Classes of weak Dembowski-Ostrom polynomials for multivariate quadratic cryptosystems

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Alam B., ÖZBUDAK F., Yayla O.

JOURNAL OF MATHEMATICAL CRYPTOLOGY, cilt.9, sa.1, ss.11-22, 2015 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1515/jmc-2013-0019
  • Dergi Adı: JOURNAL OF MATHEMATICAL CRYPTOLOGY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.11-22
  • Hacettepe Üniversitesi Adresli: Evet

Özet

T. Harayama and D.K. Friesen [12] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski-Ostrom (DO) polynomials in this framework over the finite field F-2. We extend the linearized binomial attack to multivariate quadratic cryptosystems over F-p for any prime p and redefine the weak DO polynomials for general case. We identify in finite classes of weak DO polynomials for these systems by considering highly degenerate quadratic forms over algebraic function fields and Artin-Schreier type curves to achieve our results. This gives a general answer to the conjecture stated by Harayama and Friesen and also a partial enumeration of weak DO polynomials over finite fields.