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An efficient XOR-based verifiable visual cryptographic scheme

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Abstract

Visual cryptographic (VC) schemes have been widely used in secure multimedia systems for data transmission and data storage. It divides a secret image into n random-seemingly share images printed on the transparencies. Superimposing the designed shares will display the recovered secret image which can be recognized by human visual system. It is very convenient to decode the secret since it requires no cryptographic knowledge and computation. However, there is a high chance for dishonest shareholders to present faked shares in the secret reconstruction phase, which would result in a huge damage to the honest shareholders. In this article, a secure approach to verify the cheating shares has been proposed to achieve fair reconstruction of the image secret. It is designed to share a verification image among the original shares of the XOR based VC scheme. It only increases pixel expansion by one to achieve the verification function. Cheating detection ability is attained by pairwise superimposing the shares so that any cheating behavior can be detected by the honest participant. The secret image is recovered and its recovered contrast becomes \(\frac {m}{m + 1}\) times of the original contrast where m denotes the pixel expansion of the original scheme. The verification image is probabilistically recovered and its recovered contrast is \(\frac {1}{2(m + 1)}\). Compared with traditional verifiable (k,n)-VC schemes against cheating, it overcomes the drawbacks such as requiring additional shares, additional large pixel expansion, or lower contrast. The experimental results show that the visual quality of the recovered secret image is as good as expected. The security analysis and comparative results based on various aspects of VC schemes demonstrate the better efficiency of the proposed approach over existing schemes.

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Acknowledgments

This work was supported in part by 2017 Teaching and Research Program of Lanzhou University under Grant No. 2017114, in part by the National Natural Science Foundation of China under Grant Nos. U1536102, U1536116, U1636219, and 61872289, in part by Plan for Scientific Innovation Talent of Henan Province (No. 2018JR0018) and the Science and Technology Program of Guangxi (No. 16380076), in part by China Mobile Research Fund Project (MCM20170407), and Key Laboratory of Digital Content Anti-Counterfeiting and Security Forensics of the state Administration of Press, Publication, Radio, Film and Television of the People’s Republic of China.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, China

    Xingxing Jia & Qimeng Chu

  2. School of Computing, Tsinghua University, Beijing, China

    Daoshun Wang

  3. School of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an, Shaanxi, China

    Zhenhua Chen

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  1. Xingxing Jia
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  2. Daoshun Wang
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  3. Qimeng Chu
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  4. Zhenhua Chen
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Correspondence to Xingxing Jia.

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Jia, X., Wang, D., Chu, Q. et al. An efficient XOR-based verifiable visual cryptographic scheme. Multimed Tools Appl 78, 8207–8223 (2019). https://doi.org/10.1007/s11042-018-6779-6

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