在資訊發達的現代社會中，人與人之間的情報傳遞變得非常迅速且便利。在追求速度與效率下，開始重視資訊情報的安全性，密碼學也成為研究的首要課題。
傳統密碼學需要經過複雜的數學運算才能還原機密資料，Naor & Shamir (1994)則提出(k,n)門檻式視覺機密分享概念，能將機密圖像分給n個人，並疊合在k張以上的圖像下，用人類的肉眼才能辨識機密資料內容。但是Naor & Shamir (1994) 提出的視覺機密分享法，只針對特定的k與n舉例說明，而官振宇等人 (2014)則提出系統性(3,n)設計法，能將n張機密分享投影片分派給每個人，每一張機密分享投影片都無法用肉眼辨識內容。將任意兩張機密分享投影片疊合，仍然無法辨識。只有將三張以上機密分享投影片疊合時，才可以辨識其機密分享投影片的內容。
本研究(4,n)-門檻式視覺機密分享是(3,n)-門檻式視覺機密分享的延伸研究。其目的是要將k門檻提高，以系統性方式產生(4,n)分享模型，並以圖形作驗證。

In the modern society filled with information and technology, the transmission of information among people has become fast and convenient. In the pursuit of speed and efficiency, we also begin to pay attention to the security of information in the sharing process. To secure the process in sharing information, cryptography has become a hot topic of research. Traditional cryptography requires complex mathematical operations to restore secret information. In 1994, Naor & Shamir proposed a (k,n)-threshold visual secret sharing scheme, which can share a secret image among n individuals. In the scheme, each individual will receive a share image which reveals no secret. The secret information can be restored and identified by human eyes only when k or more share images are superimposed. In their work, Naor & Shamir only showed some examples of the (k,n) scheme for specific k and n.  In 2014, Guan et al. devised a systematic method for the (3, n)-threshold visual secret sharing scheme, which can allow sharing among any number of individuals with a visual restoration threshold of k=3. That is, each share image will reveal no secret. Nor will any two share images show anything when superimposed together. The secret information will reveal only when k=3 or more share images are superimposed. In this work, we will continue to find a systematic method for the (4, n)-threshold visual secret sharing scheme.  We will empirically validate the method by examples.

目錄
 第一章 緒論	1
1.1	研究背景與動機	1
 第二章 文獻探討	2
2.1	門檻式視覺機密分享	2
2.2	(3,n)門檻式視覺機密分享	2
 第三章 方法介紹	5
3.1	名詞解釋與定義	5
3.2	(4,n)門檻式視覺機密分享	6
3.3	(4,n)分享模型下的矩陣及色差範例	7
3.3.1	假設n=5	7
3.3.2	假設n=6	10
 第四章 結果驗證	15
4.1	公式驗證	15
4.2	圖形驗證	22
4.2.1圖形範例	24
 第五章　結語	29
5.1	結論	29
5.2	未來方向	29
參考文獻	31
附錄一：基礎矩陣與分享矩陣產生程式	32
附錄二：圖形分解與疊合程式	38
圖目錄
圖: 2-1	(3,4)-門檻式視覺機密分享模型	3
圖: 2-2	基礎矩陣M與疊加向量	4
圖: 4-1	機密分享圖像生產過程	23
圖: 4-2	原始圖案基本資訊	24
圖: 4-3	(4,n)下的三種結果	24
圖: 4-4	三種不同圖片所呈現的結果	27

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