Fast Endomorphism for any Genus 2 Hyperelliptic Curve over a Finite Field of Even Characteristic.

In EUROCRYPT 2009, Galbraith, Lin and Scott constructed an efficiently computable en- domorphism for a large family of elliptic curves defined over finite fields of large characteristic. They demonstrated that the endomorphism can be used to accelerate scalar multiplication in the elliptic curve cryptosystem based on these curves. In this paper we extend the method to any genus 2 hyperelliptic curve defined over a finite field of even characteristic. We propose an efficient algorithm to generate a random genus 2 hyperelliptic curve and its quadratic twist equipped with a fast endomorphism on the Jacobian. The analysis of the operation amount of the scalar multiplication is also given.