在本論文中，我們參考單峰映射及結合三角函數，設計出一種基於一維的渾沌系統，並透過SHA256 將密鑰空間從128位元擴展到256位元，接著參考傳統DNA編碼原則，改編出一種更快速、訊號隱密性更高的的編碼方式「五行編碼」，最後在像素擴散的步驟運用XOR 運算完成整個影像加密過程。我們利用李亞普諾夫指數及分岔圖驗證渾沌系統的理想參數，透過蛛網圖及NIST SP800-22 的15 個測項驗證渾沌系統的高度渾沌性及序列隨機性，最後由初始值敏感度分析測試結果得到此渾沌系統具有高度的初始值敏感性。接著我們以Altera DE10-Standard FPGA 實現整個圖像加密系統，將明文放進SD 卡，透過FPGA 上的I/O 端口讓FPGA 進行存取，接著呼叫加密演算法將明文加密，在將密文回傳到SD卡上，影像加解密的過程都會透過FPGA 外接的VGA 口顯示在外接螢幕上。在圖像加密安全性的分析部分，我們對整個加密過程進行統計直方圖分析、相關性分析、差分密碼分析、訊息熵分析及密鑰分析，訊息熵分析包含了全局訊息熵與局部訊息熵。從我們做的加密安全性分析結果，以及比對其他加密演算法後的結果可以得知，我們所提出的圖像加密演算法是安全且有效的。

In this thesis, we refer to Logistic map and combined trigonometric functions to design a one-dimensional chaotic system, and expand the secret key space from 128 bits to 256 bits by SHA256, and then refer to DNA encoding principles to create a faster and higher signal confidentiality encoding principles, which is "Five-phases encoding". Finally, the XOR operation is used in the pixel diffusion step to complete the entire image encryption process. The ideal parameters of the chaotic system verified by Lyapunov exponent and Bifurcation diagram, and the high chaos and sequence randomness of the chaotic system verified by Cobweb plot and fifteen measurement items of NIST SP800-22, the initial value sensitivity analysis test results show that this chaotic system has a highly initial value of sensitivity. We use the Altera DE10-Standard FPGA to implement the entire image encryption system, let the FPGA access through the I/O port by SD card on the FPGA , and then call the encryption algorithm to encrypt the plaintext, and then the ciphertext was sent
back to the SD card. The whole process of image encryption and decryption will be displayed on the external screen via the VGA port connected to the FPGA. In the analysis part of image encryption security, we perform Histogram analysis, Correlation analysis, Differential attack, Shannon entropy analysis, and key analysis on the entire encryption process. Shannon entropy analysis includes global Shannon entropy and local Shannon entropy. From the analysis of encryption security and the results of comparing other encryption algorithms, we can know that the image encryption algorithm that we proposed is safe and effective.

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