The problem of performing a multiparty computation when more than half of the processors are cooperating Byzantine faults is addressed. It is shown how to compute any Boolean function of n inputs distributively, preserving the privacy of inputs held by nonfaulty processors and ensuring that faulty processors obtain the function value if and only if the nonfaulty processors do. If the nonfaulty processors do not obtain the correct function value, they detect cheating with high probability. The solution is based on a new type of verifiable secret sharing in which the secret is revealed not all at once but in small increments. This process ensures that all processors discover the secret at roughly the same time. The solution assumes the existence of an oblivious transfer protocol and uses broadcast channels. The processors are not required to have equal computing power.