We consider the problem of disseminating an update known to a set of servers to other servers in the system via a gossip protocol. Some of the servers can exhibit malicious behavior. We require that only the updates introduced by authorized clients are accepted by non-malicious servers. Spurious updates, in particular those generated by compromised nodes, are not accepted by non-malicious servers. We take the approach of collective endorsement where each server endorses an accepted update by computing a list of message authentication codes with symmetric keys allocated to it. We use a novel key allocation scheme that allocates a set of symmetric keys to each participating server to minimize the total number of keys. Our protocol is designed to minimize update diffusion time. In the absence of faulty nodes, its diffusion time is O(log n), which is the best possible time achieved when nodes only suffer from benign faults. If the actual number of Byzantine faults experienced during an update's dissemination is f, diffusion time increases to O(log n) + f. This is better than the latency of previously known protocols that take O(log n) + b time, where b is the assumed threshold that defines the maximum number of malicious servers that can be tolerated rather than f, the actual number of failures. The buffer requirements and message sizes are higher in our protocol than other known protocols, thus it trades off memory and bandwidth resources to improve latency.