International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Tonghai Yang

Publications

Year
Venue
Title
2014
EPRINT
2010
EPRINT
Computing genus 2 curves from invariants on the Hilbert moduli space
Kristin E. Lauter Tonghai Yang
We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular functions on the Hilbert moduli space and show how to compute them. We relate them to the usual three Igusa invariants on the Siegel moduli space and give an algorithm to construct curves using these new invariants. Our approach simplifies the complex analytic method for computing genus 2 curves for cryptography and reduces the amount of computation required.