Minimum-storage regenerating codes resistant to special adversary

Introduction: In order to deal with temporarily unavailable nodes in a distributed storage system, engineers apply special classes of erasure correction codes. These codes allow you to repair a temporarily unavailable node by downloading small amounts of data from the remaining ones. However, this creates safety threats in the presence of an eavesdropper. Purpose: Introducing a new mathematical model in which the eavesdropper has a limited access to all nodes in the system, and developing codes resistant to it. Methods: Information-theoretic arguments, and mixing information symbols with random ones by systematic Reed — Solomon code. Results: We introduced a new mathematical model of an eavesdropper with limited access to all nodes in a distributed storage system. Note that the proposed eavesdropper is passive, being unable to change the accessed data. We found parameters for optimal regenerating codes resistant to such adversary, and provided a technique to ensure necessary resistance. As a result, we obtained the construction of optimal minimum storage regenerating codes resistant to such adversary. Practical relevance: The proposed constructions can provide resistance to adversary while ensuring effective data repair.