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

Vishnupriya Anupindi, László Mérai

For a given hyperelliptic curve $C$ over a finite field with Jacobian $J_C$, we consider the hyperelliptic analogue of the congruential generator defined by $W_n=W_{n-1}+D$ for $n\geq 1$ and $D,W_0\in J_C$. We show that curves of genus 2 produce sequences with large linear complexity.

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