In this paper we propose a very simple and efficient encoding function from
to points of a hyperelliptic curve over
of the form
is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves.
Our new encoding is nearly a bijection to the set of
-rational points on
. This makes it easy to construct well-behaved hash functions to the Jacobian
, as well as injective maps to
which can be used to encode scalars for such applications as ElGamal encryption.
The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux’s supersingular elliptic curves.