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arXiv · 2504.21168

A Summation-Based Algorithm For Integer Factorization

Justin Friedlander
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Abstract

Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA encryption. Some approaches to factoring integers quickly include the Trial Division method, Pollard's Rho and p-1 methods, and various Sieve algorithms. This paper introduces a new method that converts an integer into a sum in base-2. By combining a base-10 and base-2 representation of the integer, an algorithm on the order of $\sqrt{n}$ time complexity can convert that sum to a product of two integers, thus factoring the original number.

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Justin Friedlander. 2025-04-29. A Summation-Based Algorithm For Integer Factorization. https://arxiv.org/abs/2504.21168

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