New Multi-authority Attribute-based Encryption Scheme on Lattices

To resolve the problem of poor security on quantum attack in attribute-based encryption over the bilinear maps, a new multi-authority attribute-based encryption scheme on lattices is proposed. Firstly, the SamepleLeft algorithm was used to extract the users private key, so it can reduce the size of private key which is related to the dimensions of concatenation matrix and the quantity of users attributes. Secondly, aiming at the problem of single access policy, the new scheme employed the Shamir secret sharing scheme which is used to construct an access tree to realized AND, OR, THRESHOLD operations on attributes, so the ciphertext can be generated by any access structure, and the expressive skill of access policy is more extensive. Lastly, the security of the proposed scheme could reduce to the hardness of decisional learning with errors problem under standard model. Comparative analysis shows that, the size of public parameters, master secret key, users private key and ciphertext are all optimized, and it has better performance than single authority schemes in some degree. Furthermore, from perspective of security and practicability, the new multi-authority attribute-based encryption scheme is more suitable for the demand of cloud environment.