A novel secret sharing scheme using multiple share images

Xiaoping Li; Yanjun Liu; Hefeng Chen; Chin-Chen Chang

doi:10.3934/mbe.2019317

Mathematical Biosciences and Engineering, 2019, 16(6): 6350-6366. doi: 10.3934/mbe.2019317. Research article Special Issues

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A novel secret sharing scheme using multiple share images

Xiaoping Li, Yanjun Liu, Hefeng Chen, Chin-Chen Chang

1 School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China.
2 Department of Information Engineering and Computer Science, Feng Chia University, Taichung 407, Taiwan.
3 Computer Engineering College, Jimei University, Xiamen 361021, China

Received: , Accepted: , Published:

Special Issues: Security and Privacy Protection for Multimedia Information Processing and communication

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Secret image sharing has been widely applied in numerous areas, such as military imaging systems, remote sensing, and so on. One of the problems for image sharing schemes is to efficiently recover original images from their shares preserved by the shareholders. However, most of the existing schemes are based on the assumption that the shares are distortion-free. Moreover, the correspondence between secret images and their shares is definite. To overcome these shortcomings, we propose a novel secret sharing scheme using multiple share images based on the generalized Chinese remainder theorem (CRT) in this paper, where all of the shares are needed to recover the original images. Two categories of distortions are considered. In the first category, some pairs of shares with the same moduli are exchanged, while in the second category, some of pixels in the pairs of shares with the same moduli are exchanged. Based on these two sharing methods, we propose a generalized CRT based recovery method. Compared with the existing CRT based methods as well as combinatorial based methods, the proposed approach is much more efficient and secure. Furthermore, the conditions for successful recovery of two images from the given distorted shares are obtained. Simulations are also presented to show the efficiency of the proposed scheme.

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Keywords: secret image sharing; Chinese remainder theorem (CRT); generalized CRT; share image; reconstruction

Citation: Xiaoping Li, Yanjun Liu, Hefeng Chen, Chin-Chen Chang. A novel secret sharing scheme using multiple share images. Mathematical Biosciences and Engineering, 2019, 16(6): 6350-6366. doi: 10.3934/mbe.2019317

References:

1. R. L. Lagendijk, Z. Erkin and M. Barni, Encrypted signal processing for privacy protection: conveying the utility of homomorphic encryption and multiparty computation, IEEE Signal Proc. Mag., 30 (2013), 82–105.
2. C. C. Chang, C. T. Li and Y. Q. Shi, Privacy-aware reversible watermarking in cloud computing environments, IEEE Access, 6 (2018), 70720–70733.
3. A. Shamir, How to share a secret, Commun. ACM, 22 (1979), 612–613.
4. G. R. Blakley, Safeguarding cryptographic keys, in Proceedings of the National Computer Conference, (1979), 313–317.
5. E. Karnin, J. Greene and M. Hellman, On secret sharing systems, IEEE T. Inform. Theory, 29 (1983), 35–41.
6. W. T. Huang, M. Langberg, J. Kliewer, et al., Communication efficient secret sharing, IEEE T. Inform. Theory, 62 (2016), 7195–7206.
7. M. Naor and A. Wool, Access control and signatures via quorum secret sharing, IEEE Trans. Parallel Distrib. Syst., 9 (1998), 909–922.
8. M. Stadler, Publicly verifiable secret sharing, in International Conference on the Theory and Applications of Cryptographic Techniques, (1996), 190–199.
9. J. H. Ziegeldorf, O. G. Morchon and K. Wehrle, Privacy in the Internet of Things: threats and challenges, Security Commun. Netw., 7 (2014), 2728–2742.
10. M. Naor and A. Shamir, Visual cryptography, in Workshop on the Theory and Application of Cryptographic Techniques, Springer, (1994), 1–12.
11. X. Yan and Y. Lu, Generalized general access structure in secret image sharing, J. Vis. Commun. Image Represent., 58 (2019), 89–101.
12. L. Tan, Y. Lu, X. Yan, et al. Weighted secret image sharing for a (k,n) threshold based on the Chinese remainder theorem, IEEE Access, 7 (2019), 59278–59286.
13. C. C. Thien and J. C. Lin, Secret image sharing, Comput. Graph., 26 (2002), 765–770.
14. P. K. Meher and J. C. Patra, A new approach to secure distributed storage, sharing and dissemination of digital image, in International Symposium on Circuits and Systems, (2006), 373–376.
15. R. Z. Wang and S. J. Shyu, Scalable secret image sharing, Signal Process.-Image, 22 (2007), 363–373.
16. C. C. Chen, W. Y. Fu and C. C. Chen, A geometry-based secret image sharing approach, J. Inf. Sci. Eng., 24 (2008), 1567–1577.
17. C. C. Chen, W. Y. Fu and C. C. Chen, A sudoku-based secret image sharing scheme with reversibility, J. Commun., 5 (2010), 5–12.
18. X. Yan, Y. Lu, L. Liu, et al., Chinese remainder theorem-based two-in-one image secret sharing with three decoding options, Digit. Signal Process., 82 (2018), 80–90.
19. C. S. Tsai, C. C. Chang and T. S. Chen, Sharing multiple secrets in digital images, J. Syst. Softw., 64 (2002), 163–170.
20. H. C. Wu and C. C. Chang, Sharing visual multi-secret using circle shares, Comput. Stand. Interfaces, 28 (2005), 123–135.
21. T. H. Chen and C. S. Wu, Efficient multi-secret image sharing based on Boolean operations, Signal Process., 91 (2011), 90–97.
22. G. Alvarez, L. H. Encinas and A. M. Del Rey, A multisecret sharing scheme for color images based on cellular automata, Inf. Sci., 178 (2008), 4382–4395.
23. Z. Eslami, S. Razzaghi and J. Z. Ahmadabadi, Secret image sharing based on cellular automata and steganography, Pattern Recognit., 43 (2010), 397–404.
24. C. C. Chang, N. T. Huynh and H. D. Le, Lossless and unlimitted multi-image sharing based on Chinese remainder theorem and Lagrange interpolation, Signal Process., 99 (2014), 159–170.
25. C. Guo, H. Zhang, Q. Q. Song, et al., A multi-threshold secret sharing scheme based on the Chiense remainder theorem, Multimed. Tools Appl., 75 (2016), 11577–11594.
26. B. Arazi, A generalization of the Chinese remainder theorem, Pac. J. Math., 70 (1977), 289–296.
27. W. Wang, X. P. Li, X. G. Xia, et al., The largest dynamic range of a generalized Chinese remainder theorem for two integers, IEEE Signal Process. Lett., 22 (2015), 254–258.
28. X. P. Li, X. G. Xia, W. J. Wang, et al., A robust generalized Chinese remainder theorem for two integers, IEEE T. Inform. Theory, 62 (2016), 7491–7504.
29. K. H. Rosen, Elementary Number Theory and Its Applications, 5^th edition, Addison-Wesley, Mass., 2010.

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