Revisit the Concept of PEKS: Problems and a Possible Solution

Since Boneh et al. propose the concept, non-interactive Public-key Encryption with Keyword Search (PEKS) has attracted lots of attention from cryptographers. Non-interactive PEKS enables a third party to test whether or not a tag, generated by the message sender, and a trapdoor, generated by the receiver, contain the same keyword without revealing further information. In this paper we investigate a non-interactive PEKS application proposed by Boneh et al. and show our observations, especially that privacy is not protected against a curious server. We propose the notion of interactive PEKS, which, in contrast to non-interactive PEKS, requires the tag to be generated interactively by the message sender and the receiver. For this new primitive, we identify two types of adversaries, namely a curious user and a curious server, and provide security formulations for the desirable properties. We propose a construction for interactive PEKS and prove its security in the proposed security model.