Factoring polynomials over finite fields


Özdemir E.

INTERNATIONAL JOURNAL OF NUMBER THEORY, cilt.17, sa.7, ss.1517-1536, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 7
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s1793042121500469
  • Dergi Adı: INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1517-1536
  • Anahtar Kelimeler: Hyperelliptic curves, Jacobian, Picard group, finite fields, polynomial factorization
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.