Successive Refinement of Shannon Cipher System Under Maximal Leakage

We study the successive refinement problem of Shannon cipher system under maximal leakage for a discrete memoryless source with arbitrary bounded distortion measures. Specifically, we generalize the threat model described by Issa, Wagner and Kamath (T-IT, 2020) to the successive refinement setting and derive the optimal asymptotic normalized maximal leakage region under a joint excess-distortion probability constraint. In the achievability part, we propose a type-based coding scheme and derive the asymptotic achievable normalized maximal leakage region. In the converse part, by analyzing the guessing scheme of the eavesdropper, we manage to show the above normalized maximal leakage region is optimal. Our results reveal the fundamental tradeoff between reliability and secrecy. Furthermore, for a successively refinable source-distortion measure triplet, we find that our coding scheme satisfies the successive refinability under the maximal leakage metric.