Optimal Normalized Maximal Leakage Region for Successive Refinement of Shannon Cipher System under Joint Excess-Distortion Probability and Expected Distortion Constraints

Core Concepts

The fundamental trade-off between reliability and secrecy in the successive refinement setting of the Shannon cipher system is characterized by deriving the asymptotically optimal normalized maximal leakage region under both joint excess-distortion probability and expected distortion constraints.

Abstract

The paper studies the successive refinement setting of the Shannon cipher system (SCS) under the maximal leakage secrecy metric for discrete memoryless sources (DMS) under bounded distortion measures. Under the joint excess-distortion probability (JEP) constraint: The authors propose a type-based coding scheme and characterize the asymptotically achievable normalized maximal leakage region. By analyzing a guessing scheme of the eavesdropper, they prove the optimality of the achievable results under mild conditions. The results reveal the fundamental trade-off between reliability and secrecy, and show that successive refinability under maximal leakage can be achieved if the source-distortion pair is successively refinable. Under the expected distortion constraint: The authors establish the achievable asymptotic normalized maximal leakage region by proposing a rate-distortion code. Using the relationship between maximal leakage and Sibson mutual information, they show that the above bound is tight under mild conditions. They further show that for DMS satisfying certain conditions, the normalized maximal leakage regions under both expected distortion and JEP are identical, although the expected distortion constraint appears to be a looser criterion.

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Successive Refinement of Shannon Cipher System Under Maximal Leakage

by Zhuangfei Wu... at arxiv.org 04-19-2024

https://arxiv.org/pdf/2308.07203.pdf

Deeper Inquiries

How can the proposed results be extended to more general multi-terminal source coding problems beyond the successive refinement setting

The proposed results can be extended to more general multi-terminal source coding problems by considering different types of constraints and metrics. For example, the techniques developed for achieving reliability and secrecy in the successive refinement setting can be adapted to scenarios with multiple encoders and decoders communicating over different channels. By modifying the coding schemes and analyzing the trade-offs between reliability and secrecy under various constraints, such as different distortion measures or communication scenarios, the results can be generalized to a broader class of multi-terminal source coding problems. Additionally, the concept of maximal leakage can be applied to other multi-terminal communication models to quantify the information leakage and establish optimal secrecy regions.

What are the implications of the floor effect observed in the numerical example, where the secrecy guarantee remains unchanged if the reliability constraint is above a certain threshold

The floor effect observed in the numerical example, where the secrecy guarantee remains unchanged if the reliability constraint is above a certain threshold, has significant implications for practical applications. This phenomenon indicates that there is a critical point beyond which increasing the reliability constraint does not provide additional secrecy benefits. Understanding this threshold can help in designing communication systems where the trade-off between reliability and secrecy needs to be carefully balanced. By identifying the point at which the secrecy guarantee saturates, system designers can optimize the performance of secure communication systems without unnecessarily increasing the reliability constraints.

Can the techniques developed in this work be applied to analyze the information leakage in other secure communication systems beyond the Shannon cipher system

The techniques developed in this work for analyzing information leakage in the Shannon cipher system can be applied to other secure communication systems beyond SCS. The concept of maximal leakage as a secrecy metric can be utilized in various scenarios where information security is crucial, such as cryptographic protocols, secure data transmission, and privacy-preserving communication schemes. By adapting the coding schemes and analysis methods to different communication models and security requirements, the results obtained in this study can be extended to evaluate and enhance the security of a wide range of secure communication systems. The insights gained from studying the trade-offs between reliability and secrecy in the context of SCS can be valuable in designing and optimizing secure communication protocols in diverse applications.