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Secret sharing schemes with detection of cheaters for a general access structure

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Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefits. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.

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This work was partially supported by spanish CICYT under project TIC97-0963.

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Author information

Authors and Affiliations

  1. Dep. Matemática Aplicada i Telemática, Universitat Politècnica de Catalunya, Mòdul C3, Campus Nord, c/Jordi Girona 1-3, 08034, Barcelona, Spain

    Sergio Cabello, Carles Padró & Germán Sáez

Authors
  1. Sergio Cabello
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  2. Carles Padró
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  3. Germán Sáez
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Cabello, S., Padró, C., Sáez, G. (1999). Secret sharing schemes with detection of cheaters for a general access structure. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_14

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  • DOI: https://doi.org/10.1007/3-540-48321-7_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

  • eBook Packages: Springer Book Archive

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