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International Conference on Information and Communications Security

ICICS 1999: Information and Communication Security pp 71–86Cite as

Linear Secret Sharing with Divisible Shares

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1726))

Abstract

Shamir secret sharing is being considered in the broader context of linear secret sharing. It is shown that any Shamir scheme built over GF(q v) can be converted into its linear equivalent defined over GF(q). A notion of uniform perfectness is introduced and it is proved that Shamir schemes built over GF(q v) are not uniformly perfect. Probabilistic linear secret sharing is next studied and bounds on probability that the resulting secret sharing is uniformly perfect are given. The probabilistic arguments are later used to show that secret sharing with shift derived from Shamir scheme allows to achieve a secret sharing which is uniformly perfect.

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Author information

Authors and Affiliations

  1. Centre for Computer Security, Research School of Information Technology and Computer Science, University of Wollongong, Northfields Avenue, Wollongong, 2522, Australia

    Josef Pieprzyk

Authors
  1. Josef Pieprzyk
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Editor information

Editors and Affiliations

  1. Macquarie University, Sydney, Australia

    Vijay Varadharajan

  2. Centre for Computer and Information Security Research School of Computer Science and Software Engineering, University of Wollongong, Australia

    Yi Mu

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© 1999 Springer-Verlag Berlin Heidelberg

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Pieprzyk, J. (1999). Linear Secret Sharing with Divisible Shares. In: Varadharajan, V., Mu, Y. (eds) Information and Communication Security. ICICS 1999. Lecture Notes in Computer Science, vol 1726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47942-0_7

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  • DOI: https://doi.org/10.1007/978-3-540-47942-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66682-0

  • Online ISBN: 978-3-540-47942-0

  • eBook Packages: Springer Book Archive

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