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An Analogue Solution to the Problem of Factorization

Ed Blakey

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.

Institution
Oxford University Computing Laboratory
Month
July
Number
RR−07−04
Year
2007