Polynomial-time Method of Determining Subset Sum Solutions

TL;DR

This paper introduces a polynomial-time algorithm for solving the subset sum problem by translating it into linear systems, potentially impacting cryptography reliant on NP-hard assumptions.

Contribution

It presents a novel polynomial-time method for subset sum, challenging the traditional NP-hard classification and its cryptographic implications.

Findings

Achieves 100% accuracy in subset sum solutions

Transforms subset sum into linear systems solvable in polynomial time

Potentially undermines cryptosystems based on NP-hardness

Abstract

Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by forming, solving, and constraining a series of linear systems whose dimensions and number are both polynomial with respect to the length of the set. Given its demonstrated 100% accuracy rate and its demonstrable justification, this algorithm may provide basis to reconsider the validity of SSP-based and NP-hard-reliant cryptosystems.