Computing Frobenius maps and factoring polynomials

Joachim von zur Gathen, Victor Shoup

Research output: Contribution to journalArticle

Abstract

A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degree n over Fq, the number of arithmetic operations in Fq is O((n2+nlog q). (log n)2 loglog n). The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.

Original languageEnglish (US)
Pages (from-to)187-224
Number of pages38
JournalComputational Complexity
Volume2
Issue number3
DOIs
StatePublished - Sep 1992

Fingerprint

Factoring
Frobenius
Polynomials
Polynomial
Computing
Probabilistic Algorithms
Order of a polynomial
Univariate
Galois field
Modulo
Trace
Ring
Innovation

Keywords

  • Subject classifications: 68Q40, 11Y16, 12Y05

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Mathematics(all)
  • Computational Theory and Mathematics

Cite this

Computing Frobenius maps and factoring polynomials. / von zur Gathen, Joachim; Shoup, Victor.

In: Computational Complexity, Vol. 2, No. 3, 09.1992, p. 187-224.

Research output: Contribution to journalArticle

von zur Gathen, Joachim ; Shoup, Victor. / Computing Frobenius maps and factoring polynomials. In: Computational Complexity. 1992 ; Vol. 2, No. 3. pp. 187-224.
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