A Storage-Efficient and Robust Private Information Retrieval Scheme   Allowing Few Servers
  Since the concept of locally decodable codes was introduced by Katz and Trevisan in 2000, it is well-known that information the-oretically secure private information retrieval schemes can be built using locally decodable codes. In this paper, we construct a Byzantine ro-bust PIR scheme using the multiplicity codes introduced by Kopparty et al. Our main contributions are on the one hand to avoid full replica-tion of the database on each server; this significantly reduces the global redundancy. On the other hand, to have a much lower locality in the PIR context than in the LDC context. This shows that there exists two different notions: LDC-locality and PIR-locality. This is made possible by exploiting geometric properties of multiplicity codes. 
Daniel Augot (LIX), Fran\c{c}oise Levy-Dit-Vehel (UMA), Abdullatif   Shikfa
cs.CR