P System Design for Integer Factorization

Membrane computing is a natural computing branch inspired by the structure of biological cells. The mathematical abstract model of a membrane computing system is called a P System, which is one of the main topics in membrane computing research for the design and verification of a P System. Integer factorization is still a world-class problem and a very important research direction. If a fast method can be found to solve the integer factorization problem, several important cryptographic systems including the RSA public key algorithm will be broken. The aim of this paper is to design a P System capable of implementing integer decomposition, taking advantage of the characteristics of parallelism of P Systems. We construct a process with a main goal to study the modal exponential function f(x) = a(x) mod N and explore the possible periodic behavior for different values of a. We attempt to compute nontrivial prime factors by the period found and constrain the operation of the P System in polynomial time.

Automated summary

Membrane computing is a natural computing branch inspired by biological cells. The P System, a mathematical abstract model, is crucial in research on membrane computing for the design and verification of P Systems. Integer factorization remains an important research direction as breaking it would impact cryptographic systems like RSA. This paper aims to design a P System that can implement integer decomposition by exploiting the parallelism of P Systems. The study focuses on the modal exponential function and explores possible periodic behavior to compute nontrivial prime factors in polynomial time.