Threshold attribute-based encryption with attribute hierarchy for lattices in the standard model

Attribute-based encryption (ABE) has been considered as a promising cryptographic primitive for realising information security and flexible access control. However, the characteristic of attributes is treated as the identical level in most proposed schemes. Lattice-based cryptography has been attracted much attention because of that it can resist to quantum cryptanalysis. In this study, lattice-based threshold hierarchical ABE (lattice-based t-HABE) scheme without random oracles is constructed and proved to be secure against selective attribute set and chosen plaintext attacks under the standard hardness assumption of the learning with errors problem. The notion of the HABE scheme can be considered as the generalisation of traditional ABE scheme where all attributes have the same level.