Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns

Abstract

In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid to the case of the database being encoded across several servers, subsets of which can collude to attempt to deduce the requested file. With the goal of studying the achievable PIR rates in realistic scenarios, we generalize results for coded data from the case of all subsets of servers of size $t$ colluding, to arbitrary subsets of the servers. We investigate the effectiveness of previous strategies in this new scenario, and present new results in the case where the servers are partitioned into disjoint colluding groups.

Updated with a corrected statement of Theorem 2

References in corpus (2)

• Private Information Retrieval from Coded Databases with Colluding Servers
• The Capacity of Robust Private Information Retrieval with Colluding Databases

Cited by in corpus (10)

• Private Information Retrieval from MDS Coded Databases with Colluding Servers under Several Variant Models
• A general private information retrieval scheme for MDS coded databases with colluding servers
• The Capacity of Private Information Retrieval with Partially Known Private Side Information
• Converse for Multi-Server Single-Message PIR with Side Information
• Fundamental Limits of Cache-Aided Private Information Retrieval with Unknown and Uncoded Prefetching
• Single-Server Multi-Message Private Information Retrieval with Side Information
• The Capacity of Private Information Retrieval with Private Side Information Under Storage Constraints
• Private Information Retrieval from MDS Coded Data with Colluding Servers: Settling a Conjecture by Freij-Hollanti et al.
• Cache-Aided Private Information Retrieval with Partially Known Uncoded Prefetching: Fundamental Limits
• t-Private Information Retrieval Schemes Using Transitive Codes