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An analogue solution to the problem of factorization

By 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 cryptographic system, for example, secure. We describe an analogue method of factorizing. Just as with traditional algorithms, there is a practical limit to the size of numbers that the method can factorize; in contrast with traditional algorithms, however, the method suffers no increase in calculation time as the input 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

Topics: Computer science (mathematics), factorization, analogue computer
Year: 2007
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