Symmetric Private Information Retrieval from MDS Coded Distributed Storage with Non-colluding and Colluding Servers

Qiwen Wang, Mikael Skoglund
2019 IEEE Transactions on Information Theory  
A user wants to retrieve a file from a database without revealing the identity of the file retrieved to the operator of the database (server), which is known as the problem of private information retrieval (PIR). If it is further required that the user obtains no information about the other files in the database, the concept of symmetric private information retrieval (SPIR) is introduced to guarantee privacy for both parties. For SPIR, the server(s) need to access some randomness independent of
more » ... the database, to protect the content of undesired files from the user. The information-theoretic capacity of SPIR is defined as the maximum number of information bits of the desired file retrieved per downloaded bit. In this paper, the problem of SPIR is studied for a distributed storage system with N servers (nodes), where all data (including the files and the randomness) are stored in a distributed way. Specifically, the files are stored by an (N, KC )-MDS storage code. The randomness is distributedly stored such that any KC servers store independent randomness information. We consider two scenarios regarding to the ability of the storage nodes to cooperate. In the first scenario considered, the storage nodes do not communicate or collude. It is shown that the SPIR capacity for MDS-coded storage (hence called MDS-SPIR) is 1 − K C N , when the amount of the total randomness of distributed nodes (unavailable at the user) is at least K C
doi:10.1109/tit.2019.2903206 fatcat:g2tnk3h7uzeltehrdmoqc6vupi