Despite all the benefits a cloud data storages offer to customers, there is a high risk of breach of confidentiality, integrity, and availability related with the uncertainty of errors and falsifications, loss of information, denial of access for a long time, information leakage, conspiracy, and technical failures. In this article, we propose a configurable, reliable, and secure distributed data storage scheme with improved data redundancy, reliability, and encoding/decoding speed. Our system utilizes a Polynomial Residue Number System (PRNS) with a new method of error correction codes and secret sharing schemes. We introduce the concept of an approximate value of a rank (AR) of a polynomial. It reduces the computational complexity of the encoding/decoding and PRNS coefficients size. Based on the properties of the approximate value and PRNS, we introduce the AR-PRNS method for error detection, correction, and controlling computational results with capabilities of scalable parallel computing. We provide a theoretical basis to configure and optimize the redundancy of stored data and encoding/decoding speed to cope with different objective preferences, workloads, and storage properties. Theoretical analysis shows that, by appropriate selection of AR-PRNS parameters, the proposed scheme increases the safety, reliability, and reduces the overhead of data storage.