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On Hyperbent Functions and Semibent Functions with Dillon-Like Exponents

YeFeng HE, WenPing MA

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Summary :

The main contribution of this paper is to characterize the hyperbentness of two infinite classes of Boolean functions via Dillon-like exponents, and give new classes of semibent functions with Dillon-like exponents and Niho exponents. In this paper, the approaches of Mesnager and Wang et al. are generalized to Charpin-Gong like functions with two additional trace terms. By using the partial exponential sums and Dickson polynomials, it also gives the necessary and sufficient conditions of the hyperbent properties for their subclasses of Boolean functions, and gives two corresponding examples on F230. Thanks to the result of Carlet et al., new classes of semibent functions are obtained by using new hyperbent functions and the known Niho bent functions. Finally, this paper extends the Works of Lisonek and Flori and Mesnager, and gives different characterizations of new hyperbent functions and new semibent functions with some restrictions in terms of the number of points on hyperelliptic curves. These results provide more nonlinear functions for designing the filter generators of stream ciphers.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.6 pp.1266-1275
Publication Date
2015/06/01
Publicized
Online ISSN
1745-1337
DOI
10.1587/transfun.E98.A.1266
Type of Manuscript
PAPER
Category
Cryptography and Information Security

Authors

YeFeng HE
  Xi'an University of Posts and Telecommunications
WenPing MA
  Xidian University

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