### Computing genus 2 curves from invariants on the Hilbert moduli space

Kristin Lauter and Tonghai Yang

##### Abstract

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.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Hyperelliptic curve cryptography
Contact author(s)
klauter @ microsoft com
History
Short URL
https://ia.cr/2010/294

CC BY

BibTeX

@misc{cryptoeprint:2010/294,
author = {Kristin Lauter and Tonghai Yang},
title = {Computing genus 2 curves from invariants on the Hilbert moduli space},
howpublished = {Cryptology ePrint Archive, Paper 2010/294},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/294}},
url = {https://eprint.iacr.org/2010/294}
}

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