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

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

Abstract: 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 ≥ n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1'</sup> =(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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">'</sup> -r)]. In the case where the capacity is known, namely when k=1, it is asymptotically capacity achieving as the number of files grows.