Beyond One-Third Faulty Replicas in Byzantine Fault Tolerant Systems

Byzantine fault tolerant systems behave correctly when no more than f out of 3f + 1 replicas fail. When there are more than f failures, traditional BFT protocols make no guarantees whatsoever. Malicious replicas can make clients accept arbitrary results, and the system behavior is totally unspecified. However, there is a large spectrum between complete correctness and arbitrary failure that traditional BFT systems ignore. This paper argues that we can and should bound the system behavior beyond f failures.

We present BFT2F, an extension to the well-known Castro-Liskov PBFT algorithm [6], to explore the design space beyond f failures. Specifically, BFT2F has the same liveness and consistency guarantees as PBFT when no more than f replicas fail; with more than f but no more than 2f failures, BFT2F prohibits malicious servers from making up operations that clients have never issued and restricts malicious servers to only certain kinds of consistency violations. Evaluations of a prototype implementation show that the additional guarantees of BFT2F come at the cost of only a slight performance degradation compared to PBFT.