Polynomial time factoring algorithm using Bayesian arithmetic

TL;DR

This paper presents a polynomial time deterministic factoring algorithm based on Bayesian arithmetic, challenging current cryptographic assumptions and suggesting a new perspective on quantum mechanics modeling.

Contribution

It introduces a novel polynomial time factoring method using Bayesian probability encoding of arithmetic, claiming P=NP and impacting cryptography.

Findings

Provides a polynomial time factoring algorithm

Challenges the assumption that P ≠ NP

Suggests implications for cryptography and quantum models

Abstract

In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion that P = NP. Now, we implement this concept in elementary arithmetic and especially in multiplication. This provides a polynomial time deterministic factoring algorithm, while no such algorithm is known to day. This result clearly appeals for a revaluation of the current cryptosystems. The Bayesian arithmetic environment can also be regarded as a toy model for quantum mechanics.