Private Information Retrieval from Colluding and Byzantine Servers with Binary Reed-Muller Codes

Abstract

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. In this work, a flexible and robust private information retrieval (PIR) scheme based on binary non-maximum distance separable (non-MDS) codes is considered. This combines previous works on PIR schemes based on transitive non-MDS codes on one hand, and PIR from MDS-coded Byzantine and nonresponsive servers on the other hand. More specifically, a PIR scheme employing binary Reed-Muller (RM) codes tolerant to colluding, Byzantine, and non-responsive servers is constructed, and bounds for the achievable rates are derived under certain conditions. The construction of such schemes turns out to be much more involved than for MDS codes. Namely, the binary query vectors have to be selected with great care to hit the desired information sets, which is technically challenging as will be shown.

Storage and Retrieval Codes in PIR Schemes with Colluding Servers

“…Punctured Reed-Muller codes can be considered as length 2 m − 1 cyclic codes, see [5,17]. Reed-Muller code based star product PIR scheme with colluding servers were studied in [20,25,37]. These t-privacy PIR schemes for coded database can be defined over the smallest field F 2 and have good performance.…”

“…Low cost cyclic code based star product PIR schemes with colluding servers are constructed from cyclic storage code with two nonzero weights studied in the classical paper [3]. In Section 7 we show that when the storage code C is the Reed-Muller code which is an extended cyclic code, in general the best choice of the retrieval code is not the Reed-Muller code as in [20,37].…”