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In recent years there has been a great progress in the application of chaos theory for cryptography. Due to the closeness in characteristics between chaos and cryptography, they together play a dynamic role in designing strong chaos-based security solutions.The major application areas of chaos theory includes many scientific disciplines, mathematics, programming, microbiology, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, robotics, and meteorology. Electroencephalography (EEG) signals contain sensitive health personal information of patient; therefore, it is obligatory to keep secret this information from any illegal and unauthorized access. The insecurity may results into wrong diagnosis and leak of the personal information of the patient and can even cost his life. In this book, a chaos-based encryption method is discussed to secure EEG data of patient before transmitting it over the insecure channel.Apart from these, various chaos techniques, its characteristics and various aspects of cryptography in concern with security is discussed in detail.