Security in Locally Repairable Storage

Abstract

Abstract-In this paper we extend the notion of locally repairable codes to secret sharing schemes. The main problem that we consider is to find optimal ways to distribute shares of a secret among a set of storage-nodes (participants) such that the content of each node (share) can be recovered by using contents of only few other nodes, and at the same time the secret can be reconstructed by only some allowable subsets of nodes. As a special case, an eavesdropper observing some set of specific nodes (such as less than certain number of nodes) does not get any information. In other words, we propose to study a locally repairable distributed storage system that is secure against a passive eavesdropper that can observe some subsets of nodes.We provide a number of results related to such systems including upper-bounds and achievability results on the number of bits that can be securely stored with these constraints. In particular, we provide conditions under which a locally repairable code can be turned into a secret sharing scheme and extend the results of secure repairable storage to cooperative repair and storage on networks. Additionally, we consider perfect secret sharing schemes over general access structures under locality constraints and give an example of a perfect secret sharing scheme that can have small locality. Lastly, we provide a lower bound on the size of a share compared to the size of the secret that shows how locality affects the sizes of shares in a perfect scheme.

Secrecy and Accessibility in Distributed Storage

“…In this work we only consider ideal storage systems. This security model is the same as in [3], [4], but while these works considered local repair of nodes, we require the property of local access.…”

“…we consider an arbitrary randomized mapping f . We note that the bounds do not depend on r and are based on the techniques from [3].…”

“…In this work, we consider this problem of local access in secure DSS. While this problem is by its motivation closely related to locally repairable codes, we stress that we are not concerned with secure storage codes that offer local repair of failed nodes, as, e.g., considered in [3], [4].…”

“…At the same time, accessing two servers is sufficient to recover each of the files, e.g., to recover file X 0 it suffices to read X 1 + Z and X 0 + X 1 + Z and calculate X 0 = (X 0 + X 1 + Z) − (X 1 + Z). Note that the goal of a secure LRC as considered in [3], [4] would be to locally recover X 0 + Z, X 1 + Z, or X 0 + X 1 + Z (codeword symbols) instead of X 0 or X 1 (data/message symbols).…”

Minimum-storage regenerating codes resistant to special adversary

“…Despite importance of repairing the content of unavailable node, this paper focus on another aspect of distributed storage systems namely safety of stored data. Due to distributed nature of such systems and as a consequence, increasing use of untrusted node providers or communication channels, they are vulnerable to different type of attacks or data leakage [12][13][14]. In this paper, we focus on threats caused by eavesdropper that gains access to some portion of stored information.…”