Counting superspecial Richelot isogenies by reduced automorphism groups (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)

Abstract

The recent cryptanalysis by Costello and Smith [10] employed the subgraphs whose vertices consist of decomposed principally polarized abelian varieties, hence it is important to study the subgraphs in isogeny-based cryptography. Katsura and Takashima [22] initiated the investigation of the decomposed abelian surface subgraphs in the genus-2 case. This paper surveys the work, aiming to provide a kind of handbook for applying our results to cryptography.