Strong Secrecy for Wireless Channels (Invited Talk)

Abstract

It is widely accepted by the information security community that a secrecy criterion based solely on minimizing the rate at which an eavesdropper extracts bits from a block of noisy channel outputs is too weak a concept to guarantee the confidentiality of the protected data. Even if this rate goes to zero asymptotically (i.e. for sufficiently large codeword length), vital information bits can easily be leaked to an illegitimate receiver. In contrast, many of the recent results in information-theoretic security for wireless channel models with continuous random variables rely on this weak notion of secrecy, even though previous work has shown that it is possible to determine the ultimate secrecy rates for discrete memoryless broadcast channels under a stronger secrecy criterion -- namely one which bounds not the rate but the total number of bits obtained by the eavesdropper. Seeking to bridge the existing gap between fundamental cryptographic requirements and ongoing research in wireless security, we present a proof for the secrecy capacity of Gaussian broadcast channels under the strong secrecy criterion. As in the discrete memoryless case, the secrecy capacity is found to be the same as in the weaker formulation. The extension to fading channels is shown to be straightforward.