Speeding up the discrete log computation on curves with automorphisms

I. Duursma; P. Gaudry; F. Morain

doi:10.1007/978-3-540-48000-6_10

Speeding up the discrete log computation on curves with automorphisms

I. Duursma
, P. Gaudry
, F. Morain

Limoges University
Laboratoire d'Informatique (LIX)

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

Abstract

We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on anomalous binary elliptic curves. This includes the first known attack on most of the hyperelliptic curves described in the literature.

Original language	English
Title of host publication	Advances in Cryptology - ASIACRYPT 1999 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
Editors	Kwok Yan Lam, Eiji Okamoto, Chaoping Xing
Publisher	Springer Verlag
Pages	103-121
Number of pages	19
ISBN (Print)	3540666664, 9783540666660
DOIs	https://doi.org/10.1007/978-3-540-48000-6_10
Publication status	Published - 1 Jan 1999
Event	5th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 1999 - Singapore, Singapore Duration: 14 Nov 1999 → 18 Nov 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1716
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 1999
Country/Territory	Singapore
City	Singapore
Period	14/11/99 → 18/11/99

Keywords

Automorphisms
Discrete logarithm
Elliptic and hyperelliptic curves

Access to Document

10.1007/978-3-540-48000-6_10

Cite this

Duursma, I., Gaudry, P., & Morain, F. (1999). Speeding up the discrete log computation on curves with automorphisms. In K. Y. Lam, E. Okamoto, & C. Xing (Eds.), Advances in Cryptology - ASIACRYPT 1999 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings (pp. 103-121). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1716). Springer Verlag. https://doi.org/10.1007/978-3-540-48000-6_10

Duursma, I. ; Gaudry, P. ; Morain, F. / Speeding up the discrete log computation on curves with automorphisms. Advances in Cryptology - ASIACRYPT 1999 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. editor / Kwok Yan Lam ; Eiji Okamoto ; Chaoping Xing. Springer Verlag, 1999. pp. 103-121 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on anomalous binary elliptic curves. This includes the first known attack on most of the hyperelliptic curves described in the literature.",

keywords = "Automorphisms, Discrete logarithm, Elliptic and hyperelliptic curves",

author = "I. Duursma and P. Gaudry and F. Morain",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1999.; 5th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 1999 ; Conference date: 14-11-1999 Through 18-11-1999",

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Duursma, I, Gaudry, P & Morain, F 1999, Speeding up the discrete log computation on curves with automorphisms. in KY Lam, E Okamoto & C Xing (eds), Advances in Cryptology - ASIACRYPT 1999 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1716, Springer Verlag, pp. 103-121, 5th International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 1999, Singapore, Singapore, 14/11/99. https://doi.org/10.1007/978-3-540-48000-6_10

Speeding up the discrete log computation on curves with automorphisms. / Duursma, I.; Gaudry, P.; Morain, F.
Advances in Cryptology - ASIACRYPT 1999 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. ed. / Kwok Yan Lam; Eiji Okamoto; Chaoping Xing. Springer Verlag, 1999. p. 103-121 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1716).

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

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KW - Elliptic and hyperelliptic curves

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DO - 10.1007/978-3-540-48000-6_10

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Duursma I, Gaudry P, Morain F. Speeding up the discrete log computation on curves with automorphisms. In Lam KY, Okamoto E, Xing C, editors, Advances in Cryptology - ASIACRYPT 1999 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Springer Verlag. 1999. p. 103-121. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-48000-6_10

Speeding up the discrete log computation on curves with automorphisms

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