Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593218 | Journal of Number Theory | 2016 | 29 Pages |
Abstract
In this paper, we compute pull-backs of Siegel theta functions to the Hilbert moduli space and consider their application to generating genus 2 curves for cryptography. We express invariants of genus 2 curves such as the Gundlach invariants and Rosenhain invariants in terms of these Hilbert theta functions. A result of independent interest is a simple formula in terms of these functions for the Eisenstein series of weight 2, which is not the pull-back of any Siegel modular form of level 1. We present an algorithm to compute minimal polynomials for the invariants, including a description of CM points and how to compute them, along with numerical examples.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kristin Lauter, Michael Naehrig, Tonghai Yang,