An Analogue Solution to the Problem of Factorization

Abstract

The task of factorizing a given integer is notoriously difficult, to the extent of rendering computationally infeasible the extraction of factors of numbers beyond a certain size. This infeasibility is what makes the RSA cryptgraphic system, for example, secure.

We describe and analogue method¹ of factorizing. Just as with traditional algorithms, there is a practical limit to the size of numbers that the method can factorize; in contract with traditional algorithms, however, the method suffers no increase in calculation time as the imput number approaches this limit.

The process described exploits a direct physical implementation of a geometric formulation of the problem of factorizing; this allows factors of numbers within the allowed range to be ascertained (or else primality guaranteed) virtually instantaneously.