GU Haihua, GU Dawu. Extending the GHS Attack of Hyperelliptic Curves[J]. Chinese Journal of Electronics, 2009, 18(4): 741-743.
Citation: GU Haihua, GU Dawu. Extending the GHS Attack of Hyperelliptic Curves[J]. Chinese Journal of Electronics, 2009, 18(4): 741-743.

Extending the GHS Attack of Hyperelliptic Curves

  • Received Date: 2008-03-01
  • Rev Recd Date: 2009-02-01
  • Publish Date: 2009-11-25
  • The security of elliptic curve cryptosystems is based on the intractability of the discrete logarithmproblem. The GHS attack provides a way of attacking elliptic curve discrete logarithm problem. Galbraith et al.extended the GHS attack to a much larger class of ellipticcurves.In this paper, we apply Galbraith et al.'s idea to theGHS attack of hyperelliptic curves over non-prime fieldsof characteristic not two. The idea is that we first construct an effciently-computable homomorphism and thenmap the hyperelliptic curve to a new hyperelliptic curve.Hence the discrete logarithm problem can be transformedinto a discrete logarithm problem on a new hyperellipticcurve for which the generalized GHS attack is potentialeffective.
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