Proofs of data possession and pollution checking for Regenerating Codes

Regenerating Codes strip a file in several servers, such that it is possible to recover the file when at least a given number of them is online. The difference between these codes and traditional erasure codes such as Reed-Solomon (RS), is that they require less bandwidth to repair failed nodes. This property is meant to improve storage reliability in cloud storage data systems. In this article, we present a method to check the availability of files that have been encoded using linear regenerating codes, by implementing two protocols that prove with high probability a node is in possession of a particular combination of data units from the original file. The constructions only use fast linear operations and are suited for real world files. Our proposal is based on the linear properties of the dot product among vectors and smart key assignments based on Combinatorics as well as Linear Algebra.