A Novel Hierarchical Identity-Based Encryption Scheme from Lattices

Hierarchical identity based encryption is a powerful public key encryption scheme where entities are arranged in a directed tree. Each entity in the tree is provided with a secret key from its parent and can delegate this secret key to its children so that a child entity can decrypt messages intended for it. Aiming at the high complexity in user's private key extraction and large expansion ratio of trapdoor size in previous hierarchical identity-based encryption schemes, in this paper, we proposed a new HIBE scheme. We first used the implicit extension method to improve preimage sampling algorithm, and then we combined the improved algorithm with MP12 trapdoor delegation algorithm to construct an efficient hierarchical identity-based encryption user's private key extraction algorithm. Finally, we integrated the new extraction algorithm and the Dual-LWE algorithm to complete our scheme. Compared with the similar schemes, the efficiency of our scheme is improved in system establishment and user's private key extraction stage, the trapdoor size grows only linearly with the system hierarchical depth, and the improved preimage sample algorithm partly solves the Gaussian parameter increasing problem induced by MP12 trapdoor delegation. The security of the proposed scheme strictly reduces to the hardness of decisional learning with errors problem in the standard model.