We study the successive refinement setting of Shannon cipher system (SCS) under the maximal leakage secrecy metric for discrete memoryless sources under bounded distortion measures. Specifically, we generalize the threat model for the point-to-point rate-distortion setting of Issa, Wagner and Kamath (T-IT 2020) to the multiterminal successive refinement setting. Under mild conditions that correspond to partial secrecy, we characterize the asymptotically optimal normalized maximal leakage region for both the joint excess-distortion probability (JEP) and the expected distortion reliability constraints. Under JEP, in the achievability part, we propose a type-based coding scheme, analyze the reliability guarantee for JEP and bound the leakage of the information source through compressed messages. In the converse part, by analyzing a guessing scheme of the eavesdropper, we prove the optimality of our achievability result. Under expected distortion, the achievability part is established similarly to the JEP counterpart. The converse proof proceeds by generalizing the corresponding results for the rate-distortion setting of SCS by Schieler and Cuff (T-IT 2014) to the successive refinement setting. Somewhat surprisingly, the normalized maximal leakage regions under both JEP and expected distortion constraints are identical under certain conditions, although JEP appears to be a stronger reliability constraint.

翻译：我们研究在最大泄露保密度量下，针对有界失真测度中的离散无记忆信源，Shannon密码系统（SCS）在逐次细化场景中的性能。具体而言，我们将点对点率失真设定下Issa、Wagner和Kamath（T-IT 2020）的威胁模型推广至多终端逐次细化设定。在对应于部分保密性的温和条件下，我们刻画了联合超额失真概率（JEP）与期望失真可靠性约束下的渐近最优归一化最大泄露区域。对于JEP，在可达性部分，我们提出一种基于类型的编码方案，分析JEP的可靠性保证，并通过压缩消息限定信息源的泄露。在逆部分，通过分析窃听者的猜测方案，我们证明了可达性结果的最优性。对于期望失真，可达性部分与JEP对应部分类似地建立。逆证过程通过将Schieler和Cuff（T-IT 2014）中SCS率失真设定的相应结果推广至逐次细化设定来完成。有些令人惊讶的是，尽管JEP看似更强的可靠性约束，但在特定条件下，JEP与期望失真约束下的归一化最大泄露区域完全相同。