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

02/04/2021

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by   Vishnupriya Anupindi, et al.

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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≥ 1 and D,W_0∈ J_C. We show that curves of genus 2 produce sequences with large linear complexity.