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Mathematics of Computation

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Faster deterministic integer factorization

Authors: Edgar Costa and David Harvey
Journal: Math. Comp. 83 (2014), 339-345
MSC (2010): Primary 11Y05
Published electronically: May 7, 2013
MathSciNet review: 3120593
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Abstract: The best known unconditional deterministic complexity bound for computing the prime factorization of an integer $ N$ is $ O(\mathsf M_{\text {\rm int}}(N^{1/4} \log N))$, where $ \mathsf M_{\text {\rm int}}(k)$ denotes the cost of multiplying $ k$-bit integers. This result is due to Bostan, Gaudry, and Schost, following the Pollard-Strassen approach. We show that this bound can be improved by a factor of $ \sqrt {\log \log N}$.

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Additional Information

Edgar Costa
Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1185

David Harvey
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia

Received by editor(s): January 31, 2012
Received by editor(s) in revised form: April 14, 2012
Published electronically: May 7, 2013
Additional Notes: The first author was partially supported by FCT doctoral grant SFRH/BD/69914/2010.
The second author was partially supported by the Australian Research Council, DECRA Grant DE120101293.
Article copyright: © Copyright 2013 by the authors