The order of communication complexity of PIR-protocols

Private information retrieval protocols (PIR-protocols) allow a user to get the desired bit of information from a database whose copy is stored in several non-linked servers in such a way that the administrators of the database know nothing about the index of the bit the user requests for. The communication complexity of a protocol is defined as the total number of the bits exchanged between the user and the servers in the protocol. In this paper, we find the order of communication complexity of PIR-protocols depending on the degree of essentiality of the server response functions.