A New Heuristic Algorithm Based on Molecular Geometry Optimization and Its Application to the Integer Factorization Problem

Abstract

In this paper, the intractable problem of finding the prime factors of an integer has been represented as the integer programming problem to be solved using nature inspired heuristics. Integer factorization is a one-way mathematical function and because of its computational intractability, it is frequently used in public key cryptography, for example in RSA encryption systems. Since integer factorization can be represented in the form of a discrete optimization task, more specifically as integer programming problem, various optimization tools can be utilized for cryptanalysis. In this contribution, we approach this problem using a heuristic algorithm designed with concepts derived from computational chemistry that involves energy minimization of a molecular geometry of a crystal. We observe that computational chemistry can provide a great insight into such problems of unknown dynamics. Future work remains to optimize the algorithm for scalability.