Qom University of TechnologyMathematics and Computational Sciences2717-27082220210501The review on elliptic curves as cryptographic pairing groups505924399110.30511/mcs.2021.525072.1017ENElahehKhamsehDepartment of Mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran.Journal Article20210213Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted<br />by an addition operation that forms a group structure. The motivation of this study is that the<br />mathematics behind that elliptic curve to the applicability within a cryptosystem. Nowadays, pair-<br />ings bilinear maps on elliptic curve are popular to construct cryptographic protocol pairings help to<br />transform a discrete logarithm problem on an elliptic curve to the discrete logarithm problem in nite<br />elds. The purpose of this paper is to introduce elliptic curve, bilinear pairings on elliptic curves as<br />based on pairing cryptography. Also this investigation serves as a basis in guiding anyone interested<br />to understand one of the applications of group theory in cryptosystem.http://mcs.qut.ac.ir/article_243991_eeec46e5d19e61e047b8298801dcb72a.pdf