A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems

Tetsuya Tamura; Kouichi Sakurai; Tsutomu Matsumoto

doi:10.1007/10719994_18

A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems

Tetsuya Tamura, Kouichi Sakurai, Tsutomu Matsumoto

Mathematical Informatics

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

Abstract

In this paper, we present algorithms, suitable for hardware implementation, for computation in the Jacobian of a hyperelliptic curve defined over GF(2n). We take curves of genus 3 and 6, designed by using 0.27- um CMOS gate array technology, and estimate the number of multiplication operations and the size and speed of hardware based on the proposed algorithm. It is shown that hardware for genus 6 curves computes an addition (resp. doubling) operation in 100 (resp. 29) clock cycles and can work at clock frequencies of up to 83 MHz We also compare a hyperelliptic curve cryptosystem with RSA and elliptic curve cryptosystems from the viewpoint of hardware implementation.

Original language	English
Title of host publication	Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings
Editors	JooSeok Song
Publisher	Springer Verlag
Pages	221-235
Number of pages	15
ISBN (Print)	3540673806, 9783540673804
DOIs	https://doi.org/10.1007/10719994_18
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)

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10.1007/10719994_18

Cite this

Tamura, T., Sakurai, K., & Matsumoto, T. (2000). A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems. In J. Song (Ed.), Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings (pp. 221-235). (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_18

A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems. / Tamura, Tetsuya; Sakurai, Kouichi; Matsumoto, Tsutomu.

Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. ed. / JooSeok Song. Springer Verlag, 2000. p. 221-235 (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

Tamura, T, Sakurai, K & Matsumoto, T 2000, A hardware-oriented algorithm for computing in Jacobians and its implementation for 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. 221-235, 2nd International Conference on Information Security and Cryptology, ICISC 1999, Seoul, Korea, Republic of, 12/9/99. https://doi.org/10.1007/10719994_18

Tamura T, Sakurai K, Matsumoto T. A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems. In Song J, editor, Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. Springer Verlag. 2000. p. 221-235. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/10719994_18

Tamura, Tetsuya ; Sakurai, Kouichi ; Matsumoto, Tsutomu. / A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems. Information Security and Cryptology - ICISC 1999 - 2nd International Conference, Proceedings. editor / JooSeok Song. Springer Verlag, 2000. pp. 221-235 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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A hardware-oriented algorithm for computing in Jacobians and its implementation for hyperelliptic curve cryptosystems

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