An information theoretic approach to provably secure communications

Jin Hong Xu

Published Jan 1, 2010• 1 citation

Abstract

With the rapid deployment of new wireless devices and pervasive use of wireless data and voice services, the demand for reliable and secure communications is becoming more and more urgent. The focus of this thesis is on the fundamental trade-off among throughput, reliability, and security of various wireless networks. Our study adopts the notion of provable security from an information theoretic perspective. Using equivocation to measure the confidentiality of messages, we establish, for various communication models, the fundamental rate-equivocation trade-off. We first study capacity bounds for discrete memoryless broadcast channels with two confidential messages, which is a generalization of Csiszár and Körner's classical model. The outer bounds are proposed for the rate equivocation region of this channel model, which, together with a previously proposed inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memoryless broadcast channel. Next, we consider another variation of Csiszár and Körner's model. The transmitter sends both a confidential message and a non-confidential message (public message) to the intended receiver. While the unintended receiver should be kept ignorant from the confidential message, we do not impose the requirement that the public message needs to be perfectly recovered by the unintended receiver. This more liberal treatment of the non-confidential message is perhaps a more reasonable model than Csiszár and Körner's model where the non-confidential message (common message) is required to be decoded by both receivers. A single-letter characterization of the achievable rate equivocation region of this model is given and the result is then extended to the case when an extra secret key is available to the transmitter and the intended receiver. Utilizing the developed framework of broadcast channels with confidential and public messages, we further study the problem of secure communication over a network in which each link may be noisy or noiseless. A single-source single-sink acyclic planar network is assumed, and the communication between the source and the sink is subject to non-cooperating eavesdropping on each link. Sufficient conditions, in terms of communication rates and network parameters, are found for provably secure communication. A constructive proof, which combines Shannon's key encryption, Wyner's random coding, and the Ford-Fulkerson algorithm, is provided which constitutes a readily implementable secure coding scheme for provably secure communications. The derived achievable rate equivocation region is tight when specializing to several special cases. In particular, when the communication network decouples into non-overlapping parallel paths, the proposed encoding scheme is optimal, i.e., it achieves the secure communication capacity for such networks.

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