On the Complexity of Hyperelliptic Discrete Logarithm Problem

  • Haroka Shizuya
  • Toshiya Itoh
  • Kouichi Sakurai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)


We give a characterization for the intractability of hyperelliptic discrete logarithm problem from a viewpoint of computational complexity theory. It is shown that the language of which complexity is equivalent to that of the hyperelliptic discrete logarithm problem is in \( \mathcal{N}\mathcal{P} \cap co - \mathcal{A}\mathcal{M} \), and that especially for elliptic curves, the corresponding language is in \( \mathcal{N}\mathcal{P} \cap co - \mathcal{N}\mathcal{P} \). It should be noted here that the language of which complexity is equivalent to that of the discrete logarithm problem defined over the multiplicative group of a finite field is also characterized as in \( \mathcal{N}\mathcal{P} \cap co - \mathcal{N}\mathcal{P} \).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Haroka Shizuya
    • 1
    • 2
  • Toshiya Itoh
    • 3
  • Kouichi Sakurai
    • 4
  1. 1.Department of Electrical Communications, Faculity of EngineeringTohoku UniversitySendaiJapan
  2. 2.Département d’I.R.O.Université de MontréalMontréalCanada
  3. 3.Department of Information Processing, The Graduate School at NagatsutaTokyo Institute of TechnologyYokohamaJapan
  4. 4.Computer & Information Systems LaboratoryMitsubishi Electric CorporationKamakuraJapan

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