由於渾沌系統良好的不可預測性、遍歷性以及對初始值的敏感度，使其非常適合運用在影像加密上。近年來有許多加密演算法被提出，但對於許多存在的演算法，他們的安全性或是運算時間並沒有辦法達到很好的平衡。因此，本論文藉由二維超渾沌系統以及平行運算設計出一個同時具安全性且高效率之影像加密演算法，並探討其加密結果。
首先，我們提出一個全新的二維超渾沌系統，並以軌跡圖、分歧圖、樣本熵、里亞普諾夫指數以及NIST SP800測試來驗證該渾沌系統的特性。發現該系統擁有更大的渾沌區間以及更優秀的軌跡分布。我們的演算法分為排列及擴散兩個部分。在排列中，我們利用二維超渾沌系統所產生的渾沌序列進行排序並將排序索引值順序運用在圖像上。接著在擴散的部分，我們使用互斥或運算以及雙向位元位移運算。
為了減少整個演算法所需的時間，我們在渾沌產生器以及加密步驟中均使用OpenCL的架構與其平行運算的特性，利用GPU實現平行運算。並同時與在CPU中串列式運行的運行時間進行比較。
接著，我們對密文圖像進行安全性分析來驗證我們所提出的加密演算法之安全性。其中包括密鑰空間分析、密鑰敏感度分析、直方圖分析、相關性分析、夏農熵分析、抵抗差分攻擊分析及穩健性分析等。從結果可以知道我們通過了所有測試，證實我們的加密系統擁有足夠的安全性。最後我們對本論文所提出的加密演算法加以討論並提出對未來的展望以及改進的方向。

Since the good unpredictability, ergodicity and sensitivity to initial values, chaotic systems are very suitable for image encryption. In recent years, many encryption algorithms have been proposed. But for many existing algorithms, there is a problem to achieve a good balance between their security and computational time. Therefore, in this paper we design an image encryption algorithm with both sufficient security and high efficiency by using 2D hyper chaotic system and parallel computation, and discusses its encryption results.
First, we propose a new two-dimensional hyper chaotic system, and verify the characteristics of the chaotic system by trajectory graph, sample entropy, Lyapunov exponent and NIST SP800 test. The result shows that the system has larger chaotic interval and better trajectory distribution. Our algorithm consists of confusion phase and diffusion phase. In confusion phase, we sort the chaotic sequence generated by our chaotic system and apply the sorting index to the image index. Then in the diffusion phase, both the xor operation and bit-shift operation are applied to scramble image.
In order to reduce the time for the entire algorithm, we apply OpenCL in the chaos generator and encryption steps, according to its architecture and parallel computing feature, we use GPU to achieve parallel computing. And at the same time we compare with executing time of serial operation in CPU.
Next, we perform some security analyses on the ciphertext image to verify the security of our proposed encryption algorithm. As the result, we passed all the tests and confirmed that our encryption system is sufficiently secure. Finally, we discuss the encryption algorithm proposed in this paper and propose future works and improvement directions.

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