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Seminar of Algebraic Geometry in East Asia
 
16:15 - 17:15, October 9, 2020 (Friday)
Zoom, Online seminar
(線上seminar Zoom)
Counting Richelot Isogenies of Superspecial Curves of Genus 2
Toshiyuki Katsura (University of Tokyo)

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.).



 

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