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arXiv · 1608.08766

A babystep-giantstep method for faster deterministic integer factorization

Markus Hittmeir
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Abstract

In 1977, Strassen presented a deterministic and rigorous algorithm for solving the problem of computing the prime factorization of natural numbers $N$. His method is based on fast polynomial arithmetic techniques and runs in time $\widetilde{O}(N^{1/4})$, which has been state of the art for the last forty years. In this paper, we will combine Strassen's approach with a babystep-giantstep method to improve the currently best known bound by a superpolynomial factor. The runtime complexity of our algorithm is of the form \[ \widetilde{O}\left(N^{1/4}\exp(-C\log N/\log\log N)\right). \]

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Markus Hittmeir. 2016-08-31. A babystep-giantstep method for faster deterministic integer factorization. https://doi.org/10.1090/mcom%2F3313

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