視覺密碼於1995年由Naor and Shimir提出，是一個簡單的影像加密方式。透過視覺密碼的加密方法，可以將機密影像分解到數張分享影像上，當疊合指定張數的分享影像後，靠我們的肉眼就可以看到機密影像的內容。解密的過程不需要電腦的輔助，使用者也不需要相關的背景知識。但使用視覺密碼來加密影像最大的缺點就像素擴展的問題，尤其在處理彩色的圖片或是產生有意義的分享影像時，像素擴展倍數就更大。
Kafri and Keren (1987)提出一個像素不擴展視覺密碼方法，稱之為隨機網格視覺密碼。隨機網格的視覺密碼利用機率的概念去分配分享影上的黑點與白點，當疊合分享影像後，屬於黑色與白色的區域會有不同比率的黑點，因此可以看出機密影像的內容。隨機網格視覺密碼的相關研究大部分都是產生雜訊式(noise-like)的分享影像為主，鮮少為有意義的分享影像相關研究。這些研究的方法有諸多的使用限制，且都無法讓分享影像和疊合影像上的色差達到理論上的最大值，造成影像的對比品質下降。
本研究由雜訊式的分享方法延伸到有義意式的分享方法，分析了分享影像與疊合影像上黑點比率的關係，找出能在疊合影像上產生最佳色差對比的黑點機率配置方法，藉此提出一個以機率為基礎的有意義視覺密碼模型。我們的方法掩蓋影像(cover image)數目可以不受限制，且可以實作出多種色差對比的影像。最重要的是提升了影像的視覺品質，讓分享影像與疊合影像的色差對比都可以達到理論上的最大值，優於其他的相關研究。

Visual Cryptography (VC) is a simple image encryption method, which proposed by Naor and Shimir in 1995. This method can encode the secret image into n shares. The secret will be decrypted by human eye when at least any k shares are stacked together, while any less than k shares can reveal no information about the secret . In decrypt process, people need neither computer computation nor any knowledge about VC. But the biggest drawback of VC is the pixel expansion problem, especially in dealing with the color image, or generating the meaningful shares, which will get an even larger pixel expansion ratio.
Kafri and Keren (1987) presented a visual secret sharing method without pixel expansion, called random-grid visual secret sharing (RGVSS), which uses the concept of probability to allocate the black and white pixel in share-image. When we superimpose all shares, the ratio of black pixel in black region is greater than the white region, therefore, the secret in the stack-image can be clearly seen by our eyes. However, most of the RGVSS researches are about generating the noise-like shares rather than generating the meaningful shares. There are not only many restrictions in encoding secret but also degrading the image contract . 
This study will discuss noise-like sharing method first and then reduce to meaningful sharing method. We first analyzed the distribution of the black pixels on the share-image and the stack-image. A probability allocation method was then proposed which can produce the best contract in both of the share-image and the stack-image. Our meaningful module can not only use different cover images for disguised, but also has the ability for setting a variety of contrast as we needed. The most important result is that this study raises the visual quality for both of the share-image and the stack-image and can achieve to their theoretical maximum. To conclude, our meaningful visual secret sharing module is superior to other related researches.

中文摘要	I
Abstract	III
目錄	V
圖目錄	VII
表目錄	VIII
第一章 導論	1
1.1研究背景與動機	1
1.2研究目標	5
1.3研究架構	5
第二章 文獻探討	7
2.1 視覺密碼基本原理	7
2.2不擴展視覺密碼	9
2.3通用型存取結構(General Access Structures)	11
2.4隨機網格(Random Grid)	12
2.5有意義分享影像的視覺密碼	15
2.6擴充型通用存取結構	18
2.7有意義的隨機網格(Friendly Random Grid Visual Secret Sharing)	18
第三章 研究方法	21
3.1 雜訊式的視覺密碼分析	21
3.2雜訊式的視覺密碼方法	23
3.3有意義的視覺密碼分析	28
3.4有意義視覺密碼演算法	32
第四章 實驗結果	38
4.1實驗一：雜訊式分享影像	39
4.2實驗二：有意義的分享影像實驗	40
4.3實驗三：本研究與Chen and Tsao (2011)的比較	45
第五章 討論與結論	53
5.1本研究的優點	53
5.2視覺效果分析	54
5.3安全性分析	56
5.4未來發展	57
5.5結論	58
參考文獻	59
圖2-1：擴展式視覺密碼實驗範例	8
圖2-2：不擴展視覺密碼實驗範例	10
圖3-1:雜訊式顏色分布機率圖	22
圖3-2:有意義式顏色分布機率圖	31
圖4-1：實驗影像	39
圖4-2：比較不同X機率下雜訊式分享影像	40
圖4-3：比較不同X機率下的有意義影像視覺效果	42
圖4-4：比較不同Y、Z、W對分享影像與疊合影像的色差影響	44
圖4-5：本研究與Chen and Tsao (2011)的黑白影像比較	50
圖4-6：本研究與Chen and Tsao (2011)的彩色影像比較	51
表2-1：(2, 2)-threshold視覺密碼分享模型	8
表2-2：Ito分享模型	10
表2-3：Shyu的分享模型	15
表2-4：Ateniese視覺編碼模型	17
表3-1：雜訊式的分享影像與疊合影像機率表	22
表3-2：雜訊式分享影像編碼表	23
表3-3：有意義的分享影像與疊合影像機率表	29
表3-4：有意義的分享影像編碼表	35
表4-1: 本研究與Chen and Tsao(2011)之比較	52
表5-1：Chen and Tsao (2011)與本研究在分享影像與疊合影像上平均透光度之比較表	55

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