Crime and Punishment in Distributed Byzantine Decision Tasks

A decision task is a distributed input-output problem in which each process starts with its input value and eventually produces its output value. Examples of such decision tasks are broad and range from consensus to reliable broadcast to lattice agreement. A distributed protocol solves a decision task if it enables processes to produce admissible output values despite arbitrary (Byzantine) failures. Unfortunately, it has been known for decades that many decision tasks cannot be solved if the system is overly corrupted, i.e., safety of distributed protocols solving such tasks can be violated in unlucky scenarios.By contrast, only recently did the community discover that some of these distributed protocols can be made accountable by ensuring that correct processes irrevocably detect some faulty processes responsible for any safety violation. This realization is particularly surprising (and positive) given that accountability is a powerful tool to mitigate safety violations in distributed protocols. Indeed, exposing crimes and introducing punishments naturally incentivize exemplarity.In this paper, we propose a generic transformation, called τscr, of any non-synchronous distributed protocol solving a decision task into its accountable version. Our τscr transformation is built upon the well-studied simulation of crash failures on top of Byzantine failures and increases the communication complexity by a quadratic multiplicative factor in the worst case.