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On \((k, n)\) Visual Cryptography Scheme with \(t\) Essential Parties

Part of the Lecture Notes in Computer Science book series (LNSC,volume 8317)

Abstract

In visual cryptography schemes (VCS), we often denote the set of all parties by \(P=\{1,2,\cdots ,n\}\). Arumugam et al. proposed a \((k,n)\)-VCS with one essential party recently, in which only subset \(S\) of parties satisfying \(S\subseteq P\) and \(|S|\ge k\) and \(1\in S\) can recover the secret. In this paper, we extend Arumugam et al.’s idea and propose a \((k,n)\)-VCS with \(t\) essential parties, say \((k,n,t)\)-VCS for brevity, in which only subset \(S\) of parties satisfying \(S\subseteq P\) and \(|S|\ge k\) and \(\{1,2,\ldots ,t\}\in S\) can recover the secret. Furthermore, some bounds for the optimal pixel expansion and optimal relative contrast of \((k,n,t)\)-VCS are derived.

Keywords

  • Visual cryptography
  • Essential parties
  • Pixel expansion
  • Relative contrast

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Acknowledgments

This work was supported by 863 Program grant No. Y370071102, the “Strategic Priority Research Program” of the Chinese Academy of Sciences grant No. XDA06010701, the IIE’s Projects grant No. Y3Z001B102 and NSFC grant No. 61303256.

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Correspondence to Teng Guo .

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Guo, T., Liu, F., Wu, C., Ren, Y., Wang, W. (2014). On \((k, n)\) Visual Cryptography Scheme with \(t\) Essential Parties. In: Padró, C. (eds) Information Theoretic Security. ICITS 2013. Lecture Notes in Computer Science(), vol 8317. Springer, Cham. https://doi.org/10.1007/978-3-319-04268-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-04268-8_4

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