Abstract The hypercube multiprocessor is a popular architecture in parallel computing environments. Recently, computer security and privacy issues have gained significance. This paper considers the security issues of a network of processors connected over a hypercube topology. We demonstrate that a covert channel can be established by exploiting the underlying message communication mechanism of the hypercube, even when the access-control denies such communication. This can occur because node-to-node communication in a hypercube may require multiple hops and two or more disjoint message communications may actually be transmitted along common links. Congestion (and the resulting delay) in such shared links can provide the basis for a covert channel. We introduce security considerations for a multiprocessor by focussing on the covert channel issue in hypercube message communication. A security model for the hypercube routing function is presented. Based on noninterference, we develop sufficient conditions for the routing mechanism to be free of covert channels. Two secure hypercube message routing approaches are proposed for store-and-forward communication strategy. The first approach (Virtual Channel) achieves security by fixed bandwidth partitioning of links, for which the price is paid in delay performance. The second approach (Bypass) prioritizes lower security class messages, for which delay of higher class messages is sacrificed. Performance (i.e., cost of security) of these two approaches are shown using simulation. Finally, a time-out feature is introduced to the Bypass approach, which disallows potential starvation of higher class messages at the expense of limited bandwidth covert channel. Maximum covert channel bandwidth (in terms of the time-out parameter) is analyzed.