A network is disclosed that includes a message originator computer and a message recipient computer, for secure electronic mail delivery. In accordance with the invention, the network includes a message delivery server that can distinguish between real and phantom messages. In operation, the message originator computer waits a random time and then transmits a first encrypted phantom message to the message delivery server. This message is to spoof an eavesdropper into believing that there is a steady stream of messages being sent from the originator computer. However, the message delivery server recognizes the message as a phantom message and discards it. When the message originator computer receives a user request to transmit a real message to the recipient computer, it waits a random time and then encrypts and transmits the real message to the message delivery server. The message delivery server recognizes the message as a real message and forwards the real message to the recipient computer. Meanwhile, the message originator computer can continue transmitting encrypted phantom messages to the message delivery server. In this manner, an eavesdropper will be tricked into believing that there is a steady stream of messages being sent from the originator computer.