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Asymptotically Fast Factorization of Integers

John D. Dixon
Mathematics of Computation
Vol. 36, No. 153 (Jan., 1981), pp. 255-260
DOI: 10.2307/2007743
Stable URL: http://www.jstor.org/stable/2007743
Page Count: 6
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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 $O(\exp\{\beta(\ln n \ln \ln n)^{1/2}\})$ for some constant $\beta > 0$. Asymptotically, this algorithm is much faster than any previously analyzed algorithm for factoring integers; earlier algorithms have all required $O(n^\alpha)$ operations where $\alpha > 1/5$.

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