Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions

M. van Dijk; T. Kevenaar; G.-J. Schrijen; P. Tuyls

doi:10.1016/j.ipl.2006.01.016

Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions

M. van Dijk, T. Kevenaar, G.-J. Schrijen, P. Tuyls

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

By using threshold schemes, λ-decompositions were introduced by Stinson [D.R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory IT-40 (1994) 118-125] and used to achieve often optimal worst-case information rates of secret sharing schemes based on graphs. By using the broader class of ramp schemes, (λ, ω)-decompositions were introduced in [M. van Dijk, W.-A. Jackson, K.M. Martin, A general decomposition construction for incomplete secret sharing schemes, Des. Codes Cryptogr. 15 (1998) 301-321] together with a general theory of decompositions. However, no improvements of existing schemes have been found by using this general theory. In this contribution we show for the first time how to successfully use (λ, ω)-decompositions. We give examples of improved constructions of secret sharing schemes based on connected graphs on six vertices. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	154-157
Journal	Information Processing Letters
Volume	99
Issue number	4
DOIs	https://doi.org/10.1016/j.ipl.2006.01.016
Publication status	Published - 31 Aug 2006
Externally published	Yes

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title = "Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions",

abstract = "By using threshold schemes, λ-decompositions were introduced by Stinson [D.R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory IT-40 (1994) 118-125] and used to achieve often optimal worst-case information rates of secret sharing schemes based on graphs. By using the broader class of ramp schemes, (λ, ω)-decompositions were introduced in [M. van Dijk, W.-A. Jackson, K.M. Martin, A general decomposition construction for incomplete secret sharing schemes, Des. Codes Cryptogr. 15 (1998) 301-321] together with a general theory of decompositions. However, no improvements of existing schemes have been found by using this general theory. In this contribution we show for the first time how to successfully use (λ, ω)-decompositions. We give examples of improved constructions of secret sharing schemes based on connected graphs on six vertices. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

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AU - van Dijk, M.

AU - Kevenaar, T.

AU - Schrijen, G.-J.

AU - Tuyls, P.

PY - 2006/8/31

Y1 - 2006/8/31

N2 - By using threshold schemes, λ-decompositions were introduced by Stinson [D.R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory IT-40 (1994) 118-125] and used to achieve often optimal worst-case information rates of secret sharing schemes based on graphs. By using the broader class of ramp schemes, (λ, ω)-decompositions were introduced in [M. van Dijk, W.-A. Jackson, K.M. Martin, A general decomposition construction for incomplete secret sharing schemes, Des. Codes Cryptogr. 15 (1998) 301-321] together with a general theory of decompositions. However, no improvements of existing schemes have been found by using this general theory. In this contribution we show for the first time how to successfully use (λ, ω)-decompositions. We give examples of improved constructions of secret sharing schemes based on connected graphs on six vertices. © 2006 Elsevier B.V. All rights reserved.

AB - By using threshold schemes, λ-decompositions were introduced by Stinson [D.R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory IT-40 (1994) 118-125] and used to achieve often optimal worst-case information rates of secret sharing schemes based on graphs. By using the broader class of ramp schemes, (λ, ω)-decompositions were introduced in [M. van Dijk, W.-A. Jackson, K.M. Martin, A general decomposition construction for incomplete secret sharing schemes, Des. Codes Cryptogr. 15 (1998) 301-321] together with a general theory of decompositions. However, no improvements of existing schemes have been found by using this general theory. In this contribution we show for the first time how to successfully use (λ, ω)-decompositions. We give examples of improved constructions of secret sharing schemes based on connected graphs on six vertices. © 2006 Elsevier B.V. All rights reserved.

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Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions

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