Models of Curves from GHS Attack in Odd Characteristic

  • Song TianEmail author
  • Wei Yu
  • Bao Li
  • Kunpeng Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9065)


The idea behind the GHS attack is to transform the discrete logarithm problem(DLP) in the Jacobian of a (hyper-)elliptic curve over an extension field into DLPs in Jacobians of covering curves over the base field. Diem gives a condition under which explicit defining equations for some coverings are computed. In this paper, we show that his method works without that condition. We also give explicit map from the covering to the original curve if the covering is hyperelliptic. Our method is based on a formula for the embedding of rational subfield of the function field of (hyper)elliptic curve in that of the hyperelliptic covering.


GHS Attack Elliptic Curve Hyperelliptic Curve 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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