Asynchronous Byzantine consensus with 2f+1 processes

Byzantine consensus in asynchronous message-passing systems has been shown to require at least 3f + 1 processes to be solvable in several system models (e.g., with failure detectors, partial synchrony or randomization). Recently a couple of solutions to implement Byzantine fault-tolerant state-machine replication using only 2f + 1 replicas have appeared. This reduction from 3f + 1 to 2f + 1 is possible with a hybrid system model, i.e., by extending the system model with trusted/trustworthy components that constrain the power of faulty processes to have certain behaviors. Despite these important results, the problem of solving Byzantine consensus with only 2f + 1 processes is still far from being well understood. In this paper we present a methodology to transform crash consensus algorithms into Byzantine consensus algorithms with different characteristics, with the assistance of a reliable broadcast primitive that requires trusted/trustworthy components to be implemented. We exemplify the methodology with two algorithms, one that uses failure detectors and one that is randomized. We also define a new flavor of consensus and use it to solve atomic broadcast, showing the practical interest of the transformations.