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 <tex>$[n, k]$</tex> generalized Reed-Solomon storage code is designed, protecting against t-collusion and handling up to <tex>$b$</tex> byzantine and <tex>$r$</tex> non-responsive servers, when <tex>$n\geq n^{\prime}=(\nu+1)k+t+2b+r-1$</tex>, for some integer <tex>$\nu\geq 1$</tex>. This scheme achieves a PIR rate of <tex>$1-\frac{k+2b+t+r-1}{n^{\prime}-r}$</tex>. In the case where the capacity is known, namely when <tex>$k=1$</tex>, it is asymptotically capacity achieving as the number of files grows.