Factoring polynomials over finite fields

Özdemir E.

INTERNATIONAL JOURNAL OF NUMBER THEORY, vol.17, no.7, pp.1517-1536, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1142/s1793042121500469
  • Journal Name: INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1517-1536
  • Keywords: Hyperelliptic curves, Jacobian, Picard group, finite fields, polynomial factorization
  • Istanbul Technical University Affiliated: Yes

Abstract

In this paper, we describe a new polynomial factorization algorithm over finite fields with odd characteristics. The main ingredient of the algorithm is special singular curves. The algorithm relies on the extension of the Mumford representation and Cantor's algorithm to these special singular curves.