Private Information Retrieval from Coded Storage Systems with Colluding, Byzantine, and Unresponsive Servers

The problem of private information retrieval (PIR) from coded storage systems with colluding, Byzantine, and unresponsive servers is considered. An explicit scheme using an [n,k] Reed-Solomon storage code is designed, protecting against t-collusion, and handling up to b Byzantine and r unresponsive servers, when n>k+t+2b+r-1. This scheme achieves a PIR rate of ((n-r-(k+2b+t-1))/n-r). In the case where the capacity is known, namely, when k=1, it is asymptotically capacity achieving as the number of files grows. Finally, the scheme is adapted to symmetric PIR.