Efficient algorithms for the construction of hyperelliptic cryptosystems

Tatsuaki Okamoto, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

The jacobian of hyperelliptic curves, including elliptic curves as a special case, offers a good primitive for cryptosystems, since cryptosystems (discrete logarithms) based on the jacobians seem to be more intractable than those based on conventional multiplicative groups. In this paper, we show that the problem to determine the group structure of the jacobian can be characterized to be in NP ∩ co-NP, when the jacobian is a non-degenerate type (“non-half-degenerate”). We also show that the hyperelliptic discrete logarithm can be characterized to be in NP ∩ co-NP, when the group structure is non-half-degenerate. Moreover, we imply the reducibility of the hyperelliptic discrete logarithm to a multiplicative discrete logarithm. The extended Weil pairing over the jacobian is the key tool for these algorithms.

Original languageEnglish
Title of host publicationAdvances in Cryptology — CRYPTO 1991, Proceedings
EditorsJoan Feigenbaum
PublisherSpringer Verlag
Pages267-278
Number of pages12
ISBN (Print)9783540551881
Publication statusPublished - Jan 1 1992
Event11th Confrence on Advances in Cryptology, CRYPTO 1991 - Santa Barbara, United States
Duration: Aug 11 1991Aug 15 1991

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume576 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th Confrence on Advances in Cryptology, CRYPTO 1991
CountryUnited States
CitySanta Barbara
Period8/11/918/15/91

Fingerprint

Cryptosystem
Discrete Logarithm
Cryptography
Efficient Algorithms
Multiplicative
Weil Pairing
Hyperelliptic Curves
Reducibility
Elliptic Curves
Imply

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Okamoto, T., & Sakurai, K. (1992). Efficient algorithms for the construction of hyperelliptic cryptosystems. In J. Feigenbaum (Ed.), Advances in Cryptology — CRYPTO 1991, Proceedings (pp. 267-278). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 576 LNCS). Springer Verlag.

Efficient algorithms for the construction of hyperelliptic cryptosystems. / Okamoto, Tatsuaki; Sakurai, Kouichi.

Advances in Cryptology — CRYPTO 1991, Proceedings. ed. / Joan Feigenbaum. Springer Verlag, 1992. p. 267-278 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 576 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Okamoto, T & Sakurai, K 1992, Efficient algorithms for the construction of hyperelliptic cryptosystems. in J Feigenbaum (ed.), Advances in Cryptology — CRYPTO 1991, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 576 LNCS, Springer Verlag, pp. 267-278, 11th Confrence on Advances in Cryptology, CRYPTO 1991, Santa Barbara, United States, 8/11/91.
Okamoto T, Sakurai K. Efficient algorithms for the construction of hyperelliptic cryptosystems. In Feigenbaum J, editor, Advances in Cryptology — CRYPTO 1991, Proceedings. Springer Verlag. 1992. p. 267-278. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Okamoto, Tatsuaki ; Sakurai, Kouichi. / Efficient algorithms for the construction of hyperelliptic cryptosystems. Advances in Cryptology — CRYPTO 1991, Proceedings. editor / Joan Feigenbaum. Springer Verlag, 1992. pp. 267-278 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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