Secure Computation of Linear Functions Over Linear Discrete Multiple-Access Wiretap Channels

In this paper, a joint source-channel coding approach is taken to the problem of securely computing a function of distributed sources over a multiple-access wiretap channel that is linear with respect to a finite field. It is shown that if the joint source distribution fulfills certain conditions and the function to be computed matches the linear structure of the channel, secrecy comes for free in the sense that the fundamental limit (i.e., the secrecy computation-capacity) is achieved without the need for stochastic encoding. Furthermore, the legitimate receiver does not need any advantage over the eavesdropper, which is in stark contrast to standard physical-layer security results.