Robust Private Information Retrieval from Coded Systems with Byzantine and Colluding Servers
Razane Tajeddine, Oliver W. Gnilke, David Karpuk, Ragnar, Freij-Hollanti, Camilla Hollanti

TL;DR
This paper introduces a robust private information retrieval scheme for coded storage systems that withstands colluding, Byzantine, and non-responsive servers, achieving near-capacity rates especially when the number of files is large.
Contribution
It presents an explicit PIR scheme using Reed-Solomon codes that handles multiple server adversities and approaches capacity in the single-file case.
Findings
Achieves PIR rate of 1-(k+2b+t+r-1)/n'
Handles up to t-collusion, b Byzantine, and r non-responsive servers
Asymptotically capacity achieving for k=1 as files grow
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 generalized Reed-Solomon storage code is designed, protecting against -collusion and handling up to byzantine and non-responsive servers, when , for some integer . This scheme achieves a PIR rate of . In the case where the capacity is known, namely when , it is asymptotically capacity achieving as the number of files grows.
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