Inner-product lossy trapdoor functions and applications

Abstract

In this paper, we propose a new cryptographic primitive called inner-product lossy trapdoor function (IPLTDF). We give a formal definition, and a concrete construction from lattices. We then show this primitive is useful to obtain efficient chosen-plaintext secure inner-product encryption (IPE) schemes. The resulting IPE scheme has almost the same public key size for multi-bit encryption compared with a recent IPE scheme proposed by Agrawal, Freeman and Vaikuntanathan [] for single-bit encryption. Unfortunately, our IPE scheme only supports attribute vectors with logarithmic length. On the positive side, our basic IPE scheme can be extended to achieve chosen-ciphertext (CCA) security. As far as we are aware, this is the first CCA-secure IPE scheme based on lattices. © 2012 Springer-Verlag.