Extending the GLS endomorphism to speed up GHS Weil descent using Magma

Jesús-Javier Chi-Domínguez, Francisco Rodríguez-Henríquez, Benjamin Smith

Let $q=2^n$, and let $E/{\mathbb{F}}_{q^{\ell }}$ be a generalized Galbraith--Lin--Scott (GLS) binary curve, with $\ell \ge 2$ and $(\ell ,n)=1$.We show that the GLS endomorphis…