資訊隱藏技術是結合了密碼技術與數位多媒體處理的重要研究領域。這些技術可廣泛應用於數位多媒體，特別是數字圖像。基於糾錯碼的資訊隱藏技術，是要提高信息嵌入率而且同時減少修改的位元的數目。到現在為止，研究基於糾錯碼的資訊隱藏技術的文獻已有很多，研究者們提出了大量有特定功能的各種方案，例如，使用漢明碼、BCH碼、Golay碼等的信息隱藏技術。基於這種矩陣編碼的資料隱藏(Matrix Code Data Hiding; MCDH)，是一種資訊隱藏機制由覆蓋函數構完成。 MCDH可以提高嵌入率並減少修改的位元數。
眾所周知的MCDH是以漢明碼 HC(n, k)為基礎，例如，利用覆蓋函數COV(1, n = 2k−1, k)被視為漢明碼資料隱藏(HDH)。此後，與HDH相比，具有更好的嵌入率的Hamming + 1 DH (H1DH)也被隨後提出。當考慮應用於像素域時，基於糾錯碼的資訊隱藏技術，與最低有效位元更動(Least Significant Bit; LSB) 和最佳像素調整步驟(Optimal Pixel Adjustment Process; OPAP)隱藏技術有極大的關聯性。事實上，這些方法只是從不同的面向來改變位元以嵌入秘密信息。
本論文整合了LSB、OPAP、H1DH的觀念，提出了Hamming + k資訊隱藏 (HkDH)方法，以及使用了重疊m個像素的HkDH方法(簡稱為Hk_mDH)。HkDH是在n個像素中嵌入2k個位元，嵌入前k個位元時，使用LSB置換，當嵌入後k個位元時，則修改2nd LSB，而修改2nd LSB會發生碰撞問題，這時則採用OPAP來解決。Hk_mDH是在2n−m個像素中嵌入2k個位元。嵌入前k個位元時，使用LSB置換，當嵌入後k個位元時，利用OPAP來修改重疊的m個像素，而修改的位置位於剩下的n−m個像素則同樣使用LSB置換。藉由重疊m個像素減少，我們可以減少更動但是降低了嵌入容量。

Data hiding (DH) is a significant research field which combines cryptography and digital multimedia processing. DH can widely used in digital multimedia, especially digi-tal images. Matrix code DH (MCDH) by covering function is based on error correcting code, which has high embedding efficiency, and meanwhile decreases the number of modified bits. Up to date, there are already MCDHs proposed. Most researches on MCDH uses using Hamming code, BCH code, and Golay code.
A we-known MCDH is based on Hamming coding HC(n, k), by covering function COV(1, n = 2k − 1, k), which is referred to as HDH. Afterwards, Hamming+ 1 DH (H1DH) was introduced, and it had a better embedding efficiency when compared with HDH. Consider DH on pixel domain. MCDH has a great relation with Least Significant Bit (LSB) and Optimal Pixel Adjustment Process (OPAP). In fact, these methods are very similar, but use different ways for modifying bits.
In this thesis, we propose Hamming+k DH (HkDH) and Hamming+k with m over-lapped pixels DH (Hk_mDH) which integrate the approaches of LSB, OPAP, and H1DH. HkDH may embed 2k secret bits in n pixels. It uses LSB substitution when embedding the first k bit, and then modified 2nd LSB when embed the second k bits. Modifying the 2nd LSB may have collision problem, we can use OPAP to solve it. On the other hand, Hk_mDH embeds 2k bits in (2n – m) pixels. It uses LSB substitution when embed the first k bits. When embedding the second k bits, the modifications in overlapped pixels adopt OPAP. The modifications in other (n – m) pixels still use LSB substitution. For Hk_mDH, we decrease modifications but reduce embedding capacity due to m over-lapped pixels.

第一章 Introduction 1
第一節 Background 1
第二節 Contribution of the Thesis 3
第三節 Organization of the Thesis 3
第二章 Previous Works 5
第一節 Matrix Coding (MC) Using Hamming Codes 5
第二節 Hamming Coding + 1 Data Hiding (H1DH) Scheme 6
第三節 Kim and Yang’s DH Scheme 8
第三章 Proposed HkDH scheme 11
第一節 HkDH Scheme Based on OPAP for Optimization 11
第二節 Hamming + k Scheme with m Overlapped Pixels 15
第三節 Theoretical Estimation of AMSE 18
第四章 Experiment and Comparison 25
第一節 Experimental Results 25
第二節 Comparison 31
第三節 Steganlysis 34
第五章 Conclusion and Future Work 37
References 39

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