Efficient Algorithms for the Construction of Hyperelliptic Cryptosystems

  • Tatsuaki Okamoto
  • Kouichi Sakurai
Conference paper

DOI: 10.1007/3-540-46766-1_21

Part of the Lecture Notes in Computer Science book series (LNCS, volume 576)
Cite this paper as:
Okamoto T., Sakurai K. (1992) Efficient Algorithms for the Construction of Hyperelliptic Cryptosystems. In: Feigenbaum J. (eds) Advances in Cryptology — CRYPTO ’91. CRYPTO 1991. Lecture Notes in Computer Science, vol 576. Springer, Berlin, Heidelberg


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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Tatsuaki Okamoto
    • 1
  • Kouichi Sakurai
    • 2
  1. 1.NTT LaboratoriesNippon Telegraph and Telephone CorporationKanagawa-kenJapan
  2. 2.Information Systems and Electronics Development LaboratoryMitsubishi Electric CorporationKamakuraJapan

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