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Cloud storages delivered as services are made available to the general public. As cloud storage provider prices become low, they have moved into the mainstream of storage technology. However, there are various factors that cause many potential users do not use it intensively. There exist high risks for confidentiality, integrity, and availability violation associated with the loss of information, denial of access, technical failures, etc. In this article, we propose a two-level secret sharing scheme (TL-SSS) based on a residue number system (RNS) for a configurable, reliable, and secure distributed data storage. RNS moduli of a special type increase the reliability of the data storage system and reduce the computational complexity of the data encoding and decoding from linear-logarithmic to linear. TL-SSS is the weighted data access structure. It creates and distributes data shares according to the characteristics of the cloud storages under various scenarios. We provide a solution that improves system reliability without reduction of the security level. In contrast to classical solutions, it can restore the data with less available shares than the state-of-the-art approaches.