Linear complexity of some sequences derived from hyperelliptic curves of genus 2

For a given hyperelliptic curve C over a finite field with Jacobian JC, we consider the hyperelliptic analogue of the congruential generator defined by Wn = Wn− 1 + D for n ≥ 1 and D, W0 ∈ JC. We show that curves of genus 2 produce sequences with large linear complexity.