Key agreement, one of the most important tools in many security mechanisms, was first proposed by Diffie and Hellman in 1976. In each key agreement protocol, two or more entities establish a shared secret key between each other by exchanging messages through a public channel. In these protocols, many cryptographic techniques could be used. These techniques are In this thesis, at first we analyze and compare the infrastructures of those protocols which use Certificate-based and ID-based methods. After introducing the preliminaries of each method, such as the Nondeterministic Polynomial Problems (NP problems) and the use of these problems for implementing the methods, we review the most important evaluation criteria and attacks which are considered for these protocols. Then we propose a new assortment for those evaluation criteria including Essential Criteria and Advanced Criteria. After that we propose a special relationship between these two aforementioned infrastructures. Although these two infrastructures have lots of differences with each other, it seems that there is a sort of duality between the protocols using these two methods. In other words, by this relationship we can reach from a protocol using one method to another protocol using the other method. In the end of this thesis, by proposing this relationship, we will evaluate and analyze this proposed relationship by exemplifying some protocols using both methods. Proposing new protocols in each infrastructure and discovering new attacks to some existing protocols are some of the most important results of this duality. Keywords: Key Agreement Protocol, Public Key Cryptography, Certificate-based Infrastructure, Identity-based Infrastructure, Elliptic curve, Bilinear Pairing, Dual relationship Key agreement, one of the most important tools in many security mechanisms, was first proposed by Diffie and Hellman in 1976. In each key agreement protocol, two or more entities establish a shared secret key between each other by exchanging messages through a public channel. In these protocols, many cryptographic techniques could be used. These techniques are In this thesis, at first we analyze and compare the infrastructures of those protocols which use Certificate-based and ID-based methods. After introducing the preliminaries of each method, such as the Nondeterministic Polynomial Problems (NP problems) and the use of these problems for implementing the methods, we review the most important e Keywords: Key Agreement Protocol, Public Key Cryptography, Certificate-based Infrastructure, Identity-based Infrastructure, Elliptic curve, Bilinear Pairing, Dual relationship
