Improved upper bounds on information-theoretic private information retrieval (extended abstract)

Private Information Retrieval (PIR) schemes allow a u*eI to retrieve the Cth bit of an n-bit database I, replicated in k semers, while keeping the value of i private from each server. A t-private PIR scheme protects the user’s privacy from any collusion of up to t servers. The main cost measure for such schemes is their communication complexity. We introduce a new technique for the construction of information-theoretic (i.e., unconditionally secure) PIR. schcmea, providing B non-trivial linear-algebraic generalization of previous techniques. Using thi technique, we improve and simplify known upper bounds on the communication complexity of PIFt schemes in the information-theoretic setting. In the case of l-private PIR, we give a simple k-server scheme with complexity O(~‘VZ”(~“-~)), improving the heat known construction whose complexity also grows linearly in r?‘(“--l) for any fixed k, but depends epponentially on k. Our improvements are mow significant for &private PIFt schemes, where t > 1. For example, we get a %private, 4server PIR scheme whose communication complexity is O(fP), compared to the previously known O(n”‘) uPPer bound.