本論文提出一個以(k, n, m)為門檻值的以布林運算與共享矩陣為基礎之多秘密影像共享技術，本方法可以分享 m 張秘密影像於 n 位秘密分享者中，經過本論文所提出的(k, n, m)多秘密影像共享技術處理後，可以產生 n 張看似隨機的分享影像，還原時需要搜集 k (k ≤ n)張分享影像即可完全還原 m 張秘密影像。
相對於其他學者提出的基於布林運算之多秘密影像共享技術，本方法提昇分享影像的自由度，(k, n, m)三個門檻值可以自由設定，同時免除連續性分享影像還原的限制。另外，本方法的分享及還原過程，主要使用 XOR 布林運算及共享矩陣查詢，因此具有極高的執行效率。

In this paper, a Boolean operation and sharing matrix based (k, n, m) multi-secret image sharing scheme is proposed. The proposed scheme shares m secret images among n shared image and collecting k (k ≤ n) shared images perfectly recover these m secret images.
Compared with other multi-secret image sharing scheme, the proposed scheme improves the usage of shared images. The three thresholds (k, n, m) can be arbitrarily assigned, and the previous recovery requirement of consecutive shared images is also removed. Moreover, the proposed Boolean and sharing matrix based scheme has good performance.

目錄
第一章 緒論	1
1.1研究背景與動機	1
1.2論文架構	3
第二章 相關研究	4
2.1結合共享矩陣實現無失真(k, n)秘密影像分享	4
2.2高效安全的多秘密影像分享方法	9
第三章 本論文方法	11
3.1共享矩陣的定義與生成	11
3.2 (k, n, m)多秘密影像分享方法一	13
3.3 (k, n, m)多秘密影像分享方法二	17
3.4 (2, 3, 2)多秘密影像分享方法二分享與還原過程	21
第四章 實驗結果及比較	25
4.1實驗結果	25
4.2比較與討論	31
第五章 結論	34
參考文獻	35
圖目錄
圖1、通過共享矩陣加密分享影像與還原影像的過程	4
圖2、共享矩陣S(k,n)的生成過程	5
圖3、(k, n, m)多秘密影像分享方法一分享流程圖	13
圖4、(k, n, m)多秘密影像分享方法一分享結果	15
圖5、(k, n, m)多秘密影像分享方法二分享流程圖	17
圖6、公式(48)中所使用函數add(a, b)效果展示	19
圖7、(k, n, m)多秘密影像分享方法二分享結果	21
圖8、(2,3,2)多秘密影像分享方法二實驗結果	22
圖9、(3,4,5)多秘密影像分享方法二實驗結果	26
圖10、(3,5,3)多秘密影像分享方法二實驗結果	27
圖11、(3,5,3)多秘密影像分享方法二分享影像竄改實驗結果	28
圖12、(3,4,5)多秘密影像分享方法一實驗結果	30
圖13、(3,4)結合共享矩陣的秘密影像分享方法[15]實驗結果	32
圖14、(3,3)基於布林運算的多秘密影像分享方法[8]實驗結果	33
表目錄
表1 秘密影像分享方法比較	31

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