This paper presents a formal model for asynchronous distributed systems with servers that may exhibit Byzantine faults or crash and subsequently recover. The model is computational and based on techniques from modern cryptography, which allows for reasoning about cryptographic protocols in a meaningful way. One of the most important problems in faulttolerant distributed computing, reliable broadcast, is then investigated in this hybrid model. A definition of reliable broadcast is presented and an implementation is given based on the protocol of Bracha.