Constructing an efficient hash function from $3$-isogenies

Hikari Tachibana, Katsuyuki Takashima, Tsuyoshi Takagi
2017 JSIAM Letters  
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 2and 3-isogeny hash functions using
more » ... and show our 3-isogeny proposal has a comparable efficiency with the 2-isogeny one.
doi:10.14495/jsiaml.9.29 fatcat:ygtkwofggrf7bobsapm3x6cdu4