Unified secure DoF analysis of K-user Gaussian interference channels

We determine the exact sum secure degrees of freedom (d.o.f.) of the K-user Gaussian interference channel. We consider three different secrecy constraints: 1) K-user interference channel with one external eavesdropper (IC-EE), 2) K-user interference channel with confidential messages (IC-CM), and 3) K-user interference channel with confidential messages and one external eavesdropper (IC-CM-EE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K-1)/2K-1. We show converses for IC-EE and IC-CM, which imply a converse for IC-CM-EE. We show achievability for IC-CM-EE, which implies achievability for IC-EE and IC-CM. We develop the converses by relating the channel inputs of interfering users to the reliable rates, and by quantifying the secrecy penalty in terms of the eavesdroppers´ observations. Our achievability uses structured signalling, channel prefixing via structured cooperative jamming, and asymptotic real interference alignment.