Application of authentication protocol and key exchange scheme are major research issues in current internet, and entity identification (users or servers) accuracy and security are thereby safeguarded by various types of verification programs. Therefore, in the last 10 years, it was accompanied with productive discussions, but those discussions mainly focus on single issues, and because of the lack of security, there still existed improvements. The concept of zero-knowledge proofs is well suited for the identification and signing within network system, which has been widely used since proposed in 1985. However, common identification methods are only fit for individual user. In an increasingly complex network environment of today, information is usually conveyed through many unidentified servers, as a result, we have to encrypt messages by adopting different kinds of session keys. As for the chaotic maps technology, it also serves as a new encryption technology, widely adopted in communication protocols and key agreements over the years. As a consequence, in this study, we are going to propose an authentication protocol with key exchange function by taking advantage of characters of zero-knowledge proofs and chaotic maps, as well as adopt the BAN-logic to prove the security of this protocol. This study also compares the results of the security analysis of our protocol and related works. As a result, our proposed protocol has more security than others. owner of this secret message. And applications of zero-knowledge proofs may save the authenticator from conveying any secret message, which effectively prevents eavesdropping or replay attacks. Application scope of zero-knowledge proofs shall include user identification [16][17][18][19], electronic voting [20,21], digital cash [22,23], blind signature [24,25], and so on. In order to extend its application scope, Schnorr [19] had proposed an improved zero-knowledge proofs in the year 1989, which is perceived as a more effective verification method suitable for using smart cards.Since 1990s, chaotic system [18,[26][27][28][29][30] has been widely used in designing a secure communication protocol. And in the past 10 years, encryption system based on chaos theory has been studied extensively. Chaotic maps include the design of symmetric encryption protocol [31-34] and hashing function [35][36][37]. Lately, chaotic system is also applied in signature scheme [38].Traditional authentication protocols do not have key exchange function, or parts of authentication protocols have key exchange function, but because of the lack of security, for this purpose, we have proposed an enhancement authentication protocol with key exchange function applied in network system by making use of characters of zero-knowledge proofs and chaotic maps, and attached it with higher security, stronger anonymity, faster efficiency, and better integrity. Moreover, we have also adopted the BAN-logic to prove the security of this protocol. In chapter 2, we have first introduced some concepts related to z...