Revisiting post-quantum hash proof systems over lattices for Internet of Thing authentications

Internet of Things (IoT) has proved to be one of a success subset of cyber-physical systems, and it is receiving much attention among end-users associated with various applications. However, with the popularization of the IoT technologies, network attacks on the IoT environment are also increasing. To mitigate these security attacks, one of the candidates’ choice is quantum-resistant authentication, but the widely used authentication schemes are inadequate because they cannot prevent the quantum computer attacks. Lattices serving as an extremely promising foundation for post-quantum cryptography have emerged, and hash proof systems (HPS) over lattices have attracted the attention in the quantum-resistant authentication. Most existing HPS schemes over lattices can be used for authentications, but most of HPSs constructions depend on the strong security scheme that can prevent the indistinguishable chosen-ciphertext attacks (CCA) and focus on single-bit encryption, which seems unpractical in the IoT environments. An open problem is how to Integrate the vector (or multi-bit) versions of HPS over lattices into IoT environment for authentication with high efficiency. In this paper, to instantiate HPS over lattices and make it more practical for IoT, we follow the methodology from foremost schemes and introduce the smooth projective hash function (SPHF) which is a special of HPS. Then we relax the CCA-secure requirement and give two elegant instantiations of SPHF with rigorous INDCPA security for the open problem by optimizing two classic encryptions over lattices. The key point of the optimization is that we use a diverse public key which cascades multiple learning with errors (LWE) instances instead of a matrix of LWE insurance while we can bypass the coarse straightforward composition.