Hierarchical visual cryptography for multisecret images based on a modified phase retrieval algorithm

  • Tieyu ZhaoEmail author
  • Yingying Chi


Visual cryptography is generally based on the base matrix scheme or the random grid scheme. These schemes may cause some problems, such as the expansion of the shares and the recovered images and the distortion of the recovered images. In this paper, we propose a modified phase retrieval algorithm and present a hierarchical visual cryptography scheme (HVCS). The scheme overcomes the problems that are mentioned and can share multiple secret images. Considering the differences in the social division of labor, there is a hierarchy between the shared images in the proposed scheme, that is, the participants have different rights. Further, to make the proposed scheme more applicable to practical needs, we propose a generalized HVCS by modifying the phase retrieval algorithm again so that each level can have more than one participant. The effectiveness and feasibility of the proposed scheme are verified by theoretical analysis and numerical simulation.


Secret sharing Visual cryptography Multiple secrets sharing Phase retrieval algorithm 



The authors would like to thank the reviewers for their valuable comments. This study was supported by the National Natural Science Foundation of China (No. 61702088); the Central University Basic Research Service Fees, China (No. N172303014); and the School PhD Fund, Northeastern University, Qinhuangdao, China (XNB201708).


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© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Information Science Teaching and Research SectionNortheastern University at QinhuangdaoQinhuangdaoChina

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