Counting Richelot isogenies between superspecial abelian surfaces

Toshiyuki Katsura, Katsuyuki Takashima
2020 The Open Book Series  
Castryck, Decru, and Smith used superspecial genus-2 curves and their Richelot isogeny graph for basing genus-2 isogeny cryptography, and recently, Costello and Smith devised an improved isogeny path-finding algorithm in the genus-2 setting. In order to establish a firm ground for the cryptographic construction and analysis, we give a new characterization of decomposed Richelot isogenies in terms of involutive reduced automorphisms of genus-2 curves over a finite field, and explicitly count
more » ... xplicitly count such decomposed (and nondecomposed) Richelot isogenies between superspecial principally polarized abelian surfaces. As a corollary, we give another algebraic geometric proof of Theorem 2 in the paper of Castryck et al.
doi:10.2140/obs.2020.4.283 fatcat:qhbwqrs375gqrjsvsozrqiga7q