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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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 $ 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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Article copyright: © Copyright 1981 American Mathematical Society

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