2017/08/17 by Qiwen Wang, Wang, Qiwen, Mikael Skoglund +1 · 2 citations
Computer Science · #Cryptography and Data Security #Privacy-Preserving Technologies in Data #Complexity and Algorithms in Graphs
paper · pdf · doi:10.48550/arxiv.1708.05673
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. We conjecture that our capacity holds also for general MDS-TSPIR schemes.