Decomposed Richelot isogenies of Jacobian varieties of hyperelliptic curves and generalized Howe curves
This work advances cryptographic analysis of superspecial Richelot isogeny graphs, primarily benefiting researchers in cryptography and algebraic geometry.
The paper characterizes decomposed Richelot isogenies for Jacobian varieties of hyperelliptic curves across any genus and introduces generalized Howe curves, linking them to these isogenies with new examples provided.
We advance previous studies on decomposed Richelot isogenies (Katsura--Takashima (ANTS 2020) and Katsura (ArXiv 2021)) which are useful for analysing superspecial Richelot isogeny graphs in cryptography. We first give a characterization of decomposed Richelot isogenies between Jacobian varieties of hyperelliptic curves of any genus. We then define generalized Howe curves, and present two theorems on their relationships with decomposed Richelot isogenies. We also give new examples including a non-hyperelliptic (resp.\,hyperelliptic) generalized Howe curve of genus 5 (resp.\,of genus 4).