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

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Information Theoretic Security (ICITS 2013)

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

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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.

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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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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Teng Guo, Feng Liu, ChuanKun Wu, YaWei Ren & Wen Wang

  2. University of Chinese Academy of Sciences, Beijing, 100190, China

    Teng Guo, YaWei Ren & Wen Wang

  3. School of Information Management, Beijing Information Science and Technology University, Beijing, 100192, China

    YaWei Ren

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  1. Teng Guo
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  2. Feng Liu
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  3. ChuanKun Wu
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  4. YaWei Ren
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  5. Wen Wang
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Correspondence to Teng Guo .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Carles Padró

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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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