The review on elliptic curves as cryptographic pairing groups

Document Type : Original Article


Department of Mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran.


Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted
by an addition operation that forms a group structure. The motivation of this study is that the
mathematics behind that elliptic curve to the applicability within a cryptosystem. Nowadays, pair-
ings bilinear maps on elliptic curve are popular to construct cryptographic protocol pairings help to
transform a discrete logarithm problem on an elliptic curve to the discrete logarithm problem in nite
elds. The purpose of this paper is to introduce elliptic curve, bilinear pairings on elliptic curves as
based on pairing cryptography. Also this investigation serves as a basis in guiding anyone interested
to understand one of the applications of group theory in cryptosystem.