On Balanced Semi-Bent Functions with High Algebraic Degrees

YeFeng HE  WenPing MA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.3   pp.1019-1022
Publication Date: 2011/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1019
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Boolean function,  Hadamard transform,  semi-bent function,  Kloosterman sum,  

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A class of balanced semi-bent functions with an even number of variables is proposed. It is shown that they include one subclass of semi-bent functions with maximum algebraic degrees. Furthermore, an example of semi-bent functions in a small field is given by using the zeros of some Kloosterman sums. Based on the result given by S.Kim et al., an example of infinite families of semi-bent functions is also obtained.