question of [13].
Obtaining such a condition presents the need for knowledge exchange between players. To this end, we introduce the joint view operation which serves as a fundamental tool for deducing maximal useful information conforming with the exchanged local knowledge. Maximality of the obtained knowledge is proved in terms of the semilattice structure imposed by the operation on the space of partial knowledge. This in turn, allows for the definition of a novel network separator notion that yields a necessary condition for achieving RMT in this model. In order to show the sufficiency of the condition, we propose the RMT Partial Knowledge Algorithm (RMT-PKA), an algorithm which employs the joint view operation to solve RMT in every instance where the necessary condition is met. To the best of our knowledge, this is the first protocol for RMT against general adversaries in the partial knowledge model. Due to the generality of the model, our results provide, for any level of topology knowledge and any adversary structure, an exact characterization of instances where RMT is possible and an algorithm to achieve RMT on such instances.
A short version of this paper, entitled “Brief Announcement: Reliable Message Transmission under Partial Knowledge and General Adversaries”, appeared in PODC 2016 [12].
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- 1.
As usual in the byzantine faults literature, the existence of authenticated channel (u, v), guarantees that once a message is sent from node u to node v, the message will be delivered intact to the receiver v and the receiver will be aware of the identity of the sender u, i.e. no tampering of the message or identity spoofing can be performed by the adversary.
- 2.
The notion of meet-semilattice can be used as well by inversing the ordering.
- 3.
By p||v (appearing in the algorithm) we will denote the concatenation of path p with node v.
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Pagourtzis, A., Panagiotakos, G., Sakavalas, D. (2017). Reliable Communication via Semilattice Properties of Partial Knowledge. In: Klasing, R., Zeitoun, M. (eds) Fundamentals of Computation Theory. FCT 2017. Lecture Notes in Computer Science(), vol 10472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55751-8_29
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