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.

翻译：对于以Jacobian $_C$为限定字段的超升利平曲线,如果以Jacobian $_C$为单位,则我们考虑W_n=W ⁇ n-1 ⁇ D$定义的同质发电机的超升利平比,即$n\geq 1美元和$D,W_0\in J_C$。我们显示,genus 2 的曲线产生大量线性复杂的序列。