On the deterministic complexity of factoring polynomials over finite fields

Research output: Contribution to journalArticle

Abstract

We present a new deterministic algorithm for factoring polynomials over Zp of degree n. We show that the worst-case running time of our algorithm is O(p 1 2(log p)2n2+∈), which is faster than the running times of previous determi nistic algorithms with respect to both n and p. We also show that our algorithm runs in polynomial time for all but at most an exponentially small fraction of the polynomials of degree n over Zp. Specifically, we prove that the fraction of polynomials of degree n over Zp for which our algorithm fails to halt in time O((log p)2n2+∈) is ((n log p)2/p). Consequently, the average-case running time of our algorithm is polynomial in n and log p.

Original languageEnglish (US)
Pages (from-to)261-267
Number of pages7
JournalInformation Processing Letters
Volume33
Issue number5
DOIs
StatePublished - Jan 10 1990

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Factoring
Galois field
Polynomials
Polynomial
Deterministic Algorithm
Polynomial time

Keywords

  • Factorization
  • finite fields
  • irreducible polynomials

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

On the deterministic complexity of factoring polynomials over finite fields. / Shoup, Victor.

In: Information Processing Letters, Vol. 33, No. 5, 10.01.1990, p. 261-267.

Research output: Contribution to journalArticle

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