Paper 2021/073

Application of Velusqrt algorithm to Huff's and general Huff's curves

Michał Wroński

Abstract

In 2020 Bernstein, De Feo, Leroux, and Smith presented a new odd-degree $\ell$-isogeny computation method called Velusqrt. This method has complexity $\tilde{O}(\sqrt{\ell})$, compared to the complexity of $\tilde{O}(\ell)$ of the classical Vélu method. In this paper application of the Velusqrt method to Huff's and general Huff's curves is presented. It is showed how to compute odd-degree isogeny on Huff's and general Huff's curves using Velusqrt algorithm and $x$-line arithmetic for different compression functions.