The stability of Web 3.0 depends on the existence of a robust decentralized storage infrastructure. One challenge associated with decentralized storage is access control in the context of data outsourcing. Many solutions to this problem have been proposed, but there still exist limitations. For instance, the implementation of an access control algorithm may consume a considerable amount of computing resources, necessitate reliance on a centralized storage service provider, and fail to effectively arbitrate against malicious behaviors. To address the these problems, we innovatively propose a Publicly Verifiable Data Access Control (PVDAC) algorithm without bilinear pairing to reduce the computational overhead and provide an efficient arbitration method. We extend the blockchain with a layer two network to reduce the token consumption associated with on-chain operations. We analyzed the security of the scheme, proved that it meets the CCA security of the ciphertext, and conducted comprehensive experiments to evaluate its performance. The results show that the proposed PVDAC scheme achieves low computational consumption by costing only 1% to 10% of the token consumption for interaction with the main chain, and meanwhile, supports public verification.