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Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme

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Listed:
  • Qindong Sun

    (School of Cyber Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China
    Shaanxi Key Laboratory of Network Computing and Security, Xi’an University of Technology, Xi’an 710048, China)

  • Han Cao

    (Shaanxi Key Laboratory of Network Computing and Security, Xi’an University of Technology, Xi’an 710048, China
    Department of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China)

  • Shancang Li

    (Department of Computer Science and Creative Technologies, University of the West of England, Bristol BS16 1QY, UK)

  • Houbing Song

    (Department of Electrical, Computer, Software and Systems Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA)

  • Yanxiao Liu

    (Department of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China
    Guangxi Key Laboratory of Trusted Software, Guilin University of Electronic Technology, Guilin 541004, China)

Abstract

Secret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise, nothing can be recovered at all. In most existing SIS schemes, the threshold on shadows for image reconstruction is fixed. However, in this work, we consider more complicated cases of SIS, such that the threshold is changeable according to the security environment. In this paper, we construct a ( k ↔ h , n ) threshold-changeable SIS (TCSIS) scheme using a bivariate polynomial, which provides h − k + 1 possible thresholds, k , k + 1 , … , h . During image reconstruction, each participant can update their shadow according to the current threshold T based only on their initial shadow. Unlike previous TCSIS schemes, the proposed scheme achieves unconditional security and can overcome the information disclosure problem caused by homomorphism.

Suggested Citation

  • Qindong Sun & Han Cao & Shancang Li & Houbing Song & Yanxiao Liu, 2022. "Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:710-:d:757297
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    References listed on IDEAS

    as
    1. Dong Xie & Lixiang Li & Haipeng Peng & Yixian Yang, 2017. "A Secure and Efficient Scalable Secret Image Sharing Scheme with Flexible Shadow Sizes," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-17, January.
    2. Lifeng Yuan & Mingchu Li & Cheng Guo & Weitong Hu & Xinjian Luo, 2016. "Secret Image Sharing Scheme with Threshold Changeable Capability," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-11, July.
    Full references (including those not matched with items on IDEAS)

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