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Detection and identification of cheaters in (t, n) secret sharing scheme

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Abstract

In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret. When shareholders present their shares in the secret reconstruction phase, dishonest shareholder(s) (i.e. cheater(s)) can always exclusively derive the secret by presenting faked share(s) and thus the other honest shareholders get nothing but a faked secret. Cheater detection and identification are very important to achieve fair reconstruction of a secret. In this paper, we consider the situation that there are more than t shareholders participated in the secret reconstruction. Since there are more than t shares (i.e. it only requires t shares) for reconstructing the secret, the redundant shares can be used for cheater detection and identification. Our proposed scheme uses the shares generated by the dealer to reconstruct the secret and, at the same time, to detect and identify cheaters. We have included discussion on three attacks of cheaters and bounds of detectability and identifiability of our proposed scheme under these three attacks. Our proposed scheme is an extension of Shamir’s secret sharing scheme.

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Authors and Affiliations

  1. Department of Computer Science and Electrical Engineering, University of Missouri, Kansas City, MO, 64110-2499, USA

    Lein Harn

  2. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Changlu Lin

  3. Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fujian, 350007, People’s Republic of China

    Changlu Lin

Authors
  1. Lein Harn
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  2. Changlu Lin
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Correspondence to Changlu Lin.

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Communicated by P. Wild.

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Harn, L., Lin, C. Detection and identification of cheaters in (t, n) secret sharing scheme. Des. Codes Cryptogr. 52, 15–24 (2009). https://doi.org/10.1007/s10623-008-9265-8

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  • DOI: https://doi.org/10.1007/s10623-008-9265-8

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