Achievable schemes and limits for local recovery on a graph

Mazumdar, Arya

doi:10.1109/allerton.2014.7028551

“…Equation (13) gives an upper-bound on the maximum ambiguity of the secret of an (n, k, ℓ, m, r)-scheme when the eavesdropper has access to more than ℓ shares.…”

Section: A Boundsmentioning

confidence: 99%

“…Another extension of local repair property for distributed storage has recently been proposed in [13], [14]. Consider a Distributed Storage System as a directed graph G such that a node of the graph represents a node of the Distributed Storage System and each node can connect to only its out-neighbors for repair.…”

Section: Security For Repairable Codes On Graphsmentioning

confidence: 99%

Security in locally repairable storage

Agarwal

¹

,

Mazumdar

²

2015

2015 IEEE Information Theory Workshop (ITW)

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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.

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“…The author is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, email: arya@umn.edu. Part of this work was presented in the IEEE International Symposium on Information Theory, 2014 [31] and in the Allerton Conference, 2014 [30]. This work was supported in part by the National Science Foundation CAREER award under grant no.…”

Section: Introductionmentioning

confidence: 99%

Storage Capacity of Repairable Networks

Mazumdar

¹

2015

IEEE Trans. Inform. Theory

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Abstract-In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that each server or storage node in a network is connectible to only some, and not all other, nodes. This may happen for reasons such as physical separation, inhomogeneity in storage platforms etc. We estimate the storage capacity of both undirected and directed networks under this model and propose some constructive schemes. From a coding theory point of view, we show that this model is approximately dual of the well-studied index coding problem.Further in this paper, we extend the above model to handle multiple server failures. Among other results, we provide an upper bound on the minimum pairwise distance of a set of words that can be stored in a graph with the local repair guarantee. The well-known impossibility bounds on the distance of locally recoverable codes follow from our result.

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Security in Locally Repairable Storage

Agarwal

¹

,

Mazumdar

²

2016

IEEE Trans. Inform. Theory

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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.

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Achievable schemes and limits for local recovery on a graph

Cited by 3 publications

References 27 publications

Security in locally repairable storage

Security in locally repairable storage

Storage Capacity of Repairable Networks

Security in Locally Repairable Storage

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