Cryptography based on pairings

Abstract

Elliptic curves have attracted a lot of cryptographic interests. One of the merits on the elliptic curve cryptosystem is that it requires a smaller key size than an RSA-type cryptosystem to reach the same security level. Recently there have been many researches on the elliptic curve cryptosystem, particularly in construction of primitives based on pairings. In this survey, we search mathematical preliminaries on the pairing and hard problems relative to the security of the cryptosystems. Also, we divide three recent research progresses and introduce classical primitives according to the fields of key agreement, identity-based encryption and signature. In addition, we agree on applications of this researches.