确定性整数分解的指数五分之一算法

David Harvey
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引用次数: 7

摘要

Hittmeir最近提出了一种确定性算法,可以在$N^{2/9+o(1)}$位运算中可证明地计算正整数$N$的质因数分解。在此突破之前,这个问题最著名的复杂度界是$N^{1/4+o(1)}$,这个结果可以追溯到20世纪70年代。在本文中,我们进一步推广了Hittmeir的技术,获得了复杂度为$N^{1/5+o(1)}$的严格的确定性因子分解算法。
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An exponent one-fifth algorithm for deterministic integer factorisation
Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of a positive integer $N$ in $N^{2/9+o(1)}$ bit operations. Prior to this breakthrough, the best known complexity bound for this problem was $N^{1/4+o(1)}$, a result going back to the 1970s. In this paper we push Hittmeir's techniques further, obtaining a rigorous, deterministic factoring algorithm with complexity $N^{1/5+o(1)}$.
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