Distributed download from an external data source in Byzantine majority settings

We consider the Download problem in the Data Retrieval Model, introduced in DISC’24, where a distributed set of peers, some of which may be Byzantine, seek to learn n bits of data stored at a trustworthy external data source. Each bit of data can be learned by a peer either through a direct and costly query of the source or through other peers that have already learned it; the goal is to design a collaborative protocol that reduces the query complexity defined as the maximum number of bits queried by any honest peer. We begin with a randomized protocol for the Download problem that achieves optimal query complexity, up to a logarithmic factor. For a stronger “dynamic” adversary that can change the set of Byzantine peers from one round to the next, we achieve optimality (within log factors) for both query complexity (in expectation) and time complexity, but with larger messages. In broadcast communication, where all peers (including Byzantine peers) are required to send the same message to all peers, we achieve (up to log factors) an optimal trade-off between query complexity, time complexity, and message size with the dynamic adversary. All of our protocols can tolerate any constant fraction $$\beta <1$$ of Byzantine peers.