**Computing theta functions in quasi-linear time in genus 2 and above**

*Hugo Labrande and Emmanuel Thomé*

**Abstract: **We outline an algorithm to compute $\theta(z,\tau)$ in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for $\theta(z,\tau)$ in genus 1. Our implementation shows a large speedup for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus $g$.

**Category / Keywords: **public-key cryptography / number theory, hyperelliptic curves, theta functions

**Date: **received 22 Feb 2016

**Contact author: **hugo at hlabrande fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20160222:213817 (All versions of this report)

**Short URL: **ia.cr/2016/179

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