Genus 2 point counting over prime fields

For counting points of jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof’s genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-ofthe-art security level of approximately 2 and desirable speed properties. This curve and its quadratic twist have a Jacobian group whose order is 16 times a prime.