Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2009; 46(4): 789-802

Printed July 1, 2009

https://doi.org/10.4134/BKMS.2009.46.4.789

Copyright © The Korean Mathematical Society.

An algorithm for computing a sequence of Richelot isogenies

Katsuyuki Takashima and Reo Yoshida

Mitsubishi Electric and Kyoto University

Abstract

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We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over $\mathbb F_{p}$ can be executed in $\mathbb F_{p^2}$ or $\mathbb F_{p^4}$. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.

Keywords: hyperelliptic curve, genus two, Richelot isogeny, isogeny graph, supersingular curve

MSC numbers: 14Q05, 11Y16, 11T71, 14K02

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