Semibent Functions From Dillon and Niho Exponents, Kloosterman Sums, and Dickson Polynomials

Authors:
Sihem Mesnager
Affiliations:
LAGA, UMR 7539, CNRS, Department of Mathematics, University of Paris VIII and University of Paris XIII, Saint-Denis Cedex, France
Venue:
IEEE Transactions on Information Theory
Year:
2011

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Abstract

Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and coding theory. In this paper, we extensively investigate the link between the semibentness property of functions in univariate forms obtained via Dillon and Niho functions and Kloosterman sums. In particular, we show that zeros and the value four of binary Kloosterman sums give rise to semibent functions in even dimension with maximum degree. Moreover, we study the semibentness property of functions in polynomial forms with multiple trace terms and exhibit criteria involving Dickson polynomials.