Optimal agreement protocol in malicious faulty processors andfaulty links

Traditionally, the problems of Byzantine agreement, consensus, and interactive consistency are studied in a fully connected network with processors in malicious failure only. Such problems are reexamined with the assumption of malicious faults on both processors and links. The proposed protocols use the minimum number of message exchanges and can tolerate the maximum number of allowable faulty components to make each fault-free processor reach a common agreement for the cases of processor failure, link failure, or processor and link failure