Private Information Delivery from Coded Storage against Byzantine and Eavesdropping Attacks

Private information delivery (PID) from coded stor-age is a problem in delivering a message to a receiver without revealing the locations of servers storing encoded pieces of the message. Although existing researches only focus on the method to keep the server locations secret to the receiver, they do not consider other types of security against storage servers; security of stored messages against the Byzantine servers and the eavesdropping servers. In this paper, we first define the security properties against these attackers in PID; 1) the t-Byzantine resistance and 2) the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex> -message confidentiality, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex> are the maximum capable numbers of Byzantine servers and eavesdropping servers, respectively. We also introduce an explicit scheme guaranteeing these properties with no deterioration of the PID's server locations privacy. The scheme can be viewed as a pre-coding method of messages using the maximum rank distance (MRD) code, and it can be applied to any PID scheme from coded storage. Furthermore, we characterize the maximum possible <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex> in terms of parameters of the underlying MRD code, and clarify the degradation in the transmission rate introduced by these properties.