Efficient divisor class halving on genus two curves

P. Birkner

doi:10.1007/978-3-540-74462-7_22

Efficient divisor class halving on genus two curves

P. Birkner

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

9 Citations (Scopus)

82 Downloads (Pure)

Abstract

Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling algorithm by reversing this process. A family of binary curves, that are not known to be weak, is covered by the proposed algorithm. Compared to previous known halving algorithms, we achieve a noticeable speed-up for this family of curves.

Original language	English
Title of host publication	Revised selected papers of the 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006) 17-18 August 2006, Montreal, Quebec, Canada
Editors	E. Biham, A.M. Youssef
Place of Publication	Berlin
Publisher	Springer
Pages	317-326
ISBN (Print)	978-3-540-74462-7
DOIs	https://doi.org/10.1007/978-3-540-74462-7_22
Publication status	Published - 2007
Event	13th Annual Workshop on Selected Areas in Cryptography (SAC 2006) - Montreal, Canada Duration: 17 Aug 2007 → 18 Aug 2007 Conference number: 13

Publication series

Name	Lecture Notes in Computer Science
Volume	4356
ISSN (Print)	0302-9743

Conference

Conference	13th Annual Workshop on Selected Areas in Cryptography (SAC 2006)
Abbreviated title	SAC 2006
Country/Territory	Canada
City	Montreal
Period	17/08/07 → 18/08/07

Access to Document

10.1007/978-3-540-74462-7_22

Metis207425Final published version, 477 KB

Cite this

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title = "Efficient divisor class halving on genus two curves",

abstract = "Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling algorithm by reversing this process. A family of binary curves, that are not known to be weak, is covered by the proposed algorithm. Compared to previous known halving algorithms, we achieve a noticeable speed-up for this family of curves.",

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language = "English",

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pages = "317--326",

editor = "E. Biham and A.M. Youssef",

booktitle = "Revised selected papers of the 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006) 17-18 August 2006, Montreal, Quebec, Canada",

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note = "13th Annual Workshop on Selected Areas in Cryptography (SAC 2006), SAC 2006 ; Conference date: 17-08-2007 Through 18-08-2007",

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Birkner, P 2007, Efficient divisor class halving on genus two curves. in E Biham & AM Youssef (eds), Revised selected papers of the 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006) 17-18 August 2006, Montreal, Quebec, Canada. Lecture Notes in Computer Science, vol. 4356, Springer, Berlin, pp. 317-326, 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006), Montreal, Quebec, Canada, 17/08/07. https://doi.org/10.1007/978-3-540-74462-7_22

Efficient divisor class halving on genus two curves. / Birkner, P.
Revised selected papers of the 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006) 17-18 August 2006, Montreal, Quebec, Canada. ed. / E. Biham; A.M. Youssef. Berlin: Springer, 2007. p. 317-326 (Lecture Notes in Computer Science; Vol. 4356).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling algorithm by reversing this process. A family of binary curves, that are not known to be weak, is covered by the proposed algorithm. Compared to previous known halving algorithms, we achieve a noticeable speed-up for this family of curves.

AB - Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling algorithm by reversing this process. A family of binary curves, that are not known to be weak, is covered by the proposed algorithm. Compared to previous known halving algorithms, we achieve a noticeable speed-up for this family of curves.

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DO - 10.1007/978-3-540-74462-7_22

M3 - Conference contribution

SN - 978-3-540-74462-7

T3 - Lecture Notes in Computer Science

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BT - Revised selected papers of the 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006) 17-18 August 2006, Montreal, Quebec, Canada

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T2 - 13th Annual Workshop on Selected Areas in Cryptography (SAC 2006)

Y2 - 17 August 2007 through 18 August 2007

ER -

Efficient divisor class halving on genus two curves

Abstract

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