Three-level storage and nested MDS codes for perfect secrecy in multiple clouds

The problem of storing data reliably and securely in multiple cloud storage providers (CSPs) with minimum cost is investigated. A jointly optimal coding and storage allocation scheme, which achieves perfect secrecy with minimum cost, is derived. The optimal coding scheme is shown to be the nested maximum-distance-separable code and the optimal amounts of data to be stored in the CSPs is proven to exhibit a three-level structure. The exact parameters of the code and the exact storage amount to each CSP can be determined numerically by simple one-dimensional search.