Eventually consistent distributed ledger despite degraded atomic broadcast

The distributed ledger or blockchain technologies originated from the Bitcoin have been rapidly widespread in recent years. However, it also gives incentive to malicious users who would like to break the system or take advantage of it (steal money, hide some information stored in the ledger, isolate a particular node from the rest of the network, and so forth). Thus, research focusing on overcoming potential attacks to distributed ledgers is required. In this article, we focus on attacks that damage underlying networks of distributed ledgers. Underlying networks offer useful communication primitives such as an atomic broadcast, however, such attacks may degrade the property of the primitives and make distributed ledgers relying on the primitives no longer work. Hence we should design algorithms to make the distributed ledgers still work even when some attacks degrade the primitives. As the first study for such situations, we consider a problem to implement distributed ledgers tolerating the degradation of an underlying atomic broadcast service that distributed ledgers are relying on. We consider the case where the uniform agreement property of the atomic broadcast is degraded, and propose new algorithms that could ensure to reach eventual consistency despite degraded atomic broadcast