Factoring polynomials over finite fields

Özdemir E.

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

  • Publication Type: Article / Article
  • Volume: 17 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1142/s1793042121500469
  • Title of Journal : INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Page Numbers: pp.1517-1536
  • Keywords: Hyperelliptic curves, Jacobian, Picard group, finite fields, polynomial factorization

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.