Classes of weak Dembowski-Ostrom polynomials for multivariate quadratic cryptosystems

Date

2015-03-01

Author

ALAM, Bilal
Özbudak, Ferruh
YAYLA, Oguz

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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.

Subject Keywords

Linearized binomial attack, Weak DO polynomials, Multivariate quadratic cryptosystems

URI

https://hdl.handle.net/11511/39477

Journal

JOURNAL OF MATHEMATICAL CRYPTOLOGY

DOI

https://doi.org/10.1515/jmc-2013-0019

Collections

Department of Mathematics, Article

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Citation Formats

B. ALAM, F. Özbudak, and O. YAYLA, “Classes of weak Dembowski-Ostrom polynomials for multivariate quadratic cryptosystems,” JOURNAL OF MATHEMATICAL CRYPTOLOGY, pp. 11–22, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39477.