An algorithm for computing a sequence of richelot isogenies

Katsuyuki Takashima; Reo Yoshida

doi:10.4134/BKMS.2009.46.4.789

An algorithm for computing a sequence of richelot isogenies

Katsuyuki Takashima^*, Reo Yoshida

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over Fp can be executed in F_p2 or F_p4. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.

Original language	English
Pages (from-to)	789-802
Number of pages	14
Journal	Bulletin of the Korean Mathematical Society
Volume	46
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.2009.46.4.789
Publication status	Published - 2009
Externally published	Yes

Keywords

Genus two
Hyperelliptic curve
Isogeny graph
Richelot isogeny
Supersingular curve

ASJC Scopus subject areas

Mathematics(all)

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10.4134/BKMS.2009.46.4.789

Cite this

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title = "An algorithm for computing a sequence of richelot isogenies",

abstract = "We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over Fp can be executed in Fp2 or Fp4. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.",

keywords = "Genus two, Hyperelliptic curve, Isogeny graph, Richelot isogeny, Supersingular curve",

author = "Katsuyuki Takashima and Reo Yoshida",

year = "2009",

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AU - Takashima, Katsuyuki

AU - Yoshida, Reo

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AB - We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over Fp can be executed in Fp2 or Fp4. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.

KW - Genus two

KW - Hyperelliptic curve

KW - Isogeny graph

KW - Richelot isogeny

KW - Supersingular curve

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JO - Bulletin of the Korean Mathematical Society

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An algorithm for computing a sequence of richelot isogenies

Abstract

Keywords

ASJC Scopus subject areas

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