指数五分之一确定性整数分解的对数-对数加速

Math. Comput. Model. Pub Date : 2021-05-24 DOI:10.1090/mcom/3708

David Harvey, Markus Hittmeir

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引用次数: 6

摘要

以第二作者最近介绍的技术为基础，并由第一作者进一步发展，我们证明了一个正整数$N$可以在最多\[ O\left( \frac{N^{1/5} \log^{16/5} N}{(\log\log N)^{3/5}}\right) \]位的操作中严格和确定地分解为素数。这比之前最著名的结果提高了$(\log \log N)^{3/5}$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A log-log speedup for exponent one-fifth deterministic integer factorisation

Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer $N$ may be rigorously and deterministically factored into primes in at most \[ O\left( \frac{N^{1/5} \log^{16/5} N}{(\log\log N)^{3/5}}\right) \] bit operations. This improves on the previous best known result by a factor of $(\log \log N)^{3/5}$.

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Math. Comput. Model.

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