We study the problem of atomic broadcast—the underlying problem addressed by blockchain protocols—in the presence of a malicious adversary who corrupts some fraction of the $n$ parties running the protocol.
Existing protocols are either robust for any number of corruptions in a
synchronous network (where
messages are delivered within some known
time $Delta$) but fail if the synchrony assumption is violated, or tolerate fewer than $n/3$ corrupted parties in an
asynchronous network (where messages can be delayed arbitrarily) and cannot tolerate more corruptions even if the network happens to be well behaved.

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We design an atomic broadcast protocol (TARDIGRADE) that, for any $t_s geq t_a$ with $2t_s + t_a

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