Revisiting RSA-polynomial problem and semiprime factorization

Abstract

This paper focuses on the RSA-polynomial problem, a cryptographic hard problem that has been recently proposed and studied in, along with its various applications. We revisit this problem and conduct a refined analysis to address an ambiguous condition that was previously introduced in the context of RSA-polynomial based semiprime factorization. By deriving an accurate attack condition, we are able to identify weak cases of the RSA-polynomial problem and expand the vulnerable bound. To facilitate this, we propose two optimized factoring attacks that leverage improved lattice-based theorems for solving bivariate integer polynomials of a specific form. The validity and effectiveness of our proposed factoring attacks are verified through both theoretical analysis and experimental results. Additionally, we examine the RSA-polynomial based commitment scheme and identify deficiencies that compromise its reliability. To address the limitations, we propose enhancements to the commitment phase of the scheme.