The BG-simulation is a powerful reduction algorithm designed for asynchronous read/write crash-prone systems. It allows a set of $(t+1)$ asynchronous sequential processes to wait-free simulate (i.e., despite the crash of up to $t$ of them) an arbitrary number $n$ of processes under the assumption that at most $t$ of them may crash. The BG simulation shows that, in read/write systems, the crucial parameter is not the number $n$ of processes, but the upper bound $t$ on the number of process crashes. The paper extends the concept of BG simulation to asynchronous message-passing systems prone to Byzantine failures. Byzantine failures are the most general type of failure: a faulty process can exhibit any arbitrary behavior. Because of this, they are also the most difficult to analyze and to handle algorithmically. The main contribution of the paper is a signature-free reduction of Byzantine failures to crash failures. Assuming $t<\min(n',n/3)$, the paper presents an algorithm that simulates a system of $n'$ processes where up to $t$ may crash, on top of a basic system of $n$ processes where up to $t$ may be Byzantine. While topological techniques have been used to relate the computability of Byzantine failure-prone systems to that of crash failure-prone ones, this simulation is the first, to our knowledge, that establishes this relation directly, in an algorithmic way. In addition to extending the basic BG simulation to message-passing systems and failures more severe than process crashes, being modular and direct, this simulation provides us with a deeper insight in the nature and understanding of crash and Byzantine failures in the context of asynchronous message-passing systems. Moreover, it also allows crash-tolerant algorithms, designed for asynchronous read/write systems, to be executed on top of asynchronous message-passing systems prone to Byzantine failures.