Linear symmetric private information retrieval for MDS coded distributed storage with colluding servers
Qiwen Wang, Mikael Skoglund · 2017
The problem of symmetric private information retrieval (SPIR) from a coded database which is distributively stored among colluding servers is studied. Specifically, the database comprises K files, which are stored among N servers using an (N, M)-MDS storage code. A user wants to retrieve one file from the database by communicating with the N servers, without revealing the identity of the desired file to any server. Furthermore, the user shall learn nothing about the other K - 1 files in the database. In the T-colluding SPIR problem (hence called TSPIR), any T out of N servers may collude, that is, they may communicate their interactions with the user to guess the identity of the requested file. We show that for linear schemes, the information-theoretic capacity of the MDS-TSPIR problem, defined as the maximum number of information bits of the desired file retrieved per downloaded bit, equals 1 - (M+T-1)/N, if the servers share common randomness (unavailable at the user) with amount at least (M+T-1)/(N-M-T+1) times the file size. Otherwise, the capacity equals zero.