Abstract:

Recently, supersingular elliptic curve isogeny cryptography has been extended to the genus-2 case by using superspecial curves of genus 2 and their Richelot isogeny graphs. In view of this situation, we examine the structure of  Richelot isogenies of superspecial curves of genus 2, and give a characterization of decomposed Richelot isogenies. We also give a concrete formula of  the number of such decomposed Richelot isogenies up to isomorphism between superspecial principally polarized abelian surfaces. This is a joint work with Katsuyuki Takashima (Mitsubishi Electic Co.).