最近Xiong等人提出用於物聯網環境中，安全、可靠、且容錯的一種秘密影像分享（Secret Image Sharing ; SIS）。Xiong 等人的 SIS 有驗證和改錯功能。另一個應用於智慧型交通管理(ITS)大數據環境的Liu 等人的 SIS，它有漸進式擷取影像的功能。與 Xiong 等人的 SIS 相比，Liu 等人的 SIS的子影像會受雜訊干擾，但是其漸進式回復影像比Xiong 等人的 SIS只能是門檻式的全有或全無的擷取影像，更適合應用於智慧型交通管理的影像擷取。Liu 等人的漸進式秘密影像分享 (Progressive Secret Image Sharing ; PSIS ) 是為智慧交通系統設計的，通過區域卷積神經網路將交通影像細分為具有不同安全等級的影像區域。可以逐步擷取包含關鍵交通訊息的秘密影像，例如車輛的車牌號碼、車輛外觀、駕駛人臉。漸進式回復影像特別適用於交通影像的管理，例如ITS中不同的管理階級的人可以提取具有不同安全等級的影像。
Liu 等人的 PSIS沒有驗證和改錯能力，Xiong 等人的 SIS 雖然有驗證和改錯功能但不能漸進式回復影像。本論文“物聯網環境中具驗證和糾錯的漸進式秘密影像分享機制”，我們提出有驗證和改錯能力的 PSIS (簡寫成PSISA)。我們的PSISA機制結合了(nk+1)個SIS，(k+i, k+i)-SIS其中0i(nk)，以達到漸進式解碼功能。使用(k+i, k+i)-SIS的額外的(nki) 像素做驗證、並同時採用里德-所羅門碼來改正錯誤功能。為了提高漸進式解碼清晰的比率、並同時兼顧子影像的大小，本文也提出兩種修改方案(i)只使用(k, k)-SIS、(ii) 使用(k, k)-SIS與(n, n)-SIS。方案(i)有最佳的漸進式解碼比率，方案(ii)雖然沒有好的漸進式解碼比率但是比方案(i)有較小的子影像。不同的(k+i, k+i)-SIS結合就是在漸進式解碼比率與子影像的大小兩者間做取捨。
我們所提的(k, n)-PSISA是第一個漸進式秘密影像分享同時具驗證和改錯功能的機制。如果物聯網數據被惡意攻擊者篡改，或者在傳輸、儲存過程中出現錯誤，子影像就會受到損害，導致無法完成恢復原始秘密影像且會讓數據丟失產生不可靠性。因此我們所提的(k, n)-PSISA方案非常適用於物聯網環境。理論分析和實驗結果也呈現了所提方案的正確性。

Recently, Xiong et al. proposed a secure, reliable, and fault-tolerant secret image sharing (SIS) in IoT environment, which provides authentication and error correction capabilities. Another SIS applied in big data environment for intelligent traffic management (ITS), Liu et al.’s SIS, has progressive recovery. When compared with Xiong et al.’s SIS, the shadow image (referred to as shadow) of Liu et al.’s SIS will be interfered with noise, but it can gradually recover image and is more suitable for image extraction in traffic management than the threshold (all-or-nothing) recovery of Xiong et al.’s SIS. Liu et al.’s progressive SIS (PSIS) is designed for ITS. The traffic surveillance image is first subdivided into sub image areas with different security levels through Region Convolution Neural Network (RCNN). Traffic images containing key traffic information, such as the vehicle's license plate number, vehicle appearance, and driver's face, can be gradually extracted step-by-step. The progressive recovery is especially suitable for ITS. For example, the other scenario could be that people of different management levels (e.g., including prosecutors and police officers with different privileges) in ITS can extract images with different security levels.
Liu et al.’s SIS has no authentication and error correction capabilities, while Xiong et al.’s SIS cannot progressively recover secret. In the thesis, we propose PSIS with authentication and error correction (PSISA). Our PSISA combines (nk+1) SISs, (k+i, k+i)-SIS where 0i(nk), to achieve progressive recovery. By using extra (nk+1) pixels in the (k+i, k+i)-SIS as authentication pixels and Reed-Solomon code, the proposed (k, n)-PSISA has authentication and error correction capabilities, respectively. Consider progressive ratio and shadow size. Two modified (k, n)-PSISAs are designed: (i) using (k, k)-SIS, (ii) using (k, k)-SIS and (n, n)-SIS. Scheme (i) has the best progressive, while scheme (ii) has the less shadow size. The combination of various (k+i, k+i)-SISs could trade-off the progressive ratio for the shadow isize.
Our (k, n)-PSISA is the first mechanism for progressive secret image sharing with both verification and error correction functions. If IoT data are tampered with by malicious attackers, or errors occur during transmission and storage, compromised shadows may result in the erroneous recovery. Thus, the proposed (k, n)-PSISA is very suitable for IoT environment. Theoretical analyses and experimental results also demonstrate the correctness.

Chapter 1 Introduction 1
Chapter 2 Preliminaries 7
2.1 The Conventional (k, n)-SIS Using Polynomial 7
2.2 Yang and Chu’s (k, n)-PSIS 10
Chapter 3 The Proposed (k, n)-PSISA 15
3.1 Motivation 15
3.2 Design Concept 17
3.3 Sharing and Recovery Phases 26
3.4 Property Analysis 30
Chapter 4 The Modified (k, n)-PSISA 35
4.1 Construction Method and Property Analysis 35
4.2 Reduction of Shadow Size 39
Chapter 5 Experiment and Discussion 43
5.1 Experimental Results 43
5.2 Comparison and Discussion 52
5.3 Discussion 55
Chapter 6 Conclusion and Future Work 59
References 63

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