Access control systems allow organizations to control user access to their resources with high reliability and availability. Blockchain technology can help in this case. However, when it comes to storing access control data, especially the matrix that defines user rights to files (DAC model) may be too large to be handled by blockchain as is. Thus, a decentralized access control model that results in a small amount of data storage on the blockchain can be beneficial in terms of the reliability of blockchain networks while allowing it to scale by adding large numbers of users and files. We present access control DAC model which uses a Merkle tree to store data, minimizes the storage size on the blockchain. This solution can be used with a variety of file storage systems, regardless of the used file storage technology. The proposed approach suggests additionally caching some requests to increase scaling. The proposed model was tested on 500 objects in a distributed environment.