On the sum secure degrees of freedom of two-unicast layered wireless networks

In this paper, we study the sum secure degrees of freedom (d.o.f.) of two-unicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where the message of each source-destination pair must be kept information-theoretically secure from the unintended receiver. We show that the sum secure d.o.f. can take 0, 1, 3/2, 2 and at most countably many other positive values, which we enumerate.