Multimedia Tools and Applications

, Volume 77, Issue 16, pp 20569–20596 | Cite as

Greyscale-images-oriented progressive secret sharing based on the linear congruence equation

  • Lintao LiuEmail author
  • Yuliang Lu
  • Xuehu YanEmail author
  • Huaixi Wang


Secret image sharing (SIS) can be applied to protect a secret image when the secret is transmitted in public channels. However, classic SIS schemes, e.g., visual secret sharing (VSS) and Shamir’s polynomial-based scheme, are not suitable for progressive encryption of greyscale images, because they will lead to many problems, such as “All-or-Nothing”, lossy recovery, complex computations and so on. Based on the linear congruence equation, three novel progressive secret sharing (PSS) schemes are proposed to overcome these problems: (k, k) threshold LCSS and (k, n) threshold LCPSS aim to achieve general threshold progressive secret sharing with simple computations. Furthermore, extended LCPSS (ELCPSS) is developed to generate meaningful shadow images, which enable simple management and misleading the enemy. Both theoretical proofs and experimental results are given to demonstrate the validity of the proposed scheme.


Secret sharing Progressive secret sharing Greyscale image Linear congruence Simple computations 



The authors wish to thank the anonymous reviewers for their suggestions to improve this paper.

This work is supported by the National Natural Science Foundation of China (Grant Number: 61602491).


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.National University of Defense TechnologyHefeiChina

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