Machine learning for moduli space of genus two curves and an application to post-quantum cryptography

• URL: http://arxiv.org/abs/2403.17250v1
• Date: Mon, 25 Mar 2024 22:52:50 GMT
• Title: Machine learning for moduli space of genus two curves and an application to post-quantum cryptography
• Authors: Elira Shaska, Tony Shaska,
• Abstract summary: We use machine learning to study the locus $mathcal L_n$ of genus two curves with $(n, n)$-split Jacobian. Such curves are important in isogeny based cryptography.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We use machine learning to study the locus ${\mathcal L}_n$ of genus two curves with $(n, n)$-split Jacobian. More precisely we design a transformer model which given values for the Igusa invariants determines if the corresponding genus two curve is in the locus ${\mathcal L}_n$, for $n=2, 3, 5, 7$. Such curves are important in isogeny based cryptography. During this study we discover that there are no rational points ${\mathfrak p} \in {\mathcal L}_n$ with weighted moduli height $\leq 2$ in any of ${\mathcal L}_2$, ${\mathcal L}_3$, and ${\mathcal L}_5$. This extends on previous work of the authors to use machine learning methods to study the moduli space of genus 2 algebraic curves.

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