We introduce a secure communication setup of an interference channel whose transmitted signals are fed into interleavers. The interleavers apply random permutations to the signals, and the realizations of the permutations are made known to the receivers but not the transmitters. This communication setup can also model a situation in which the encoders are ignorant of the codebooks of one another, while the decoders are cognizant of the codebooks. We study the capacity region of a two-user secure Z-interference channel, and prove that an asymptotically optimal strategy of the interfered user is to use a constant composition random code. Consequently we establish the result that the capacity region of this channel, in the weak interference regime, is obtained by the Han-Kobayashi coding scheme. Further, we present an outer bound for the secure additive doubly weak interference channel, and an outer bound on the capacity region of the secure additive interference channel with mixed interference.