Asymptotically fast factorization of integers

Author:
John D. Dixon

Journal:
Math. Comp. **36** (1981), 255-260

MSC:
Primary 10A30; Secondary 10A25

MathSciNet review:
595059

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Abstract: The paper describes a "probabilistic algorithm" for finding a factor of any large composite integer *n* (the required input is the integer *n* together with an auxiliary sequence of random numbers). It is proved that the expected number of operations which will be required is for some constant . Asymptotically, this algorithm is much faster than any previously analyzed algorithm for factoring integers; earlier algorithms have all required operations where .

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0595059-1

Article copyright:
© Copyright 1981
American Mathematical Society