The review on elliptic curves as cryptographic pairing groups

Abstract

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 the mathematics behind that elliptic curve to the applicability within a cryptosystem. Nowadays, pairings bilinear maps on elliptic curves are popular to construct cryptographic protocol pairings that help to transform a discrete logarithm problem on an elliptic curve into a discrete logarithm problem in finite fields. The purpose of this paper is to introduce elliptic curves and bilinear pairings on elliptic curves based on pairing cryptography. Also, this investigation serves as a basis for guiding anyone interested to understand one of the applications of group theory in cryptosystems.

Keywords

• elliptic curve
• bilinear map
• pairing-based cryptography