Efficient Proofs of Retrievability Using Expander Codes

Proofs of Retrievability (PoR) protocols ensure that a client can fully retrieve a large outsourced file from an untrusted server. Good PoRs should have low communication complexity, small storage overhead and clear security guarantees. We design a good PoR based on a family of graph codes called expander codes. We use expander codes based on graphs derived from point-line incidence relations of finite affine planes. Høholdt et al. showed that, when using Reed-Solomon codes as inner codes, these codes have good dimension and minimum distance over a relatively small alphabet. Moreover, expander codes possess very efficient unique decoding algorithms. We take advantage of these results to design a PoR scheme that extracts the outsourced file in quasi-linear time and features better concrete parameters than state-of-the-art schemes w.r.t storage overhead and size of the outsourced file.