由於資訊科技快速成長，我們可以即時的透過網路得到大量的資訊。然而一些秘密資訊不能被公開，因此資訊安全則扮演著一個重要的角色。一個叫做(k, n)門檻方法的秘密影像分享是一個較佳的方法能用來保護秘密影像。這項技術將秘密影像分成n張子影像，並由n個參與者保管。假如我們收集到k張的子影像就可以還原出秘密影像，如果只收集到少於k張的子影像，則無法還原秘密影像。
在本篇論文中，我們根據Ulutas [Ulut2009]的方法實作了一個影像分享及還原的系統，我們使用彩色影像作為秘密影像，並且使用中國餘式定理來還原秘密影像。在我們所提出的方法中需要額外的影像來確保可以還原出無失真的秘密影像。但假如缺少該張影像，我們仍然可以還原出與秘密影像非常相似的失真影像，其與秘密影像只有一個位元的差異。在實驗結果中，這兩張影像的PSNR值可以達到50dB以上。這表示我們所提出的秘密影像分享方法是非常有效的。

Due to the fast growth of information technology, we can get plenty of information over the Internet in time. However, some secret information cannot be released in public. Thus, information security plays an important role. A (k, n) threshold scheme for secret image sharing might be a useful method to protect a secret image. It distributes a secret image to n shadow images preserved by n participants. If we collect at least k shadow images, we can reveal the secret image. Fewer than k shadow images cannot reveal the secret image.
In this thesis, based on Ulutas’s scheme [Ulut2009], we implement a useful image sharing and revealing system which uses color image as secret image and Chinese remainder theorem to reveal the secret image. The proposed method needs a necessary image to ensure that we can reveal the lossless secret image. However, if we do not use the necessary image, we can still reveal the distortion image with only the difference of the least significant bit. In the experimental results, we demonstrate the PSNR value between an original image and the revealed image is over 50 dB. It shows that the proposed approach is a simple but efficient secret image sharing approach.

[Asmu1983] C. Asmuth and J. Bloom, “A Modular Approach to Key Safeguarding,” IEEE Trans. On Information Theory, Vol. 29, No. 2, 208-210, 1983.
[Blak1979] G.R. Blakley, “Safeguarding cryptographic keys,” Proceedings of the National Computer Conference, American Federation of Information Proceeding Societies, Vol. 48, 313-317, 1979.
[Mign1983] M. Mignotte, “How to share a secret,” In T. Beth, editor, Lecture Notes in Computer Science, Vol. 149, 371-375, 1983.
[Sham1979] A. Shamir, “How to share a secret,” Communications of the ACM, Vol. 22, No.11, 612-613, 1979.
[Shyu2008] S.J. Shyu and Y.R. Chen, “Threshold Secret Image Sharing by Chinese Remainder Theorem,” IEEE Asia-Pacific Services Computing Conference, 1332-1337, 2008.
[Thie2002] C.C. Thien and J.C. Lin, “Secret image sharing,” Computer & Graphics, Vol. 26, No.1 765-771, 2002.
[Trap2006] W. Trappe and L.C. Washington, Introduction to Cryptography with Coding Theory, Pearson International Edition, 2006.
[Tsai2013] M.H. Tsai and C.C. Chen, “A Study on Secret Image Sharing,” The Sixth International Workshop on Image Media Quality and Its Applications, 135-139, 2013.
[Ulut2009] M. Ulutas, V.V. Nabiyev, and G. Ulutas, “A New Secret Image Sharing Technique Based on Asmuth Bloom’s Scheme,” Application of Information and Communication Technologies, 1-5, 2009.
[Web01] http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html, last access on March 17, 2014.
[Web02] http://en.wikipedia.org/wiki/Secret_sharing, last access on March 17, 2014.
[Web03] http://en.wikipedia.org/wiki/Secret_sharing_using_the_Chinese_remaind
er_theorem, last access on March 17, 2014.