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Large scale cryptocurrencies require the participation of millions ofparticipants and support economic activity of billions of dollars, which hasled to new lines of work in binary Byzantine Agreement (BBA) and consensus. Thenew work aims to achieve communication-efficiency---given such a large $n$, noteveryone can speak during the protocol. Several protocols have achievedconsensus with communication-efficiency, even under an adaptive adversary, butthey require additional strong assumptions---proof-of-work, memory-erasure,etc. All of these protocols use multicast: every honest replica multicastsmessages to all other replicas. Under this model, we provide a newcommunication-efficient consensus protocol using Verifiable Delay Functions(VDFs) that is secure against adaptive adversaries and does not require thesame strong assumptions present in other protocols.  A natural question is whether we can extend the synchronous protocols to thepartially synchronous setting---in this work, we show that using multicast, wecannot. Furthermore, we cannot achieve always safe communication-efficientprotocols (that maintain safety with probability 1) even in the synchronoussetting against a static adversary when honest replicas only choose tomulticast its messages. Considering these impossibility results, we describe anew communication-efficient BBA protocol in a modified partially synchronousnetwork model which is secure against adaptive adversaries with highprobability.

A Lower Bound for Byzantine Agreement and Consensus for Adaptive Adversaries using VDFs