Over Fp vs. Over F2n and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems

Yasuyuki Sakai; Kouichi Sakurai

doi:10.1007/10719994_8

Over F_p vs. Over F²ⁿ and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems

Yasuyuki Sakai, Kouichi Sakurai

Mathematical Informatics

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

Abstract

We consider the performance of hyperelliptic curve cryptosystems over the fields Fp vs. F_2n. We analyze the complexity of the group law of the Jacobians JC(F_p) and JC(F_2n) and compare their performance taking into consideration the effiectiveness of the word size (32- bit or 64-bit) of the applied CPU (Alpha and Pentium) on the arithmetic of the definition field. Our experimental results show that JC(F_2n) is faster than JC(F_p) on an Alpha, whereas JC(F_p) is faster than JC(F_2n) on a Pentium. Moreover, we investigate the algorithm of the Jacobian and the definition-field arithmetic to clarify our results from a practical point of view, with theoretical analysis.

Original language	English
Title of host publication	Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings
Editors	JooSeok Song
Publisher	Springer Verlag
Pages	82-101
Number of pages	20
ISBN (Print)	3540673806, 9783540673804
DOIs	https://doi.org/10.1007/10719994_8
Publication status	Published - Jan 1 2000
Event	2nd International Conference on Information Security and Cryptology, ICISC 1999 - Seoul, Korea, Republic of Duration: Dec 9 1999 → Dec 10 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1787
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	2nd International Conference on Information Security and Cryptology, ICISC 1999
Country/Territory	Korea, Republic of
City	Seoul
Period	12/9/99 → 12/10/99

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/10719994_8

Cite this

Sakai, Y., & Sakurai, K. (2000). Over F_p vs. Over F²ⁿ and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems. In J. Song (Ed.), Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings (pp. 82-101). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1787). Springer Verlag. https://doi.org/10.1007/10719994_8

Over F_p vs. Over F²ⁿ and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems. / Sakai, Yasuyuki; Sakurai, Kouichi.

Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. ed. / JooSeok Song. Springer Verlag, 2000. p. 82-101 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1787).

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

Sakai, Y & Sakurai, K 2000, Over F_p vs. Over F²ⁿ and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems. in J Song (ed.), Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1787, Springer Verlag, pp. 82-101, 2nd International Conference on Information Security and Cryptology, ICISC 1999, Seoul, Korea, Republic of, 12/9/99. https://doi.org/10.1007/10719994_8

Sakai Y, Sakurai K. Over F_p vs. Over F²ⁿ and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems. In Song J, editor, Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. Springer Verlag. 2000. p. 82-101. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/10719994_8

Sakai, Yasuyuki ; Sakurai, Kouichi. / Over F_p vs. Over F²ⁿ and on pentium vs. on alpha in software implementation of hyperelliptic curve cryptosystems. Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. editor / JooSeok Song. Springer Verlag, 2000. pp. 82-101 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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