Craig Costello

Computing Supersingular Isogenies on Kummer Surfaces

2018 · Lecture notes in computer science

We apply Scholten’s construction to give explicit isogenies between the Weil restriction of supersingular Montgomery curves with full rational 2-torsion over $$\mathbb {F}_{p^2}$$ and corresponding abelian surfaces over $$\mathbb {F}_{p}$$ . Subsequently, we show that …

Montgomery curves and their arithmetic

2017 · arXiv (Cornell University)

Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic …