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 non-responsive 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\geq n^{\prime}=(\nu+1)k+t+2b+r-1, for some integer \nu\geq 1. This scheme achieves a PIR rate of 1-\frac{k+2b+t+r-1}{n^{\prime}-r}. In the case where the capacity is known, namely when k=1, it is asymptotically capacity achieving as the number of files grows.