Symposium on Information Theoretic Approaches to Security and Privacy

Information Theoretic Security (ITS) was introduced by Claude Shannon in 1948. In Shannon's setting the legitimate parties share a common secret key but communicate over a public noiseless channel, which can be wiretapped by an eavesdropper. Shannon's main result was to establish the minimum key-rate necessary to guarantee ITS against the eavesdropper. Wyner introduced the wiretap channel in 1975, where the legitimate parties communicate over a (possibly) noisy channel, which could be wiretapped by an eavesdropper over another noisy channel. Wyner established the maximum communication rate in this setting, while guaranteeing ITS (in an asymptotic sense) against the eavesdropper.

In this talk we will review the above results and then introduce a new setting where a single (common) message must be transmitted to two receivers over a wiretap channel. In addition we assume that the transmitter shares an independent secret key with each of the two receivers not known to the eavesdropper. We will explain how the coding techniques developed by Shannon and Wyner can be unified in this setting. By focusing on the "degraded" channel model, we will discuss conditions under which the following approaches are optimal (i) using secret-keys as one-time pads and ignoring the contribution of the noisy channel (ii) ignoring the secret-keys and only relying on the noisy channel (iii) hybrid schemes that combine both approaches.