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Threshold Secret Sharing Through Multivariate Birkhoff Interpolation

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Computation, Cryptography, and Network Security

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Abstract

Secret sharing schemes have been well studied and widely used in different aspects of real life applications. The original secret sharing scheme was proposed by Adi Shamir in 1979. A similar scheme was also invented independently in the same year by George Blakley. Shamir’s scheme is based on Lagrange interpolation while Blakley’s approach uses principles of hyperplane geometry. In 2007, Tamir Tassa proposed a hierarchical secret sharing scheme through univariate Birkhoff interpolation (a generalization of Lagrangian and Hermitian interpolation). In the contribution at hand we investigate the idea of generalizing Tassa’s scheme through multivariate Birkhoff interpolation. We consider the problem of finding secret sharing schemes with multilevel structures and partially ordered sets of levels of participants. In order to ensure that our scheme meets the necessary requirements, we use totally nonsingular matrices.

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, GR-26110, Patras, Greece

    Vasileios E. Markoutis

  2. A.T.E.I. of Epirus, 110, GR-47100, Arta, Greece

    Gerasimos C. Meletiou

  3. Department of Informatics, University of Piraeus, 18534, Piraeus, Greece

    Aphrodite N. Veneti

  4. Computational Intelligence Laboratory (CILab), Department of Mathematics, University of Patras, GR-26110, Patras, Greece

    Michael N. Vrahatis

Authors
  1. Vasileios E. Markoutis
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  2. Gerasimos C. Meletiou
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  3. Aphrodite N. Veneti
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  4. Michael N. Vrahatis
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Correspondence to Vasileios E. Markoutis .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Engineering, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Markoutis, V.E., Meletiou, G.C., Veneti, A.N., Vrahatis, M.N. (2015). Threshold Secret Sharing Through Multivariate Birkhoff Interpolation. In: Daras, N., Rassias, M. (eds) Computation, Cryptography, and Network Security. Springer, Cham. https://doi.org/10.1007/978-3-319-18275-9_14

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