Integer factorization as subset-sum problem

This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer factorization to a specific instance of the multiple choice subset-su...

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Veröffentlicht in:Journal of number theory Jg. 249; S. 93 - 118
1. Verfasser: Hittmeir, Markus
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.08.2023
Schlagworte:
Factorization
Primality
11Y05
11A51
Factorization
Primality
ISSN:0022-314X, 1096-1658
Online-Zugang:Volltext
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Zusammenfassung:This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer factorization to a specific instance of the multiple choice subset-sum problem. As an application, we will improve upon special purpose factorization algorithms for integers composed of divisors with small difference. In particular, we will refine the runtime complexity of Fermat's factorization algorithm by a large subexponential factor. Our first procedure is deterministic, rigorous, easy to implement and has negligible space complexity. Our second procedure is heuristically faster than the first, but has non-negligible space complexity.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2023.02.010