Cryptosystems Based on Elliptic Curve Pairing

The purpose of this paper is to introduce pairing over elliptic curve and apply it to ID based key agreement schemes and privacy preserving key agreement schemes. The key words here are ID based scheme, pairing over elliptic curve and privacy reserving scheme. Elliptic curve is one of the popular research topics in cryptography because it has some useful features. One of them is a bilinear function such as Tate pairing. Bilinear function has excellent properties suitable to applications in cryptography. Some schemes are proposed using the bilinear function so far and ID based cryptosystems are the one of the most important applications. ID is any information like name, mail address, phone number, any public information can be used. Another recent problem is privacy. Careless use of ID may leak privacy of the person corresponding to the ID. In this paper we introduce pairing over elliptic curve and propose ID based key agreement schemes and privacy preserving key agreement scheme.

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