Nowadays, as Cloud computing becomes popular, a need for a DFS(distributed file system) is increased. But, in the current Cloud computing environments, there is no DFS framework that is sufficient to protect sensitive private information from attackers. Therefore, we designed and proposed a secure scheme for distributed file systems. The scheme provides confidentiality and availability for a distributed file system using a secret sharing method. In this paper, we measured the speed of encryption and decryption for our proposed method, and compared them with that of SEED algorithm which is the most popular algorithm in this field. This comparison showed the computational efficiency of our method. Moreover, the proposed secure read/write model is independent of Hadoop DFS structure so that our modified algorithm can be easily adapted for use in the HDFS. Finally, the proposed model is evaluated theoretically using performance measurement method for distributed secret sharing model.