Nearly Private Information Retrieval

A private information retrieval scheme is a protocol whereby a client obtains a record from a database without the database operators learning anything about which record the client requested. This concept is well studied in the theoretical computer science literature. Here, we study a generalization of this idea where we allow a small amount of information about the client's intent to be leaked. Despite having relaxed the privacy requirement, we are able to prove three fairly strong lower bounds on such schemes, for various parameter settings. These bounds extend previously known lower bounds in the traditional setting of perfect privacy and, in one case, improve upon the previous best result that handled imperfect privacy.