Revisiting Integer Factorization using Closed Timelike Curves

TL;DR

This paper examines the use of Closed Timelike Curves in computation, identifies flaws in previous algorithms for factoring, and proposes a corrected approach to leverage CTCs for solving problems like integer factorization.

Contribution

The paper finds a flaw in Brun's CTC-based factoring algorithm and introduces a modified algorithm to address this issue.

Findings

Identified a flaw in Brun's original algorithm.

Proposed a corrected algorithm for integer factorization using CTCs.

Enhanced understanding of CTCs' role in computational complexity.

Abstract

Closed Timelike Curves are relativistically valid objects allowing time travel to the past. Treating them as computational objects opens the door to a wide range of results which cannot be achieved using non relativistic quantum mechanics. Recently, research in classical and quantum computation has focused on effectively harnessing the power of these curves. In particular, Brun (Found. Phys. Lett., 2003) has shown that CTCs can be utilized to efficiently solve problems like factoring and QSAT (Quantified Satisfiability Problem). In this paper, we find a flaw in Brun's algorithm and propose a modified algorithm to circumvent the flaw.