Year: 2024
Type: preprint
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 $\mathbb{Q}(\sqrt{N})$.
Source: arXiv (Cornell University)
Authors: Murru, Nadir, Salvatori, Giulia
Institutions: Politecnico di Torino, University of Trento
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G507880695
OpenAlex ID: W4403556463