Private Stream Search at the same communication cost as a regular search: Role of LDPC codes

Private Stream Search allows users to perform keyword-based queries to a database without revealing any information about the keywords they are searching. Using homomorphic encryption, Ostrovsky and Skeith proposed a computationally secure solution to this problem in 2005. However, their solution requires the server to send an answer of size O(mS log m) bits when m documents of S bits match the query, while a non-private query only requires mS bits. In this work we propose two new communication optimal constructions, both allowing a communication expansion factor (compared to a non-private query) asymptotically equal to 1 when m and S increase. More precisely, our first scheme requires m(S + O(log t)) bits (where t is the size of the database) and our second scheme m(S +C) where C is a constant depending on the chosen computational security level.