Robust Private Information Retrieval from Coded Systems with Byzantine and Colluding Servers

A private information retrieval (PIR) scheme on coded storage systems with colluding, byzantine, and nonresponsive servers is presented. Furthermore, the scheme can also be used for symmetric PIR in the same setting. An explicit scheme using an [n, k] generalized Reed-Solomon storage code is designed, protecting against t-collusion and handling up to b byzantine and r non-responsive servers, when n ≥ n′ = (ν +1)k+ t+2b+ r− 1, for some integer ν ≥ 1. This scheme achieves a PIR rate of 1− k+2b+t+r−1 n′ . In the case where the capacity is known, namely when k = 1, it is asymptotically capacity achieving as the number of files grows.