Optimal Resilience Sample Clauses

Optimal Resilience. The famous results by Xxxxx et al. [8] showed the impossibility of a permissioned consensus protocol even with public key infrastructure cannot tolerate 1/3 or more Byzantine corruptions in an asynchronous network. Conceptually, suppose n nodes are divided into three distinct sets: S1, S2 and SB, where the nodes in S1 and S2 are honest and the ndoes in SB are malicious. Due to the asynchronous network, the messages between S1 and S2 are delayed arbi- trarily long. Without loss of generality, we assume n = 3t + 1 and S1 = S2 = t, SB = t + 1. If the protocol only needs 2t nodes to proceed, the nodes in SB can send inconsistent messages to S1 and S2. Then, the nodes in S1 and S2 may agree on the different values, respectively, so the agreement breaks. If the protocol needs more than 2t nodes to proceeds, the nodes in SB just crash. Then, the protocol will halt forever and the termination breaks. | ∫ | | | | | | Thus, once the malicious users are more than n−1 , either the agreement or the termination breaks. To achieve partition- resilience, both RBA and HBA tolerates 1/3 corruptions, which is the optimal according to the argument above.
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