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

arXiv:2403.17250v1 Announce Type: cross
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 …

application arxiv cryptography cs.cr curve design machine machine learning math.ag post-quantum post-quantum cryptography precisely quantum quantum cryptography space study