A Review on the Isomorphism Classes of Hyperelliptic Curves of Genus 2 over Finite Fields Admitting a Weierstrass Point

The reduced equations for the isomorphism classes of hyperelliptic curves of genus 2 admitting a Weierstrass point over a finite field of arbitrary characteristic, are shown and the number of such classes is included. This work picks up in a unified way a series of previous results published by several authors by using different methodologies. These classifications are of interest in designing and implementing of hyperelliptic curve cryptosystems.

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