Extending the GHS Attack of Hyperelliptic Curves

The security of elliptic curve cryptosystems is based on the intractability of the discrete logarithm problem. 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 elliptic curves. In this paper, we apply Galbraith et al.'s idea to the GHS attack of hyperelliptic curves over non-prime fields of characteristic not two. The idea is that we first construct an efficiently-computable homomorphism and then map the hyperelliptic curve to a new hyperelliptic curve. Hence the discrete logarithm problem can be transformed into a discrete logarithm problem on a new hyperelliptic curve for which the generalized GHS attack is potential effective.