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We revisit the recent secure degrees of freedom (s.d.o.f.) results forone-hop multi-user wireless networks by considering three fundamental wirelessnetwork structures: Gaussian wiretap channel with helpers, Gaussian multipleaccess wiretap channel, and Gaussian interference channel with secrecyconstraints. We present main enabling tools and resulting communication schemesin an expository manner, along with key insights and design principles emergingfrom them. The main achievable schemes are based on real interferencealignment, channel prefixing via cooperative jamming, and structuredsignalling. Real interference alignment enables aligning the cooperativejamming signals together with the message carrying signals at the eavesdroppersto protect them akin to one-time-pad protecting messages in wired systems. Realinterference alignment also enables decodability at the legitimate receivers byrendering message carrying and cooperative jamming signals separable, andsimultaneously aligning the cooperative jamming signals in the smallestpossible sub-space. The main converse techniques are based on two key lemmaswhich quantify the secrecy penalty by showing that the net effect of aneavesdropper on the system is that it eliminates one of the independent channelinputs; and the role of a helper by developing a direct relationship betweenthe cooperative jamming signal of a helper and the message rate. These twolemmas when applied according to the unique structure of individual networksprovide tight converses. Finally, we present a blind cooperative jamming schemefor the helper network with no eavesdropper channel state information at thetransmitters that achieves the same optimal s.d.o.f. as in the case of fulleavesdropper channel state information.

Secure Degrees of Freedom of Multi-user Networks: One-Time-Pads in the Air via Alignment