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Secure hyperelliptic cryptosystems and their performance

  • Yasuyuki Sakai
  • Kouichi Sakurai
  • Hirokazu Ishizuka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1431)

Abstract

We investigate the discrete logarithm problem over jacobian varieties of hyperelliptic curves suitable for public-key cryptosystems, and clarify practical advantages of hyperelliptic cryptosystems compared to the elliptic cryptosystems and to RSA. We focus on the curves defined over the ground field of characteristic 2, and we present hyperelliptic cryptosystems from the jacobian associated with curves C : v 2 + v=u 2g+1 of genus g=3 and 11, which are secure against the known attacks. We further discuss the efficiency in implementation of such secure hyperelliptic cryptosystems.

Keywords

Public key Hyperelliptic curve Discrete logarithm Jacobian 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Yasuyuki Sakai
    • 1
  • Kouichi Sakurai
    • 2
  • Hirokazu Ishizuka
    • 1
  1. 1.Mitsubishi Electric CorporationKanagawaJapan
  2. 2.Kyushu UniversityFukuokaJapan

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