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Secret image sharing based on cellular automata and steganography. (English) Zbl 1186.94477
Summary: Recently, C. Lin and W. Tsai [(*) “Secret image sharing with steganography and authentication”, J. Syst. Softw. 73, 405–414 (2004)] and C. Yang, T. Chen, K. Yu and C. Wong [(**)“Improvements of image sharing with steganography and authentication”, J. Syst. Softw. 80, 1070–1076 (2007)] proposed secret image sharing schemes combining steganography and authentication based on Shamir’s polynomials. The schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants. To achieve better authentication ability, C. Chang, Y. Hsieh and C. Lin [(***) “Sharing secrets in stego images with authentication”, Pattern Recognition 41, 3130–3137 (2008; Zbl 1147.68503)] proposed an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1/16.
In this paper, we employ linear cellular automata, digital signatures, and hash functions to propose a novel \((t,n)\)-threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255/256. Employing cellular automata instead of Shamir’s polynomials not only improves computational complexity from \(O(n\log ^2 n)\) to \(O(n)\) but obviates the need to modify pixels of cover images unnecessarily. Compared to previous methods [(*), (**), and (***)], we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed. We further present some experimental results.

MSC:
94A62 Authentication, digital signatures and secret sharing
68Q80 Cellular automata (computational aspects)
68U10 Computing methodologies for image processing
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[1] Lin, C.; Tsai, W., Secret image sharing with steganography and authentication, The journal of systems and software, 73, 405-414, (2004)
[2] Yang, C.; Chen, T.; Yu, K.; Wang, C., Improvements of image sharing with steganography and authentication, The journal of systems and software, 80, 1070-1076, (2007)
[3] Chang, C.; Hsieh, Y.; Lin, C., Sharing secrets in stego images with authentication, Pattern recognition, 41, 3130-3137, (2008) · Zbl 1147.68503
[4] N. Noar, A. Shamir, Visual cryptography, Advances in Cryptology: Eurocrypt’94, vol. 48, Springer, Berlin, 1995, pp. 1-12.
[5] Stinson, D., Visual cryptography and threshold schemes, IEEE potentials, 18, 13-16, (1999)
[6] Shyu, S., Efficient visual secret sharing scheme for color images, Pattern recognition, 39, 866-880, (2006) · Zbl 1105.68454
[7] Yang, T.C.C.N., Aspect ratio invariant visual secret sharing schemes with minimum pixel expansion, Pattern recognition, 26, 2, 193-206, (2005)
[8] Wu, Y.; Thien, C.; Lin, J., Sharing and hiding sector images with size constraint, Pattern recognition, 37, 1377-1385, (2004)
[9] Shamir, A., How to share a secret, Communications of the ACM, 22, 612-613, (1979) · Zbl 0414.94021
[10] Blakley, G., Safeguarding cryptographic keys, AFIPS conference Proceedings, 48, 313-317, (1979)
[11] Chang, C.; Chen, T.; Chung, L., A steganographic method based upon JPEG and quantization table modification, Information sciences, 141, 123-138, (2002) · Zbl 1021.68589
[12] Johnson, N.; Jajodia, S., Exploring steganography: seeing the unseen, IEEE comput., 31, 2, 26-34, (1998)
[13] Marvel, L.M.; Boncelet, C.G.; Retter, C.T., Spread spectrum image steganography, IEEE transactions on image process, 8, 8, 1075-1083, (1999)
[14] Wu, D.; Tsai, W., A steganographic method for images by pixel-value differencing, Pattern recognition letters, 24, 9-10, 1613-1626, (2003) · Zbl 1048.68040
[15] Chan, C.; Cheng, L., Hiding data in images by simple LSB substitution, Pattern recognition, 37, 3, 474-496, (2004) · Zbl 1072.68534
[16] Chang, C.; Hsiao, J.; Chan, C., Finding optimal least-significant-bits substitution in image hiding by dynamic programming strategy, Pattern recognition, 36, 7, 1583-1595, (2003)
[17] Wang, R.; Lin, C.; Lin, J., Image hiding by optimal LSB substitution and genetic algorithm, Pattern recognition, 34, 3, 671-683, (2001) · Zbl 1012.68882
[18] Chang, C.; Chan, C.; Fan, Y., Image hiding scheme with modulus function and dynamic programming, Pattern recognition, 39, 6, 1155-1167, (2006) · Zbl 1096.68756
[19] Thien, C.; Lin, J., A simple and high-hiding capacity method for hiding digitby-digit data in images based on modulus function, Pattern recognition, 36, 12, 2875-2881, (2003) · Zbl 1059.68154
[20] Wang, S.J., Steganography of capacity required using modulo operator for embedding secret image, Applied mathematics and computation, 164, 1, 99-116, (2005) · Zbl 1070.94020
[21] Thien, C.; Lin, J., An image-sharing method with user-friendly shadow images, IEEE transactions on circuits systems, 1161-1169, (2003)
[22] del Rey, A.M.; Mateus, J.P.; Sanchez, G.R., A secret sharing scheme based on cellular automata, Applied mathematics and computation, 170, 1356-1364, (2005) · Zbl 1083.94536
[23] G. Álvarez Marañón, L.H. Encinas, A.M. del Rey, Sharing secret color images using cellular automata with memory, CoRR 0312034 (2003).
[24] Aho, A.; Hopcroft, J.; Ullman, J., The design and analysis of computer algorithms, (1974), Addison-Wesley Reading, MA
[25] Toffoli, T.; Margolus, N., Invertible cellular automata: a review, Physica D, 45, 229-253, (1990) · Zbl 0729.68066
[26] Alonso-Sanz, R., Reversible cellular automata with memory: two dimensional patterns from a single seed, Physica D, 175, 1-30, (2003) · Zbl 1008.37008
[27] Thien, C.; Lin, J., Secret image sharing, Computer graphics, 26, 5, 765-770, (2002)
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