Degradable agreement in the presence of Byzantine faults

The authors consider a system consisting of a sender that wants to send a value to certain receivers. Byzantine agreement protocols have previously been proposed to achieve this in the presence of arbitrary failures. The imposed requirement typically is that the fault-free receivers must all agree on the same value. An agreement protocol is proposed that achieves Lamport´s Byzantine agreement (L. Lamport et al., 1982) up to a certain number of faults and a degraded form of agreement with a higher number of faults. The degraded form of agreement allows the fault-free receivers to agree on at most two different values, one of which is necessarily the default value. The proposed approach is named degradable agreement. An algorithm for degradable agreement is presented along with bounds on the number of nodes and network connectivity necessary to achieve degradable agreement