How to Hash into Elliptic Curves

Abstract

We describe a new explicit function that given an elliptic curve E defined over \(\mathbb F_{p^n}\) , maps elements of \(\mathbb F_{p^n}\) into E in deterministic polynomial time and in a constant number of operations over \(\mathbb F_{p^n}\) . The function requires to compute a cube root. As an application we show how to hash deterministically into an elliptic curve.