Extensive Study on the Security of Private Information Delivery from Coded Storage

Private information delivery (PID) from coded storage is a problem in delivering a message to a receiver without revealing the locations of servers storing encoded pieces of the message. Vaidya et al. introduced an explicit PID scheme based on maximum distance separable (MDS) codes. However, their scheme still has the limitation of the maximum possible number of servers due to the use of MDS codes. Moreover, it has no security against external adversaries who corrupt and eavesdrop on the data stored on servers. In this paper, we focus on the following two topics to solve the above problems: (1) performance characterization of a PID scheme with an arbitrary linear code; and (2) security of stored messages against the Byzantine servers and the eavesdropping servers. For (1), we first reformulate a PID scheme from coded storage based on a linear code. We also formally define two properties of PID from coded storage: the correctness and the privacy, where the correctness means the recoverability of the original message at the receiver, and the privacy means the confidentiality of locations of servers storing the message. Furthermore, we characterize the conditions of a PID scheme attaining the correctness and privacy in terms of the Hamming weight of the linear code employed in the scheme. For (2), we define new security properties against Byzantine and eavesdropping servers in PID: the t-Byzantine resistance and the μ-message confidentiality, where t and μ are the maximum capable numbers of Byzantine servers and eavesdropping servers, respectively. Moreover, we also introduce an explicit scheme guaranteeing these properties with no deterioration of the correctness and privacy.