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IEEE International Symposium on Information Theory (ISIT)

Secrecy-reliability tradeoff for semi-deterministic wiretap channels at finite Blocklength

Wei Qing Yang, Rafael F. Schaefer, H. Vincent Poor

Published Jun 1, 2017• 19 citations
Publisher

Abstract

This paper studies the maximum secrecy rate for a semi-deterministic wiretap channel, in which the channel between the transmitter and the legitimate receiver is deterministic, while that between the transmitter and the eavesdropper is a discrete memoryless channel. For a given decoding error probability and information leakage (measured by the total variation distance), the optimal second-order secrecy rate is derived. Unlike the secrecy capacity, the second-order secrecy rate characterizes the optimal tradeoff between secrecy and reliability at finite blocklength.

DOI
10.1109/isit.2017.8006906

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This paper studies the maximum secrecy rate for a semi-deterministic wiretap channel, in which the channel between the transmitter and the legitimate receiver is deterministic, while that between the transmitter and the eavesdropper is a discrete memoryless channel. For a given decoding error probability and information leakage (measured by the total variation distance), the optimal second-order secrecy rate is derived. Unlike the secrecy capacity, the second-order secrecy rate characterizes the optimal tradeoff between secrecy and reliability at finite blocklength.
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.
This work discusses the bounds for the wiretap channel (WTC) in the finite blocklength regime, characterizing the behavior of the performance trade-off between information delivery to the legitimate receiver and information leakage to the eavesdropper as a function of blocklength. Since the error probability at the legitimate receiver is the same as that of a conventional point-to-point channel, the characterization of the former builds on the finite blocklength analysis for that case. The information leakage bound relies on the analysis of the corresponding leakage density. This paper extends these concepts by incorporating the use of the Berry-Esseen theorem in assessing the convergence rates of leakage and secrecy metrics to their asymptotic values, which provides a refined analytical tool to evaluate the performance of secrecy systems under finite blocklength constraints. Furthermore, this approach facilitates a quantification of the trade-offs involved, integrating concepts such as the aggregate leakage rate and empirical average leakage, thus enabling a more comprehensive understanding of how system parameters affect the overall secrecy performance. This allows for a more detailed exploration of the dependencies between blocklength, secrecy, and reliability trade-offs required to balance effective communication against security imperatives. These analyses also highlight the critical balance necessary between ensuring low probability of error for the legitimate receiver while maintaining stringent secrecy requirements against an eavesdropper. Furthermore, the study introduces metrics such as aggregate leakage rate and empirical average leakage, providing new insights into how these factors interplay to influence the overall performance of secure communication systems.
We derive lower bounds to the second-order coding rates for the wiretap channel. The decoding error probability and the information leakage measured in terms of the variational distance secrecy metric are fixed at some constants εrand εsrespectively. We leverage on the connection between wiretap channel coding and channel resolvability to derive tighter secrecy bounds than those available in the literature. We then use central limit theorem-style analysis to evaluate these bounds for the discrete memoryless wiretap channel with cost constraints and the Gaussian wiretap channel.
The coding problem over wiretap channels is to realize an encoder and a decoder such that the legitimate receiver can correctly decode transmitted secret messages while the eavesdropper knows little about the secret messages. Traditionally, the secrecy of messages to the eavesdropper has been measured in terms of mutual information. Recently, several researches on the wiretap channels employ the bit error rate after decoding by the eavesdropper as a secrecy measure. In this note, we show that the secrecy capacity with respect to the bit error rate criterion is different from that with the traditional mutual information criterion. In addition to that, the encoder can be deterministic for the bit error rate criterion, while it must be stochastic for the mutual information criterion.
The secrecy capacity of an extended communication model of wiretap channelII is determined. In this channel model, the source message is encoded into a digital sequence of length N and transmitted to the legitimate receiver through a discrete memoryless channel (DMC). There exists an eavesdropper who is able to observe arbitrary μ = N α digital symbols from the transmitter through a second DMC, where 0 ≤ α ≤ 1 is a constant real number. A pair of an encoder and a decoder is designed to let the receiver be able to recover the source message with a vanishing decoding error probability and keep the eavesdropper ignorant of the message. This communication model includes a variety of wiretap channels as special cases. The coding scheme is based on that designed by Ozarow and Wyner for the classic wiretap channel II.