For a given function of user data, a querier must recover with at least a prescribed probability, the value of the function based on a user-provided query response. Subject to this requirement, the user forms the query response so as to minimize the likelihood of the querier guessing a list of prescribed size to which the data value belongs based on the query response. We obtain a general converse upper bound for maximum list privacy. This bound is shown to be tight for the case of a binary-valued function through an explicit achievability scheme that involves an add-noise query response.

翻译：对于给定的用户数据函数，查询者必须基于用户提供的查询响应，以至少达到规定概率恢复函数值。在此要求下，用户构建查询响应，以最小化查询者基于该响应猜测数据值所属的预定大小列表的可能性。我们推导了最大列表隐私的通用逆向上界。对于二值函数情形，该上界被证明是紧的，并通过一种显式的可实现方案得以验证，该方案涉及添加噪声的查询响应。