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Lecture notes in computer science

Simultaneous Secrecy and Reliability Amplification for a General Channel Model

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets, Bruce M. Kapron, Valerie King, Stefano Tessaro

Published Jan 1, 2016• 0 citations
Publisher
DOI
10.1007/978-3-662-53641-4_10

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JUCS - Journal of Universal Computer Science•Nov 28, 2021•1 citation
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.
In this paper, we consider the problem of polar coding for secure communications over the two-way wiretap channel, where two legitimate users communicate with each other simultaneously, while a passive eavesdropper overhears a combination of their exchanged signals. We design a low complexity polar coded cooperative jamming scheme that achieves the whole secrecy rate region of the general two-way wiretap channel under the strong secrecy criterion. The chaining method is used to make proper alignment of polar indices. The randomness required to be shared between two legitimate users is treated as a limited resource and we show that its rate can be made negligible by increasing the blocklength and the number of chained blocks. For the special case when the eavesdropper channel is degraded with respect to the legitimate ones, a simplified scheme is proposed which can simultaneously ensure reliability and weak secrecy within a single transmission block.
One of the problems of information - theoretic security concerns secure communication over a wiretap channel. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). We introduce and investigate the E - capacity - equivocation region and the E - secrecy capacity function for the wiretap channel, which are, correspondingly, the generalizations of the capacity - equivocation region and secrecy - capacity studied by Csiszár and Körner (1978). The E - capacity equivocation region is the closure of the set of all achievable rate - reliability and equivocation pairs, where the rate - reliability function represents the optimal dependence of rate on the error probability exponent (reliability). By analogy with the notion of E - capacity, we consider the E - secrecy capacity function that for the given E is the maximum rate at which the message can be transmitted being kept perfectly secret from the wiretapper.