Attribute-based encryption (ABE) mechanism on lattices can against quantum attack and guarantees fine-grained access control of encrypted data, and it has been widely used in cloud computing and privacy protection. However, the high complexity of the trapdoor generation and delegation and preimage sampling are the main barriers for the development of ABE schemes in a post-quantum world. Thus, we proposed a security and efficient multi-authority ABE scheme from lattices in this paper. The scheme is based on the theory of MP12 and is proved to be secure under the standard model. In this scheme, we construct an optimized sampling algorithm to generate a $mathbb {Z}_{q}$ -invertible matrix with a lower runtime. Based on it, combining the trapdoor generation and delegation algorithm in MP12, we designed multiple attribute authorities which can manage different attribute sets and generate private keys for the user independently. In addition, the Shamir’s secret sharing technique is introduced to support policies expressed in any monotone access structures. Compared with the existing related schemes, the proposed scheme can improve the functional agility and the flexibility of the access policy prominently, and it also can achieve a better performance with less lattice dimension, trapdoor storage occupation, and ciphertext expansion rate. The analysis shows that our scheme is feasible and superior in the large-scale distributed environment.
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