Classes of weak Dembowski-Ostrom polynomials for multivariate quadratic cryptosystems


Journal of Mathematical Cryptology, vol.9, no.1, pp.11-22, 2015 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1515/jmc-2013-0019
  • Journal Name: Journal of Mathematical Cryptology
  • Journal Indexes: Scopus
  • Page Numbers: pp.11-22


© 2015 by De Gruyter 2015.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 F2. We extend the linearized binomial attack to multivariate quadratic cryptosystems over Fp for any prime p and redefine the weak DO polynomials for general case. We identify infinite 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.