  In this paper, the problem of securely computing a function over the binary
modulo-2 adder multiple-access wiretap channel is considered. The problem
involves a legitimate receiver that wishes to reliably and efficiently compute
a function of distributed binary sources while an eavesdropper has to be kept
ignorant of them. In order to characterize the corresponding fundamental limit,
the notion of secrecy computation-capacity is introduced. Although determining
the secrecy computation-capacity is challenging for arbitrary functions, it
surprisingly turns out that if the function perfectly matches the algebraic
structure of the channel and the joint source distribution fulfills certain
conditions, the secrecy computation-capacity equals the computation capacity,
which is the supremum of all achievable computation rates without secrecy
constraints. Unlike the case of securely transmitting messages, no additional
randomness is needed at the encoders nor does the legitimate receiver need any
advantage over the eavesdropper. The results therefore show that the problem of
securely computing a function over a multiple-access wiretap channel may
significantly differ from the one of securely communicating messages.
