A distributed computing system can operate in the face of malicious failures on the part of some of its constituent devices, and provide a minimum of message delays between receiving a client request and providing a response, when each device within the system verifies the sender of any message it receives, and the propriety of the message. The sender can be verified through message authentication schemes or digital signature schemes. The propriety of a message can be verified by receiving a sufficiently large number of equivalent, properly authenticated messages. If the number of malicious devices is represented by the variable “M”, a sufficient number of equivalent, properly authenticated messages to verify that the message is true can be any number of messages greater than M. Furthermore, to verify that a leader device is not maliciously submitting different proposals to different devices using the same proposal number, a quorum of devices can be required to select a proposal, where a quorum is a sufficiently large number of devices such that any other quorum has, as a majority of its devices, non-malicious devices from the first quorum. Therefore, the distributed computing system can operate properly with M number of malicious failures and F number of total failures, and with a minimum of message delays, if the number of constituent devices in the distributed computing system is greater than 3F+2M. Additionally, if the distributed computing system can revert to a more traditional algorithm if too many devices fail or become malicious, it can use a message-delay-reducing algorithm while having as few as 2Q+F+2M+1 constituent devices, where Q is the number of devices that can fail and still allow the system to use a message-delay-reducing algorithm.