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We determine the exact sum secure degrees of freedom (d.o.f.) of the K-userGaussian 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-userinterference channel with confidential messages and one external eavesdropper(IC-CM-EE). We show that for all of these three cases, the exact sum secured.o.f. is K(K-1)/(2K-1). We show converses for IC-EE and IC-CM, which imply aconverse for IC-CM-EE. We show achievability for IC-CM-EE, which impliesachievability for IC-EE and IC-CM. We develop the converses by relating thechannel inputs of interfering users to the reliable rates of the interferedusers, and by quantifying the secrecy penalty in terms of the eavesdroppers'observations. Our achievability uses structured signaling, structuredcooperative jamming, channel prefixing, and asymptotic real interferencealignment. While the traditional interference alignment provides some amount ofsecrecy by mixing unintended signals in a smaller sub-space at every receiver,in order to attain the optimum sum secure d.o.f., we incorporate structuredcooperative jamming into the achievable scheme, and intricately design thestructure of all of the transmitted signals jointly.

Secure Degrees of Freedom of K-User Gaussian Interference Channels: A Unified View