In recent years, there have been a few proposals to add a small amount of trusted hardware at each replica in a Byzantine fault tolerant system to cut back replication factors. These trusted components eliminate the ability for a Byzantine node to perform equivocation, which intuitively means making conflicting statements to different processes. In this paper, we define non-equivocation and study its power in the context of distributed protocols that assume a Byzantine fault model. We show that non-equivocation alone does not allow for reducing the number of processes required to reach agreement in the presence of Byzantine faults in the asynchronous communication model, by proving a lower bound of n > 3f processes for agreement with nonequivocation. However, when we add the ability to guarantee the transferable authentication of network messages (e.g., using digital signatures), we show that it is possible to use non-equivocation to transform any protocol that works under the c...