Leakage Thresholds and Security Trade-offs in Finite Blocklength Wiretap Channels

Abstract

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.