秘密影像分享是結合了密碼與數位影像技術的研究，使秘密影像能夠在一種安全的協議下被妥善的保護以及分享。秘密影像分享技術是一種需要滿足門檻值條件，才能夠解回秘密影像。此種技術可以有各種不同的應用，能有效率、妥善地防止惡意攻擊、及竊取等等的破壞行為。有關秘密影像分享，現有文獻已有大量的研究和實作。一般而言，秘密影像分享大部分是 (k, n) 門檻式機制。所謂門檻方案，k為解回秘密的門檻值，n則為子影像的數目。k張以上的子影像可解回秘密影像，若是少於k張子影像則不能解回。其中 k值是固定的，也稱為全有或全無解碼模型 (all-or-nothing decoding model)。另外一種秘密影像分享的解密模型，我們稱之為漸進式的解碼模型 (progressive decoding model)。k張子影像可解回部份秘密影像，(k+1)張子影像解得更清晰秘密影像，直到所有n張子影像解回完整的秘密。

本論文研究門檻值可變的秘密影像。從一個原本是(k, n)漸進式的解密模型，因安全環境的改變，門檻轉換成變全有或全無解碼模型。這個安全環境改變的原因可能是解回秘密的迫切性增加。我們等不及這種漸進式的解密，需所有n個使用者都到位參與解才能回完整秘密。在我們的方案中，每位參與者只需要保留一個初始子影像。在漸進式的解碼模型，這些初始子影像不需要任何修改即可用來做漸進式解回秘密影像。另一方面，當選擇全有或全無解碼模型時，系統管理者會發佈額外的訊息，k個參與者藉由這些公佈的額外訊息與自己的初始子影像就能採用全有或全無的模型解回秘密影像。我們提出了兩種門檻值可變的(k, n)漸進式秘密影像分享機制，他們各自公佈的訊息量不一樣。

Secret image sharing is a combination of cryptographic and digital imaging, so that secret images can be properly protected and shared under a secure protocol. Secret image sharing needs to meet the threshold conditions to be able to retrieve the secret image, it can apply on various applications, which can efficiently prevent malicious attacks, stealing, and other sabotages also have a lot of research and implementation of existing literature. In SIS-(k, n) scheme, k is the threshold for retrieving secrets, and n is the number of sub-images. Recover the secret image if sub-images more than k, otherwise it cannot be recovery. We called all-or-nothing decoding model when the k is fixed. In another type, we called progressive decoding model. The k sub-images can recover part of the secret images then the (k+1) sub-images resolve the secret images more clearly, until all n sub-images resolve the all secret.

The thesis proposes thresholds changeable SIS-scheme. In the (k, n) progressive decryption model, due to changes in the environment, the threshold will convert to all-or-nothing decoding model. Since the security environment may increase urgency to recover the secret. It not convenience for urgency, cause this model requires all n users engage then be able to recover the secret. In our scheme, each participant only needs to keep an initial sub-image. In the progressive decoding model, these initial sub-images can be used to progressively retrieve the secret image without any modification. On the other hand, when the all-or-nothing decoding model is selected, the dealer will publish additional information then the k participants use all-or-nothing by the additional information and their sub-images. We propose two (k, n) progressive SIS-schemes with thresholds changeable and each of which has different amount of information.

第一章 介紹 1
1.1 背景知識 1
1.2 論文貢獻 2
1.3 論文架構 3
第二章 預備知識 5
2.1 基於多項式的(k, n)秘密影像分享
2.2 Yang-Chu's (k, n)秘密影像分享
第三章 主要機制 9
3.1 論文動機 9
3.2 主要方案 11
第四章 範例與實驗 19
4.1 範例一 Yang-Chu's方案 19
4.2 範例二 主要方案三 21
4.3 範例三 主要方案四 22
第五章 結論與未來展望 26
參考文獻 28

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