In this thesis, we implement a (k, n) secret image sharing algorithm based on Thien and Lin’s scheme with modifications to reduce some distortion. The secret image is processed and split into n shadow images. We can reconstruct the secret image by using Lagrange interpolation when we collect k or more shadow images. Firstly, we propose an elegant method using the concept of generators in a multiplicative cyclic group to shuffle the secret image. The security is based on the difficulty of solving the discrete logarithm problem. We also present a truncated method to reduce the truncation distortion. We replace zero points in the range [0, 250] with those grayscale of pixels greater than 250 with positions of zero occurrences under 251. Experimental results show that the proposed method can suffer from the truncation distortion while preserves the security.

Chapter 1 Introduction 1
Chapter 2 Secret Image Sharing Based on (k, n)-Threshold Scheme 4
2.1 Methodology 4
2.1.1 The image sharing algorithm 4
2.1.2 The image recovering algorithm 5
2.2 Analysis 6
2.2.1 Suppression 6
2.2.2 Security 6
2.2.3 Discussion 7
Chapter 3 Proposed Secret Image Sharing Methods 9
3.1 The proposed secret image sharing method 9
3.1.1 Improvement of security 9
3.1.2 To reduce the truncation distortion 11
3.2 The proposed secret image recovering method 13
Chapter 4 Experimental Results 15
Chapter 5 Conclusion and Future Work 21
References 22

[Blak1979] G.R. Blakley, “ Safeguarding cryptographic keys,” Proceedings of the National Computer Conference, New York, American Federation of Information Processing Societies, vol. 48, 313-317, 1979.
[Chan2008] C.C. Chang, Y.P. Hsieh, and C.H. Lin,” Sharing secrets in stego images with authentication,” Pattern Recognition, vol. 41, no. 10, 3130-3137, 2008.
[Chen2009] C.C. Chen, C.C. Chen, and Y.C. Lin, “Weighted modulated secret image sharing method,” Journal of Electronic Imaging, vol. 18, no. 4, 1-6, 2009.
[John1998] N.F. Johnson and S. Jajodia, “Exploring steganography: Seeing the Unseen,” IEEE Computer, vol. 31, no. 2, 26-34, 1998.
[Lin2003] C.C. Lin and W.H. Tsai, “Visual cryptography for gray-level images by dithering techniques,” Pattern Recognition Letters, vol. 24, no. 1-3, 349-358, 2003.
[Lin2004] C.C. Lin and W.H. Tsai, “Secret image sharing with steganography and authentication,” Systems and Software, vol. 73, no. 3, 405-414, 2004.
[Naor1995] M. Naor and A. Shamir, “Visual Cryptography advances in Cryptology,” in Eurpocrypt’94, 1-12, Springer-Verlag, Berlin, 1995.
[Podi2001] C.I. Podilchuk and E.J. Delp, “Digital Watermarking: Algorithms and Applications,” IEEE Signal Processing Magazine, vol. 18, no. 4, 33-46, 2001.
[Sham1979] A. Shamir, “How to share a secret,” Communications of the ACM, vol. 22, no. 11, 612-613, 1979.
[Stin1999] D. Stinson, “Visual cryptography and threshold schemes,” IEEE Potential, vol. 18, no. 1, 13-16, 1999.
[Thie2002] C.C. Thien and J.C. Lin, “Secret image sharing,” Computer & Graphics, vol. 26, no.1 765-770,2002.
[Thie2003] C.C. Thien and J.C. Lin, “An Image-Sharing method with user-friendly shadow images,” IEEE Transactions on Circuits and. Systems for Video Technology, vol. 13, no. 12, 1161-1169, 2003.
[Wang2006] R.Z. Wang and C.H. Su, “Secret image sharing with smaller shadow images,” Pattern Recognition Letters, vol. 27 no. 6, 551-555, 2006.
[Yang2004] C.N. Yang, “New Visual Secret Sharing Schemes Using Probabilistic Method,” Pattern Recognition Letters, vol. 25, no. 4, 481-494, 2004.
[Yang2007a]C.N. Yang, T.S. Chen, and C.C. Wang, “Improvements of image sharing with steganography and authentication,” Systems and Software, vol. 80, no. 7, 1070-1076, 2007.
[Yang2007b]C.N. Yang, K.H. Yu, and R. Lukac, “User-Friendly Image Sharing Using Polynomials with Different Primes,” Imaging Systems and Technology, vol. 17, no. 1, 40-47, 2007.
[web01]http://en.wikipedia.org/wiki/Lagrange_interpolation, last access on May 27, 2010.
[web02]http://en.wikipedia.org/wiki/Discrete_logarithm, last access on May 27, 2010.