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Cloud-based services have powerful storage functions and can provide accurate computation. However, the question of how to guarantee cloud-based services access control and achieve data sharing security has always been a research highlight. Although the attribute-based proxy re-encryption (ABPRE) schemes based on number theory can solve this problem, it is still difficult to resist quantum attacks and have limited expression capabilities. To address these issues, we present a novel linear secret sharing schemes (LSSS) matrix-based ABPRE scheme with the fine-grained policy on the lattice in the research. Additionally, to detect the activities of illegal proxies, homomorphic signature (HS) technology is introduced to realize the verifiability of re-encryption. Moreover, the non-interactivity, unidirectionality, proxy transparency, multi-use, and anti-quantum attack characteristics of our system are all advantageous. Besides, it can efficiently prevent the loss of processing power brought on by repetitive authorisation and can enable precise and safe data sharing in the cloud. Furthermore, under the standard model, the proposed learning with errors (LWE)-based scheme was proven to be IND-sCPA secure. [ABSTRACT FROM AUTHOR]