| Summary: | In this paper, the <i>K</i>-user interference channel with secrecy constraints is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure retrospective interference alignment scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving positive secure degrees of freedom (SDoF) is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: Phase one, in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses the delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the secrecy constraints. We present our achievable scheme for three models, namely: (1) <i>K</i>-user interference channel with confidential messages (IC-CM), and we show that <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msqrt> <mi>K</mi> </msqrt> <mo>-</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> SDoF is achievable; (2) <i>K</i>-user interference channel with an external eavesdropper (IC-EE); and 3) <i>K</i>-user IC with confidential messages and an external eavesdropper (IC-CM-EE). We show that for the <i>K</i>-user IC-EE, <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msqrt> <mi>K</mi> </msqrt> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> SDoF is achievable, and for the <i>K</i>-user IC-CM-EE, <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msqrt> <mi>K</mi> </msqrt> <mo>-</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> is achievable. To the best of our knowledge, this is the first result on the <i>K</i>-user interference channel with secrecy constrained models and delayed CSIT that achieves an SDoF which scales with <inline-formula> <math display="inline"> <semantics> <msqrt> <mi>K</mi> </msqrt> </semantics> </math> </inline-formula>, square-root of number of users.
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