A New Shift-Add Secret Sharing Scheme for Partial Data Protection with Parallel Zigzag Decoding

This paper studies distributed storage for protecting the confidentiality of partial data in the presence of storage node failures. It is required that not only the original data can be reconstructed from the remaining surviving nodes, but also the data lost by a failed node can be repaired from as few nodes as possible. The minimum number of surviving nodes required to repair a failed node is called the repair degree. Inspired by the zigzag-decodable secret sharing scheme, we propose a new shift-add secret sharing scheme based on the XOR and bitwise-shift operations, in which confidential data is protected by using random keys generated from non-confidential data. The reliability and repairability of the proposed scheme are measured by the message loss probability and the maximum repair degree among all nodes, respectively, and then compared with three benchmark schemes. In contrast to conventional zigzag-decodable codes, the special structure of our proposed scheme allows the design of fast parallel algorithms for modern devices with multi-core processors, which have a linear speedup in decoding time compared with various versions of serial zigzag decoding. Experiments are implemented on a multi-core computer, and the empirical results on decoding time are consistent with our theoretical observations.