Communication Efficient Secret Sharing

Huang, Wentao; Langberg, Michael; Kliewer, Joerg; Bruck, Jehoshua

doi:10.1109/tit.2016.2616144

Cited by 65 publications

(103 citation statements)

References 25 publications

(72 reference statements)

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“…There are several previous works that have considered Shamir's scheme in the context of networks [17] and distributed storage systems [18], [19]. In these works, there is only one secret, as in the original Shamir's scheme, to be distributed to users either as nodes of a network [17] or as users of a distributed storage system [18], [19], in a collusion-resistant way. However, we consider a multi-user secret sharing scenario, where there is one designated secret for each user, and the secret shares are distributed over a set of storage nodes.…”

Section: Shamir's Scheme and Related Workmentioning

confidence: 99%

Distributed Multi-User Secret Sharing

Soleymani

Mahdavifar

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We consider a distributed secret sharing system that consists of a dealer, n storage nodes, and m users. Each user is given access to a certain subset of storage nodes, where it can download the stored data. The dealer wants to securely convey a specific secret sj to user j via storage nodes, for j " 1, 2, . . . , m, in such a way that no user gets any information about other users' secrets in an information-theoretic sense. To this end, the dealer encodes secrets into several secret shares and loads them into the storage nodes. Given a certain number of storage nodes we find the maximum number of users that can be served in such systems and construct schemes that achieve this. We further define two major properties for such distributed secret sharing systems; communication complexity is defined as the total amount of data that users need to download in order to reconstruct their secrets; and storage overhead is defined as the total size of data loaded by the dealer into the storage nodes normalized by the total size of secrets. Lower bounds on minimum communication complexity and storage overhead are characterized given any n and m. Furthermore, we construct distributed secret sharing protocols, under certain conditions on the system parameters, that simultaneously attain these lower bounds, thereby providing schemes that are optimal in terms of both the communication complexity and the storage overhead. It is shown how to modify the proposed protocols in order to construct schemes with balanced storage load and communication complexity.

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Section: Shamir's Scheme and Related Workmentioning

confidence: 99%

Distributed Multi-User Secret Sharing

Soleymani

Mahdavifar

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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“…Interestingly, the lower bound on the repair bandwidth of an MDS vector code given in (2.3) continues to hold even when the contacted nodes contribute different number of symbols during the repair process [11], i.e., for every i ∈ [n] and R ⊆ [n]\{i} such that |R| = d, we have…”

Section: Background and Related Workmentioning

confidence: 99%

“…Given this vector representation of the MDS code, the repair bandwidth of an MDS code is lower bounded by [4,11] …”

Section: Introductionmentioning

confidence: 99%

MDS Code Constructions with Small Sub-packetization and Near-optimal Repair Bandwidth

Rawat

Tamo

Guruswami

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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An (n, M ) vector code C ⊆ F n is a collection of M codewords where n elements (from the field F) in each of the codewords are referred to as code blocks. Assuming that F ∼ = B , the code blocks are treated as -length vectors over the base field B. Equivalently, the code is said to have the sub-packetization level . This paper addresses the problem of constructing MDS vector codes which enable exact reconstruction of each code block by downloading small amount of information from the remaining code blocks. The repair bandwidth of a code measures the information flow from the remaining code blocks during the reconstruction of a single code block. This problem naturally arises in the context of distributed storage systems as the node repair problem [4]. Assuming that M = |B| k , the repair bandwidth of an MDS vector code is lower bounded by (n − 1)/(n − k) · symbols (over the base field B) which is also referred to as the cut-set bound [4]. For all values of n and k, the MDS vector codes that attain the cut-set bound with the sub-packetization level = (n − k) n/(n−k) are known in the literature [23,36].This paper presents a construction for MDS vector codes which simultaneously ensures both small repair bandwidth and small sub-packetization level. The obtained codes have the smallest possible sub-packetization level = O(n − k) for an MDS vector code and the repair bandwidth which is at most twice the cut-set bound. The paper then generalizes this code construction so that the repair bandwidth of the obtained codes approach the cut-set bound at the cost of increased sub-packetization level. The constructions presented in this paper give MDS vector codes which are linear over the base field B.

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“…The optimal rate is known to be n−r−z n , namely, the maximum message size is achieved when k = n − r − z [11]. Constructions of rate-optimal schemes are well known, such as Shamir's (ramp) secret sharing scheme [20].…”

Section: Setup and Definitionsmentioning

confidence: 99%

Secure RAID schemes for distributed storage

Huang

Bruck

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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We propose secure RAID, i.e., low-complexity schemes to store information in a distributed manner that is resilient to node failures and resistant to node eavesdropping. We generalize the concept of systematic encoding to secure RAID and show that systematic schemes have significant advantages in the efficiencies of encoding, decoding and random access. For the practical high rate regime, we construct three XOR-based systematic secure RAID schemes with optimal or almost optimal encoding and decoding complexities, from the EVENODD codes and B codes, which are array codes widely used in the RAID architecture. The schemes can tolerate up to two node failures and two eavesdropping nodes. For more general parameters we construct systematic secure RAID schemes from Reed-Solomon codes, and show that they are significantly more efficient than Shamir's secret sharing scheme. Our results suggest that building "keyless", information-theoretic security into the RAID architecture is practical.

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Communication Efficient Secret Sharing

Cited by 65 publications

References 25 publications

Distributed Multi-User Secret Sharing

Distributed Multi-User Secret Sharing

MDS Code Constructions with Small Sub-packetization and Near-optimal Repair Bandwidth

Secure RAID schemes for distributed storage

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