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Detection of Cheaters in Vector Space Secret Sharing Schemes

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Abstract

A perfect secret sharing scheme is a method of distributing shares of a secret among a set P of participants in such a way that only qualified subsets of P can reconstruct the secret from their shares and non-qualified subsets have absolutely no information on the value of the secret. In a secret sharing scheme, some participants could lie about the value of their shares in order to obtain some illicit benefit. Therefore, the security against cheating is an important issue in the implementation of secret sharing schemes. Two new secret sharing schemes in which cheaters are detected with high probability are presented in this paper. The first one has information rate equal to 1/2 and can be implemented not only in threshold structures, but in a more general family of access structures. We prove that the information rate of this scheme is almost optimal among all schemes with the same security requirements. The second scheme we propose is a threshold scheme in which cheaters are detected with high probability even if they know the secret. The information rate is in this case 1/3 In both schemes, the probability of cheating successfully is a fixed value that is determined by the size of the secret.

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada i Telemàtica, Universitat Politècnica de Catalunya, Modul C3, Campus Nord, c/Jordi Girona, 1-3, 08034, Barcelona, Spain

    Jorge Luis Villar

Authors
  1. Carles Padro
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  2. Germán Sáez
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  3. Jorge Luis Villar
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Padro, C., Sáez, G. & Villar, J.L. Detection of Cheaters in Vector Space Secret Sharing Schemes. Designs, Codes and Cryptography 16, 75–85 (1999). https://doi.org/10.1023/A:1008378426278

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