A Novel Perfect Privacy Preserving Single Database Private Information Retrieval with Non-trivial Communication

Most of the existing user privacy preserving techniques rely on the existing intractability assumption based data privacy concepts that greatly reduces the chances of providing perfect privacy (i.e., no information about the user interest is revealed over the curious server) to the user. In order to fill this gap, we have presented a perfect privacy preserving single database scheme with non-trivial communication cost using the concept called Private Information Retrieval (PIR). We have suc-cessfully overcome the basic requirement of $\Omega(n)$ communication for any single database information-theoretic private information retrieval as claimed by Chor et.al [1] by breaking the dependency of both user privacy and data privacy on a single intractability assumption where n is the size of the database.In the proposed scheme, information-theoretic queries are generated by extending the query input domain to$\mathbb {Z-{N}^{+1}}$ (i.e., all queries can select their inputs from $\mathbb {Z-{N}^{+1}}$ with identically distributed probability) where N is the RSA composite modulus which is an improvement to the quadratic residuosity based user privacy preserving technique presented in [2] (Note that in [2], query may contain computationally indistinguishable input either from quadratic residue set or from quadratic non-residue set). We have presented a new recursive trapdoor bit based linking function which takes the information-theoretic query and the database and produces a non-trivial communication response. Additionally, we have extended the proposed scheme to a new scheme with reduced communication by using a new compression method.