GU Haihua and GU Dawu, “Extending the GHS Attack of Hyperelliptic Curves,” Chinese Journal of Electronics, vol. 18, no. 4, pp. 741-743, 2009,
Citation: GU Haihua and GU Dawu, “Extending the GHS Attack of Hyperelliptic Curves,” Chinese Journal of Electronics, vol. 18, no. 4, pp. 741-743, 2009,

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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