Attribute-Based Hash Proof System Under Learning-With-Errors Assumption in Obfuscator-Free and Leakage-Resilient Environments

Node attributes such as MAC and IP addresses, and even GPS position, can be considered as exclusive identity in the distributed networks such as cloud computing platform, wireless body area networks, and Internet of Things. Nodes can exchange or transmit some important information in the networks. However, with the openness and exposure of node in the networks, the communications between the nodes are facing a lot of security issues. In particular, sensitive information may be leaked to the attackers in the presence of side-channel attacks, memory leakages, and time attacks. In this paper, we present a new notion of attribute-based hash proof system ( <inline-formula> <tex-math notation="LaTeX">$\mathsf{AB\mbox{-}HPS}$</tex-math></inline-formula>) in the bounded key-leakage model, to be resistant to the possible quantum attackers. The notion of <inline-formula> <tex-math notation="LaTeX">$\mathsf{AB\mbox{-}HPS}$</tex-math></inline-formula>s is so attractive and powerful and can be considered as implicit proofs of membership for languages. We also give a construction of <inline-formula> <tex-math notation="LaTeX">$\mathsf{AB\mbox{-}HPS}$</tex-math></inline-formula> in lattices and prove the security of indistinguishability of valid and invalid ciphertext and leakage smoothness under the decisional learning-with-errors assumption. We also provide the general leakage-resilient attribute-based encryption construction using <inline-formula> <tex-math notation="LaTeX">$\mathsf{AB\mbox{-}HPS}$</tex-math></inline-formula> as the primitive without indistinguishable obfuscator. Finally, we discuss some extensions to improve the schemes in larger space for the message, larger alphabet for the attribute, and arbitrary access structure for the policy, respectively. We also give the performance evaluation in theoretic analysis and practical computation.