A Geometric Square-Based Approach to RSA Integer Factorization

TL;DR

This paper introduces a geometric square-based method for RSA factorization that leverages square differences and recurrence relations, showing promise for small semiprimes but limited effectiveness on larger, real-world RSA moduli.

Contribution

The paper proposes a novel geometric approach to RSA factorization using square differences and recurrence relations, offering a new perspective on the problem.

Findings

Efficient for small semiprimes

Fails to factor large RSA challenges like RSA-100 in practical time

Highlights potential and limitations of the geometric method

Abstract

We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that allows rapid convergence when the RSA modulus has closely spaced prime factors. Although this method is efficient for small semiprimes, it does not yet succeed in factoring large challenges like RSA-100 in practical time, highlighting both its potential and current limitations.