Local mutual-information differential privacy (LMIDP) is a privacy notion that aims to quantify the reduction of uncertainty about the input data when the output of a privacy-preserving mechanism is revealed. We study the relation of LMIDP with local differential privacy (LDP), the de facto standard notion of privacy in context-independent (CI) scenarios, and with local information privacy (LIP), the state-of-the-art notion for context-dependent settings. We establish explicit conversion rules, i.e., bounds on the privacy parameters for a LMIDP mechanism to also satisfy LDP/LIP, and vice versa. We use our bounds to formally verify that LMIDP is a weak privacy notion. We also show that uncorrelated Gaussian noise is the best-case noise in terms of CI-LMIDP if both the input data and the noise are subject to an average power constraint.

翻译：本地互信息差分隐私（LMIDP）是一种隐私概念，旨在量化当隐私保护机制的输出被泄露时，输入数据不确定性的减少程度。我们研究了LMIDP与本地差分隐私（LDP，上下文无关场景中的事实标准隐私概念）以及本地信息隐私（LIP，上下文相关场景中的最先进概念）之间的关系。我们建立了显式的转换规则，即LMIDP机制同时满足LDP/LIP的隐私参数边界，反之亦然。利用这些边界，我们正式验证了LMIDP是一种弱隐私概念。我们还证明，在输入数据和噪声均受平均功率约束的情况下，不相关高斯噪声是CI-LMIDP意义下的最优噪声。