2021/08/16 by Toshiyuki Katsura, Katsura, Toshiyuki, Katsuyuki Takashima +1 · 1 citation
Computer Science · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2108.06936
openalex publication_date 2021/08/16 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28
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).