Prepositioned Shared Secret and/or Shared Control Schemes

Simmons, Gustavus J.

doi:10.1007/3-540-46885-4_44

Cited by 33 publications

(16 citation statements)

References 14 publications

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“…These participants are then effectively "sleeping participants" until the time of enrollment, when the dealer broadcasts their share to them, encrypted under the key that they were issued at setup. This is essentially the same technique used in [18] to remotely activate threshold schemes.…”

Section: A Enrollmentmentioning

confidence: 99%

Updating the Parameters of a Threshold Scheme by Minimal Broadcast

Barwick

Jackson

Martin

2005

IEEE Trans. Inform. Theory

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Abstract-Threshold schemes allow secret data to be protected among a set of participants in such a way that only a prespecified threshold of participants can reconstruct the secret from private information (shares) distributed to them on a system setup using secure channels. We consider the general problem of designing unconditionally secure threshold schemes whose defining parameters (the threshold and the number of participants) can later be changed by using only public channel broadcast messages. In this paper, we are interested in the efficiency of such threshold schemes, and seek to minimize storage costs (size of shares) as well as optimize performance in low-bandwidth environments by minimizing the size of necessary broadcast messages. We prove a number of lower bounds on the smallest size of broadcast message necessary to make general changes to the parameters of a threshold scheme in which each participant already holds shares of minimal size. We establish the tightness of these bounds by demonstrating optimal schemes.

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Section: A Enrollmentmentioning

confidence: 99%

Updating the Parameters of a Threshold Scheme by Minimal Broadcast

Barwick

Jackson

Martin

2005

IEEE Trans. Inform. Theory

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“…All you have to do is to envision a system of equations that corresponds to the particular scheme. Some excellent papers on generalized secret-sharing schemes are [1462,1463,1464].…”

Section: Advanced Threshold Schemesmentioning

confidence: 99%

Applied cryptography: Protocols, algorithms, and source code in C

1994

Computer Law & Security Review

771

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“…among n participants in such a way that any I; of them can recover tlie secret, but any k -1, or fewer, have absolutely no information on the secret (see [26] for a compreherisive bibliography on (k, 71) tlireshold schemes).…”

Section: Introductionmentioning

confidence: 99%

“…The idea of protecting against cheating by one or more participants is addressed in [IS], (261, [19], [23] and [O]. €'repositioned schemes are studied in [26].…”

Section: Introductionmentioning

confidence: 99%

Graph Decompositions and Secret Sharing Schemes

Blundo

Santis

Stinson

et al. 1993

Advances in Cryptology — EUROCRYPT’ 92

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A b s t r a c tIn this paper, we continue a study of secret sliaring schemes for access structures based on graphs. Given a graph G, we require that a subset of participants can compnte a secret key if llley contain an edge of G; otherwise, they can obtain no information regarding the key. We study the information rate of such schemes, which mensiires how much information is being distributed as shares as compared to the size of the secret key, and the average information rate, which is the ratio between the secret size and the arithmetic mean of the size of the shares. We give both upper and lower bounds on the optimal information rate and average information rate that can be obtained. Upper bounds arise by applying entropy arguments due to Capocelli e t al [lo]. Lower bounds come from constructions that are based on graph decompositions. Application of these constructions requires solving a particular linear programming problem. We prove some general results concerning the information rate and avcrage iiiforniation rate for paths, cycles and trees. Also, we study the 30 (connected) graphs on a t most five vertices, obtaining exact values for the optimal information rate in 26 of the 30 cases, and for the optinid average information rate in 28 of the 30 cases.

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Prepositioned Shared Secret and/or Shared Control Schemes

Abstract: Secret sharing is simply a special form of key distribution.

Cited by 33 publications

References 14 publications

Updating the Parameters of a Threshold Scheme by Minimal Broadcast

Updating the Parameters of a Threshold Scheme by Minimal Broadcast

Applied cryptography: Protocols, algorithms, and source code in C

Graph Decompositions and Secret Sharing Schemes

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