I‑AIMS Institute for Artificial Intelligence
and Mathematical Sciences
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Machine learning for M₂ and an application to isogeny based cryptography

Elira Shaska, Tanush Shaska

I-AIMS paper 2024-03 · Published in J. Algebraic Combin. 61 (2025), Paper 23 · 2025

We use machine learning to study the moduli space of genus two curves and more specifically distribution of fine moduli points and detecting if a genus two curve has (n,n)-split Jacobian. We show that there are very few rational moduli points with small weighted height and (n,n)-split Jacobian for n = 2, 3, 5. Moreover, using a K-Neighbors Classifier we are able to detect splitting with an accuracy of 99.9%. This shows that artificial neural networks and machine learning techniques could be quite reliable on arithmetic questions in the moduli space of genus two curves and can possibly be used to applications in isogeny based cryptography.

MSC classes: Primary 68T07; Secondary 68T20, 68Q32

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References

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