本論文主要討論基於混沌同步之改良式El-Gamal密碼系統設計與即時影像加密系統技術之設計與實現，首先討論連續時間的混沌系統之離散化，並確保此離散混沌系統仍保有原先連續時間的混沌系統之隨機特性；其次，提出離散滑動模式同步控制器之設計，確保主僕離散混沌系統能夠同步；再次，結合離散混沌系統同步，利用離散時間混沌系統的隨機特性，提出改良式El-Gamal密碼系統。此方法利用混沌同步之特性，亦即主系統及僕系統獲得相同之混沌訊號，並將其訊號取代El-Gamal演算法之公開金鑰以達到隱藏公鑰之目的，有效改善傳統El-Gamal密文過長與計算耗時的問題，同時可以提昇其安全性。最後透過嵌入式系統，實現此提出之改良式El-Gamal密碼系統並整合影像加密技術，完成高安全性之即時影像加密系統。

This paper is concerned with the design of an improved El-Gamal cryptosystem based on chaos synchronization and the design and implementation of a real-time image encryption system. First, we discretize continuous-time chaotic systems that still retain the random characteristics of continuous-time chaotic systems; then, a discrete sliding mode controller (DSMC) is proposed to ensure that the master and slave discrete chaotic system can be synchronized; next, the improved El-Gamal cryptosystem is proposed by using the random characteristics of discrete-time chaotic systems. This method uses the characteristics of chaos synchronization—that is, the master system and slave system obtain the same chaotic signal, which replaces the public key of the El-Gamal algorithm to meet the requirement of a hidden public key. Therefore, it can effectively improve the traditional El-Gamal algorithm with long ciphertext and time-consuming calculation. Not only can El-Gamal security characteristics be retained, but its security is also enhanced. Finally, we use embedded systems to realize the high-security real-time image encryption system with the improved El-Gamal cryptosystem.

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