Can We Access a Database Both Locally and Privately?

We consider the following strong variant of private information retrieval (PIR). There is a large database x that we want to make publicly available. To this end, we post an encoding X of x together with a short public key \(\mathsf{pk}\) in a publicly accessible repository. The goal is to allow any client who comes along to retrieve a chosen bit \(x_i\) by reading a small number of bits from X, whose positions may be randomly chosen based on i and \(\mathsf{pk}\), such that even an adversary who can fully observe the access to X does not learn information about i.

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