Cloud Data Storage and Private Information Retrieval Algorithms

The authors consider the private information retrieval (PIR) problem, in particular, the problem of ensuring secure queries to a database. Previously, the authors considered this problem for a cloud database in the presence of an active adversary who does not interfere with the execution of the PIR protocol but can carry out an attack with known open queries. In the proposed algorithms, bit number i is represented as an l-ary number with d digits. An algorithm for database placement on the cloud and an algorithm for bit querying with the use of permutations in the digits of a bit number, where bit number i is defined in a base-l number system, are proposed. The permutations are regarded as secret encryption keys. The communication complexity and the probability of guessing the bit number in a single attack with a known open query for bit number i, as well as in an attack with an unlimited number of known open queries, are estimated.