In the era of big data, reducing the computational complexity of servers in data centers will be an important goal. We propose Low Complexity Secure Codes (LCSCs) that are specifically designed to provide information theoretic security in cloud distributed storage systems. Unlike traditional coding schemes that are designed for error correction capabilities, these codes are only designed to provide security with low decoding complexity. These sparse codes are able to provide (asymptotic) perfect secrecy similar to Shannon cipher. The simultaneous promise of low decoding complexity and perfect secrecy make these codes very desirable for cloud storage systems with large amount of data. The design is particularly suitable for large size archival data such as movies and pictures. The complexity of these codes are compared with traditional encryption techniques.
Our final goal is to demonstrate that perfect secrecy as defined by Shannon in @cite_29 can be achieved without any need to store keys. Note that the original approach of Shannon cipher system @cite_29 is not practical since for each bit of information, we need to store one bit of key which practically doubles the storage capacity requirement. We demonstrate that without generating any key, it is feasible to achieve perfect secrecy asymptotically. Since in this work we generate equivalent of key by means of combining of contents together (encoding function), it is clear that this encoding function cannot be shared by Alice with the cloud or Eve. This is one fundamental difference between this work and common problem of wiretap channel. One can consider this as the private key that is generated by Alice to secure the contents and won't be shared with anyone.
@cite_29
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THE problems of cryptography and secrecy systems furnish an interesting application of communication theory.1 In this paper a theory of secrecy systems is developed. The approach is on a theoretical level and is intended to complement the treatment found in standard works on cryptography.2 There, a detailed study is made of the many standard types of codes and ciphers, and of the ways of breaking them. We will be more concerned with the general mathematical structure and properties of secrecy systems.