This paper studies the tradeoff in privacy and utility in a single-trial multi-terminal guessing (estimation) framework using a system model that is inspired by index coding. There are $n$ independent discrete sources at a data curator. There are $m$ legitimate users and one adversary, each with some side information about the sources. The data curator broadcasts a distorted function of sources to legitimate users, which is also overheard by the adversary. In terms of utility, each legitimate user wishes to perfectly reconstruct some of the unknown sources and attain a certain gain in the estimation correctness for the remaining unknown sources. In terms of privacy, the data curator wishes to minimize the maximal leakage: the worst-case guessing gain of the adversary in estimating any target function of its unknown sources after receiving the broadcast data. Given the system settings, we derive fundamental performance lower bounds on the maximal leakage to the adversary, which are inspired by the notion of confusion graph and performance bounds for the index coding problem. We also detail a greedy privacy enhancing mechanism, which is inspired by the agglomerative clustering algorithms in the information bottleneck and privacy funnel problems.

中文翻译：

---

受索引编码启发的猜测框架中的隐私-效用权衡

本文使用受索引编码启发的系统模型研究了单次试验多终端猜测（估计）框架中隐私和效用的权衡。数据策展人有 $n$ 个独立的离散来源。有 $m$ 合法用户和一个对手，每个人都有一些关于来源的辅助信息。数据管理者向合法用户广播扭曲的来源功能，这也被对手窃听。在效用方面，每个合法用户都希望完美地重建一些未知源，并在剩余未知源的估计正确性上获得一定的增益。在隐私方面，数据管理者希望最大限度地减少最大泄漏：敌手在收到广播数据后估计其未知源的任何目标函数的最坏情况猜测增益。给定系统设置，我们推导出最大泄漏到对手的基本性能下限，其灵感来自混淆图的概念和索引编码问题的性能界限。我们还详细介绍了一种贪婪的隐私增强机制，该机制受到信息瓶颈和隐私漏斗问题中的凝聚聚类算法的启发。