The Research And Application Of The Authenticated Key Agreement Protocols Based On Elliptic Curve Cryptography

Elliptic curve is one of the most prominent mathematics theory in twenty century. And it is the most important research branch in algebraic geometry. The arithmetic of elliptic curve is widely used in cryptography. The elliptic curve cryptography(ECC) is increasingly mature and it has replaced RSA step by step because of its stronger secu-rity and higher efficiency. The development of technology based on ECC is especially remarkable in the last ten years. Considering the security, efficiency, cost of deploy and manage, many new cryptosystems have been proposed, such as the traditional public key infrastructure, Identity-Based Public Key Cryptography, Certificateless Public Key Cryptography and so on.To overcome the problem of the complicated certificate management in traditional public key cryptosystems, people start to research Identity-Based Public Key Cryptog-raphy and Certificateless Public Key Cryptography. The bilinear pairing on elliptic curve is a good choice to implement them. But the relative computation cost of the pairing is approximately twenty times higher than that of the scalar multiplication over elliptic curve group.To improve the performance of relative protocols, we give a new definition of the authenticated key agreement protocols based on ECC and the security model for them. And based on the security model, we proposed a new certificateless authenticated key a-greement protocol without bilinear pairings, a new efficient identity-based authenticated multiple key exchange protocol without bilinear pairings, a new ID-based three-party authenticated key exchange protocol without bilinear pairings for Mobile-Commerce. All of our protocols are based on ECC, so they avoid the computation of bilinear pair-ings. With the running time being saved greatly, our schemes are more practical than the the other schemes for practical application in the same security level. At last, un-der the research of chaotic maps, we propose a new extended chaotic maps-based key agreement protocol and give its security proof and efficiency analysis.