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arXiv · 2409.03486

Integer Factorization via Continued Fractions and Quadratic Forms

Nadir Murru·Giulia Salvatori
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Abstract

We propose a novel factorization algorithm that leverages the theory underlying the SQUFOF method, including reduced quadratic forms, infrastructural distance, and Gauss composition. We also present an analysis of our method, which has a computational complexity of $O \left( \exp \left( \frac{3}{\sqrt{8}} \sqrt{\ln N \ln \ln N} \right) \right)$, making it more efficient than the classical SQUFOF and CFRAC algorithms. Additionally, our algorithm is polynomial-time, provided knowledge of a (not too large) multiple of the regulator of $\mathbb{Q}(\sqrt{N})$.

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Nadir Murru, Giulia Salvatori. 2024-09-05. Integer Factorization via Continued Fractions and Quadratic Forms. https://arxiv.org/abs/2409.03486

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