Extending the GHS Attack of Hyperelliptic Curves

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.