資料隱藏是被廣泛運用的資訊安全技術。嵌入的秘密容量、以及隱寫圖像的影 像品質是兩格評估資料隱藏技術的重要指標。在 2006 年， Zhang 和 Wang 等人 提出了 Exploiting Modification Direction (EMD) 的概念。隨後，Kuo 和 Wang 等人 延伸 EMD 的方法至 Generalized EMD (GEMD)方法，改進了 EMD 的嵌入容量。 GEMD方法，能在入n 個載體像素 (coverpixel) 嵌入 n+1 個位元。在2016年， Kuo 等人更進一步提出植基於 Sparse Modified Signed-Digit (SMSD)，把秘密資料 嵌入 n 個載體像素隱藏技術。相較之前的 EMD 以及 Generalized EMD (GEMD) 方法，SMSD 的方法達到了更高的嵌入量和更好的隱寫影像品質。
在這篇論文中，我們提出了兩種新的 Enhanced MSD (EMSD) 的資料隱藏技 術，EMSD-I 與 EMSD-II。這兩種方法基本是源自於 SMSD，但是放寬了 SMSD 的 “1”不能相鄰的限制。他們能比基於 SMSD 的資料隱藏技術有更好的嵌入量以 及維持著隱寫圖像的品質。當 SMSD 有連續的 “1”有些值就無法表示，EMSD 使 用了「摺疊」的概念來解決，可以使得原本沒有辦法表示的數字在採用適當的模除 計算就能表示。如此一來，使用 EMSD 便可以進一步的提高嵌入量。
EMSD-I是基於 SMSD 並只使用了一個「摺疊」點的特性。有別於 EMSD-I， EMSD-II不只使用了一次摺疊，而是根據 n 的大小，儘可能使用多個「摺疊」點以 增加嵌入量。隨著 n 變得越大，EMSD-II的資訊嵌入量在隨著 n 越來越大時會比 EMSD-I更多。本論文的貢獻是對 n 值推導出「摺疊」點，以及模除值的通識。最 後，得到的結論是 EMSD-II 是一個通則的資料隱藏方法，而 EMSD-I 是 EMSD-II 的特例。

Data hiding (DH) is widely used in information security area. Embedding capacity and visual quality of stego-image are two major evaluations for DH. In 2006, Zhang and Wang first proposed the notion of Exploiting Modification Direction (EMD) to implement DH. Subsequently, Kuo and Wang extend EMD to Generalized EMD (GEMD) based to design DH, which has more embedding capacity when compared with EMD. GEMD embeds (n+1) bits data into n cover pixels. Then, Kuo et al. further propose a Sparse Modified Signed-Digit (SMSD) to design DH using of n cover-pixels each time. Compared with EMD and GEMD, SMSD based DH achieves the higher embedding capacity and the better stego-image quality.
In this thesis, we introduce two Enhanced MSD (EMSD) based DHs, referred to as EMSD-I and EMSD-II. These two DHs are based on SMSD. As we know, SMSD has the property that there is no adjacent “1”. However, our EMSD based DH uses a SMSD allowing the neighbor “1”s. EMSD-I and EMSD-II based DHs have more embedding capacities than SMSD based DH, and meanwhile retains the visual quality of stego-image. In fact, when using the SMSD with adjacent “1”s, there are some values that cannot be represented. In the proposed EMSD, we solve this problem by applying the notion of “folding”, which means choose the appropriate modulus number. Finally, the unrepresented values can be represented by another value after modular operation. As a result, we have more embedding capacity when using this type of SMSD with adjacent “1”s.
EMSD-I is an extension of SMSD, which only uses the “folding” point once. On the other hand, EMSD-I uses the folding points as many times as possible according to various values of n. It is obvious that as n gets larger, the embedding capacity of EMSD-II will be much larger than EMSD-I. Our contribution is to figure out “folding” points for various values of n, and theoretically find the modulus number in EMSD-II. As a conclusion, EMSD-II based DH is a generalized form using SMSD with adjacent “1”s, and EMSD-I is a special case of EMSD-II.

第一章 Introduction 1
1.1 Background 1
1.2 Contribution of the thesis 2
1.3 Organization of the thesis 3
第二章 Preliminaries 5
2.1 EMD based data hiding methods 5
2.2 Sparse MSD data hiding 8
第三章 Proposed EMSD Scheme 11
第四章 Evaluation and Comparisons 25
第五章 Conclusion and Future Work 31
第六章 Appendix 33
第七章 References 35

[FRID01] J. Fridrich, M. Golijan, R. Du, “Reliable detection of LSB steganography in grayscale and color images.” In: ACM Workshop on Multimedia and Security, pp. 27-30, 2001.
[JEDW89] J. Jedwab, C.J. Mitchell. “Minimum weight modified signed-digit representations and fast exponentiation.” Electronics Letters, Vol.25, no.17, pp.1171-1172, 1989.
[KUO13] W.C. Kuo, C.C. Wang. “Data hiding based on generalized exploiting modification direction method.” Image Science Journal, Vol.61, no.6, pp.484-490, 2013.
[KUO14] W.C. Kuo, Y.H. Chen, C.T. Chuang. “High-capacity steganographic method based on division arithmetic and generalized exploiting modification direction, ” Journal of Information Hiding and Multimedia Signal Processing, Vol.5, no.2, pp.213-222, 2014.
[KUO16] W.C. Kuo, C.C. Wang, H.C. Hou. “Signed digit data hiding scheme, ” Information Processing Letters, Vol.116, no.2, pp.183-191, 2016.
[LEE07] C.F. Lee, Y.R. Wang, C.C. Chang, “A steganographic method with high embedding capacity by improving exploiting modification direction.” In: the Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing, pp.497-500, 2007.
[WANG10] J. Wang, Y. Sun, H. Xu, K. Chen, H.J. Kim, S.H. Joo. “An improved section-wise exploiting modification direction method, ” Signal Processing, Vol.90, no.11, pp.2954-2964, 2010.
[WANG12] X.T. Wang, C.C. Chang, C.C. Lin, M.C. Li, “A novel multi-group exploiting direction method based on switch map, ” Signal Processing, Vol.92, no.6, pp.1525-1535, 2012.
[WANG17] C.C. Wang, W.C. Kuo, Y.C.Huang, L.C. Wuu. “A high capacity data hiding scheme based on re-adjusted GEMD, ” Multimedia Tools and Applications, Vol.8, pp.1-15, 2017.
[ZHAN06] X. Zhang, S. Wang. “Efficient steganographic embedding by exploiting modification direction.” IEEE Communication Letters, Vol.10. no.11, pp.781-783, 2006.