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

  • Zengpeng Li
  • Jiuru WangEmail author
  • Wenyin Zhang
Original Research


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.


Internet of Thing Hash proof system Lattice-based cryptography Vector encryption 



The authors would like to thank the anonymous reviewers for their helpful advice and comments. This work was supported by the National Natural Science Foundation of China (No.61802214), the Natural Science Foundation of Shandong Province (No.ZR2019BF009, ZR2018LF007, ZR2017MF050, ZR2016YL011), the Shandong Provincial Key Research and Development Program of China (2018GGX101005, 2017CXGC0701, 2016GGX109001), the Project of Shandong Province Higher Educational Science and Technology Program (No.J17KA049), and the Applied Basic Research Project of Qingdao under Grant (No.19-6-2-6-cg). The first version of this work was done when the first author was affiliated with Harbin Engineering University, China.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Qingdao UniversityQingdaoChina
  2. 2.Linyi UniversityLinyiChina

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