List Privacy Under Function Recoverability

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 the maximum list privacy which is shown to be tight for the special case of a binary-valued function through an explicit achievability scheme for the query response.