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Classes of weak Dembowski-Ostrom polynomials for multivariate quadratic cryptosystems
Date
2015-03-01
Author
ALAM, Bilal
Özbudak, Ferruh
YAYLA, Oguz
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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