## 1 Introduction
Meanwhile, [PERSON] [28] proposed a scheme that manages each attribute across different domains, eliminates the single-point bottleneck of the existing multi-authority blockchain-based CP-ABE schemes, and reduces computation and communication overhead between the user and the multiple attribute authorities. In 2022, [PERSON] [29] proposed a secure and trusted agricultural product traceability system (BCST-APTS) supported by blockchain and CP-ABE encryption technology, thereby ensuring the efficient sharing and supervision of data stored in the Permissioned Blockchain. However, most of the aforementioned works based their security on cryptographic assumptions related to bilinear maps. It is very natural to seek for solutions to the known attacks on group-based constructions by quantum computers. To address the threat of quantum computing, lattice-based cryptography is a promising approach that provides a new set of assumptions based on finding short vectors in lattices and is believed to be hard for quantum computers. Additionally, new cryptographic protocols have been proposed which rely on the hardness of solving certain lattice problems, including Learning with Errors (LWE). These protocols are expected to provide strong protection against the attacks of quantum computers. At present, lattice-difficulty problems that are provably secure mainly consist of small integer solution problems (SIS) and learning with errors problems (LWE). These two difficult problems are as hard as approximate lattice problems from the worst case to the average case reduction. Recently, several lattice-based encryption schemes have been proposed consecutively, which mainly focus on identity-based encryption [30; 31; 32] digital signature [33], and zero-knowledge proof [34]. In May 2021, [PERSON] et al. [35] constructed an ABE algorithm based on ciphertext policy according to the LWE-difficulty problem and realized a CP-ABE scheme that could resist quantum attacks. In addition, for a comprehensive analysis of our security measures, we considered the potential impacts of active and passive side-channel attacks (SCA), fault attacks, and power analysis attacks [36]. We recognize the increasing importance of Post-Quantum Cryptography (PQC) in secure applications, such as smartphones and blockchain systems, as it replaces traditional ECC/RSA algorithms. Therefore, we studied relevant literature [37; 38; 39]. Furthermore, we acknowledged the significance of NIST lightweight standardization and considered fault attacks as a consideration for side-channel attacks, referring to the research work of [PERSON] et al. [40; 41; 42] in this field. The contributions of this scheme are as follows:  
(a) Form the LWE-CPABE algorithm suitable for blockchain to resist the quantum attacks, improve the CP-ABE scheme proposed by [PERSON], design the CP-ABE algorithm supporting policy update, and realize the dynamic access control of the data;  
(b) Use a threshold proxy re-encryption scheme following a key encapsulation mechanism (KEM) approach to implement distributed key management for the LWE-CPABE algorithm, design the transaction generation algorithm and transaction verification contract, and realize the correctness and integrity verification of the intra-transaction data and the outsourcing storage data;  
(c) Carry out the security analysis and simulation experiment, and the results show that this scheme is secure and efficient and is suitable for distributed data sharing and access control.