Linear Time Solution to Prime Factorization by Tissue P Systems with Cell Division

Abstract

Prime factorization is useful and crucial for public-key cryptography, and its application in public-key cryptography is possible only because prime factorization has been presumed to be difficult. A polynomial-time algorithm for prime factorization on a quantum computer is given by P. W. Shor in 1997. In this work, a linear-time solution for prime factorization is given on a kind of biochemical computational devices - tissue P systems with cell division, instead of physical computational devices.