Deterministic factoring with oracles - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Applicable Algebra in Engineering, Communication and Computing Year : 2021

Deterministic factoring with oracles

Factorisation d'entiers déterministes à l'aide d'oracles

Abstract

We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer $N$ unconditionally, in deterministic polynomial time, given the value of the Euler totient $ϕ(N)$? We show that this can be done, under certain size conditions on the prime factors of N. The key technique is lattice basis reduction using the LLL algorithm. Among our results, we show for example that if $N$ is a squarefree integer with a prime factor $p > √ N$ , then we can recover p in deterministic polynomial time given $ϕ(N)$. We also shed some light on the analogous problems for Carmichael's function, and the order oracle that is used in Shor's quantum factoring algorithm.
Fichier principal
Vignette du fichier
hal-oracles.pdf (343.4 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01715832 , version 1 (23-02-2018)
hal-01715832 , version 2 (12-08-2021)

Identifiers

Cite

François Morain, Guénaël Renault, Benjamin Smith. Deterministic factoring with oracles. Applicable Algebra in Engineering, Communication and Computing, 2021, ⟨10.1007/s00200-021-00521-8⟩. ⟨hal-01715832v2⟩
905 View
796 Download

Altmetric

Share

Gmail Facebook X LinkedIn More