Efficient doubling on genus two curves over binary fields

Tanja Lange; Marc Stevens

doi:10.1007/978-3-540-30564-4_12

Efficient doubling on genus two curves over binary fields

Tanja Lange, Marc Stevens

Mathematics and Computer Science

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

30 Citations (Scopus)

Abstract

In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes. This paper investigates how to compute faster doubling over fields of characteristic two. We derive explicit doubling formulae making strong use of the defining equation of the curve. We analyze how many field operations are needed depending on the curve making clear how much generality one loses by the respective choices. Note, that none of the proposed types is known to be weak – one only could be suspicious because of the more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only half the time of an addition. Combined with a sliding window method this leads to fast computation of scalar multiples. We also speed up the general case.

Original language	English
Title of host publication	Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers
Editors	H. Handschuh, M.A. Hasan, R.L. Wainwright, L.M. Liebrock
Place of Publication	Berlin
Publisher	Springer
Pages	170-181
Number of pages	12
ISBN (Print)	3-540-24327-5
DOIs	https://doi.org/10.1007/978-3-540-30564-4_12
Publication status	Published - 1 Dec 2004

Publication series

Name	Lecture Notes in Computer Science
Volume	3357
ISSN (Print)	0302-9743

Keywords

Binary fields
Explicit group operations
Fast arithmetic
Hyperelliptic curves

Access to Document

10.1007/978-3-540-30564-4_12

Cite this

Lange, T., & Stevens, M. (2004). Efficient doubling on genus two curves over binary fields. In H. Handschuh, M. A. Hasan, R. L. Wainwright, & L. M. Liebrock (Eds.), Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers (pp. 170-181). (Lecture Notes in Computer Science; Vol. 3357). Springer. https://doi.org/10.1007/978-3-540-30564-4_12

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Lange, T & Stevens, M 2004, Efficient doubling on genus two curves over binary fields. in H Handschuh, MA Hasan, RL Wainwright & LM Liebrock (eds), Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers. Lecture Notes in Computer Science, vol. 3357, Springer, Berlin, pp. 170-181. https://doi.org/10.1007/978-3-540-30564-4_12

Efficient doubling on genus two curves over binary fields. / Lange, Tanja; Stevens, Marc.

Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers. ed. / H. Handschuh; M.A. Hasan; R.L. Wainwright; L.M. Liebrock. Berlin : Springer, 2004. p. 170-181 (Lecture Notes in Computer Science; Vol. 3357).

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

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Lange T, Stevens M. Efficient doubling on genus two curves over binary fields. In Handschuh H, Hasan MA, Wainwright RL, Liebrock LM, editors, Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers. Berlin: Springer. 2004. p. 170-181. (Lecture Notes in Computer Science). doi: 10.1007/978-3-540-30564-4_12

Efficient doubling on genus two curves over binary fields

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