Private Information Retrieval From Coded Storage Systems With Colluding, Byzantine, and Unresponsive Servers.

Razane Tajeddine, Oliver W. Gnilke, David A. Karpuk, Ragnar Freij-Hollanti, Camilla Hollanti

Abstract: 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.