Constructing an efficient hash function from $3$-isogenies

Abstract

Charles et al. proposed hash functions based on the difficulty of computing isogenies between supersingular elliptic curves. Yoshida and Takashima then improved the 2-isogeny hash function computation by using some specific properties of 2-torsion points. In this paper, we extend the technique to 3-isogenies and give the efficient 3-isogeny hash computation based on a simple representation of the (backtracking) 3-torsion point. Moreover, we implement the 2- and 3-isogeny hash functions using Magma and show our 3-isogeny proposal has a comparable efficiency with the 2-isogeny one.