Factoring Numbers with elliptic curves

TL;DR

This paper introduces a probabilistic polynomial-time algorithm that reduces the problem of factoring squarefree integers to counting points on elliptic curves modulo n, with high success probability.

Contribution

It presents a novel reduction from integer factorization to elliptic curve point counting, advancing computational number theory methods.

Findings

Algorithm operates in probabilistic polynomial time.

Successfully reduces factorization to elliptic curve point counting.

Achieves high probability of success for the reduction.

Abstract

In the present paper we provide a probabilistic polynomial time algorithm that reduces the complete factorization of any squarefree integer $n$ to counting points on elliptic curves modulo $n$, succeeding with probability $1-\varepsilon$, for any $\varepsilon<0$ .