Linear Complexity of Sequences Derived From Hyperelliptic Curves of Genus 2.
Vishnupriya Anupindi
Pseudorandom sequences, that is, sequences which are generated with deterministic algorithms but look random, have many applications, for example in cryptography, in wireless communication or in numerical methods. In this thesis, we are interested in studying the properties of pseudorandomness of sequences derived from hyperelliptic curves of genus 2.
In particular, we look at two different ways of generating sequences, that is, the linear congruential generator and the Frobenius endomorphism generator over hyperelliptic curves of genus 2. We show that these sequences possess good pseudorandom properties in terms of linear complexity. Our method uses an embedding of the Jacobian into the projective space of dimension 8 provided by David Grant, which gives explicit addition formulas for elements on the Jacobian.