臺灣博碩士論文加值系統

透過網際網路的通訊以及社群網路，數位內容資料快速地傳播。因此，保護數位多媒體內容的安全成為重要的議題。秘密影像分享是結合了密碼與影像處理。所謂的秘密影像分享機制是將秘密影像分成多份子影像，分散給參與者保管。結合特定組合的子影像，就能解回秘密影像。若不是特定的子影像組合，則秘密影像無法回復。最常使用的秘密影像分享是 (k, n)-門檻式秘密影像分享機制，其中k≤n, k為解回秘密的門檻值，n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。
秘密影像分享機制的最重要一個分支是植基於Shamir的 (k, n) 秘密分享，將秘密像素嵌入至 (k-1) 次方多項式中的所有係數。代入影像的ID，可以產生n張子影像。由於多項式的k個係數都用來藏秘密像素，因此子影像大小可以縮小為秘密影像的1/k倍。此時秘密影像需要先隨機排列，才能產生雜亂的子影像。如果我們不排列秘密影像，子影像會有殘存的秘密影像。
本論文「植基於最大距離可分離碼的秘密影像分享機制」，我們採用里德所羅門碼 (一種最大距離可分離碼)來建置一種新型的(k, n)-秘密影像分享機制。我們的秘密影像分享機制可解決子影像上有殘存的秘密影像問題，而且不需要重新排列秘密影像。同時我們的機制跟基於Shamir秘密分享的(k, n)-秘密影像分享機制一樣，子影像大小也可以縮小為秘密影像的1/k倍。由於使用的里德所羅門碼是使用伽羅瓦代數體 GF(2^8)，所以解回的秘密影像沒有失真。

Through Internet and social network, digital multimedia can be rapidly delivered and shared in network. Therefore, protecting digital image is an important issue. Secret image sharing (SIS) combines methods and techniques from cryptography and image processing. A SIS scheme shares a secret message into shadow images, which are referred to as shadows, in the way that if shadows are combined in a specific way, the secret image can be recovered. SIS scheme is usually implemented as a threshold (k, n)-SIS scheme, where k≤n, that divides a secret image into n shadows. By collecting any k shadows, we can reconstruct the secret image, but use of (k1) or fewer shadows will not gain any information about the secret image.
The most important category of (k, n)-SIS scheme is based on Shamir’s (k, n) secret sharing. In (k, n)-SIS scheme, we embed secret pixels into all coefficients in (k1)-degree polynomial to share the secret image and meantime reduced shadow size to 1/k of secret image size. However, this polynomial-based (k, n)-SIS scheme needs permuting the pixels of secret image. If we do not permute secret image first, there will be a problem of remanent secret image on shadows.
In this thesis, we adopt Reed Solomon code, a maximum distance separable code, to propose a (k, n)-SIS scheme. Our (k, n)-SIS scheme solves the problem of remanent secret image on shadows, and does not need permuting secret image. Meantime, we can reduce the shadow size like polynomial-based (k, n)-SIS that reduces shadow size to 1/k of secret image size. Since the Reed Solomon code is based on Galois Field GF(2^8), our reconstructed image is distortion-less.

Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 3
1.3 Contribution of the Thesis 4
1.4 Organization of the Thesis 4
Chapter 2 Preliminaries 5
2.1 Polynomial-based (k, n)-SIS Scheme 5
2.2 Reed-Solomon Code 6
Chapter 3 The Proposed SIS Schemes 9
3.1 Motivation 9
3.2 The Proposed (k, n)-SIS Scheme Using RS code 12
Chapter 4 Experimental Results and Discussion 18
4.1 Experimental Results 18
4.2 Discussion 20
Chapter 5 Conclusion and Future Work 22
References 23

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