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.