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 此論文共提出三個數位影像機密分享方法，分別對以下三個問題進行考量：(1) 一般化存取結構分享多張機密影像；(2) 以大小固定的私鑰分享多張機密影像；(3) 利用中國餘式定理於門檻機制之單張機密影像分享。我們分別對這些問題提出創新的機密影像分享機制。　　本文所提的第一個機制，以 Shamir 的 (n, n) 門檻式機密分享機制為基礎，可在一般化存取結構下，對多張數位影像進行機密分享；此機制可能在某些存取結構下，使每一位參與者拿到大小不同的分享圖。第二個問題即盼改善這個分享者拿到大小不同分享圖的缺點。我們分別對門檻式和一般化存取結構設計其機密分享機制，使每一位參與者只需持有大小固定的私鑰，即可分享多張影像。此機制使每一位參與者所需持有的資訊變小且易於攜帶（甚至可以直接記憶腦中），確為機密影像分享的研究帶來新的思考方向。　　針對第三個問題，我們運用中國餘式定理，提出了兩個門檻式的機密影像分享機制，有別於諸多機密影像分享之研究大多沿用 Shamir 以多項式建構機密分享的概念，中國餘式定理的引入，可為機密影像分享研究領域拓展出新的視野。　　文章中亦對於所提出的機制，個別分析其安全性；並進行實作實驗。實驗結果驗證了所提方法的可行性與實用性。
 In this thesis we study three problems in secret image sharing: (1) sharing multiple images in general access structures, (2) sharing multiple images using constant-size keys, and (3) sharing one image in a threshold structure by Chinese remainder theorem. We design novel schemes for these three problems.　　For the first problem, our scheme, which is based on Shamir’s (n, n) threshold scheme, is the first result for sharing more than one secret image among participants with any given general access structure. One major disadvantage for this approach is that the sizes of the shadows for all participants may be different for a certain access structure. The second problem is meant to deals with this disadvantage so that each participant only takes a constant-size key, instead of various-size shadows. We propose schemes for threshold and general structures, respectively. This is a new development in secret image sharing in the view that the size of information distributed to each participant is so small that it is very easy to carry (or just to memorize).　　Regarding the third problem, we devise two new threshold secret image sharing schemes. Applying Chinese remainder theorem, instead of following Shamir’s idea of using polynomial interpolation for secret sharing, reveal new possibilities in the area of secret image sharing.　　The secrecy analyses of these schemes are discussed. We also implement our designs and the experimental results demonstrate the feasibility and applicability of the proposed schemes.
 摘 要 iiAbstract iii致 謝 iv目 錄 v表目錄 vi圖目錄 vii第一章 簡介 11.1 研究背景與動機 11.2 研究問題 21.3 研究目的 2第二章 文獻探討 42.1 機密分享及其發展概況 42.2 Shamir (r, n) 門檻機制 72.3 一般化存取結構 102.4 機密影像分享 122.5 中國餘式定理與機密分享 132.5.1 Mignotte 的門檻式機密分享機制 142.5.2 Asmuth-Bloom 的門檻式機密分享機制 15第三章 研究成果與討論 173.1 一般化存取結構分享多張機密影像 173.2 以大小固定的私鑰分享多張機密影像 243.2.1 在門檻機制下之多張機密影像分享 253.2.2 一般化存取結構下之機密影像分享 293.3 利用中國餘式定理於門檻機制之單張機密影像分享 373.3.1 基於 Miggto之 (r, n) 機密影像分享機制 373.3.2 基於 Asmuth-Bloom之 (r, n) 機密影像分享機制 41第四章 實驗結果 464.1 一般化存取結構依群組考量之多張機密影像分享實作 464.2 利用大小固定私鑰之多張機密影像分享實作 514.3 利用中國餘式定理之機密影像分享實作 55第五章 結論 60參考文獻 63附錄A、解多項式展開係數 66附錄B、GF(p) 與GF(2n) 70附錄C、互質模數表 73
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 1 Shamir秘密分享於數位影像之研究 2 不需儲存排列影像金鑰之秘密影像分享機制 3 視覺密碼及秘密影像分享之研究 4 植基於最大距離可分離碼的秘密影像分享機制 5 網路防禦技術之研究 6 植基於Blakley機制的秘密影像分享 7 多層次友善介面圖像分享 8 基於線性系統之機密分享 9 具有等比例特性的(k, n)比例式秘密影像分享機制 10 低傳輸風險的機密影像分享機制 11 利用有意義的數位影子影像共享機密訊息 12 具可調分存圖像之友善介面圖像分享 13 基於中國餘式定理的影像分享機制 14 Shamir秘密分享於數位影像之研究 15 多回合的秘密分享系統中有效之欺騙者驗證法

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 1 基於中國餘式定理的影像分享機制 2 針對大型題庫進行測驗卷編製研究 3 Shamir秘密分享於數位影像之研究 4 影像之視覺式分享，權重式分享，修復與高品質資訊隱藏 5 以螞蟻族群演算法產生植基於試題反應理論之測驗卷 6 應用粒子群最佳化於學生分組之研究 7 具隱藏及確認能力之無失真多機密影像分享 8 機密影像視覺密碼系統之研究 9 以隨機亂數為基礎的影像機密分享 10 具有等比例特性的(k, n)比例式秘密影像分享機制 11 低傳輸風險的機密影像分享機制 12 高容量JPEG資訊隱藏及其在影像分享、驗證與修復之應用 13 布林與餘數運算在影像分享之研究 14 基於視覺密碼之數位版權研究 15 應用像素不擴展視覺密碼技術之浮水印方法

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