Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F2n

Yasuyuki Sakai; Kouichi Sakurai

doi:10.1007/3-540-49649-1_8

Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F₂ⁿ

Yasuyuki Sakai, Kouichi Sakurai

Mathematical Informatics

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

23 Citations (Scopus)

Abstract

We investigate the discrete logarithm problem over jacobians of hyperelliptic curves suitable for public-key cryptosystems. We focus on the case when the definition field has small characteristic 2, 3, 5 and 7, then we present hyperelliptic cryptosystems that resist against all known attacks. We further implement our designed hyperelliptic cryptosystems over finite fields F₂ⁿ in software on Alpha and Pentium-II computers. Our results indicate that if we choose curves carefully, hyperelliptic cryp-tosystems do have practical performance.

Original language	English
Title of host publication	Advances in Cryptology – ASIACRYPT 1998 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
Editors	Kazuo Ohta, Dingyi Pei
Publisher	Springer Verlag
Pages	80-94
Number of pages	15
ISBN (Print)	3540651098, 9783540651093
DOIs	https://doi.org/10.1007/3-540-49649-1_8
Publication status	Published - 1998
Event	4th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 1998 - Beijing, China Duration: Oct 18 1998 → Oct 22 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1514
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 1998
Country/Territory	China
City	Beijing
Period	10/18/98 → 10/22/98

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-49649-1_8

Cite this

Sakai, Y., & Sakurai, K. (1998). Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F₂ⁿ. In K. Ohta, & D. Pei (Eds.), Advances in Cryptology – ASIACRYPT 1998 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings (pp. 80-94). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1514). Springer Verlag. https://doi.org/10.1007/3-540-49649-1_8

Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F₂ⁿ. / Sakai, Yasuyuki; Sakurai, Kouichi.

Advances in Cryptology – ASIACRYPT 1998 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. ed. / Kazuo Ohta; Dingyi Pei. Springer Verlag, 1998. p. 80-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1514).

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

Sakai, Y & Sakurai, K 1998, Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F₂ⁿ. in K Ohta & D Pei (eds), Advances in Cryptology – ASIACRYPT 1998 - 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. 1514, Springer Verlag, pp. 80-94, 4th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 1998, Beijing, China, 10/18/98. https://doi.org/10.1007/3-540-49649-1_8

Sakai Y, Sakurai K. Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F₂ⁿ. In Ohta K, Pei D, editors, Advances in Cryptology – ASIACRYPT 1998 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Springer Verlag. 1998. p. 80-94. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-49649-1_8

Sakai, Yasuyuki ; Sakurai, Kouichi. / Design of hyperelliptic cryptosystems in small characteristic and a software implementation over F₂ⁿ. Advances in Cryptology – ASIACRYPT 1998 - International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. editor / Kazuo Ohta ; Dingyi Pei. Springer Verlag, 1998. pp. 80-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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