Chapter

Advances in Cryptology - CRYPTO 2009

Volume 5677 of the series Lecture Notes in Computer Science pp 303-316

How to Hash into Elliptic Curves

  • Thomas IcartAffiliated withSagem Sécurité, Université du Luxembourg

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.