Two applications of an incomplete additive character sum to estimating nonlinearity of Boolean functions

Authors:
Yusong Du;Fangguo Zhang
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou, P.R. China and Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou, P.R. China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, P.R. China and State Key Laboratory of Information Security, Institute of Software Chinese Academy of Sciences, Bei ...
Venue:
ICICS'11 Proceedings of the 13th international conference on Information and communications security
Year:
2011

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Abstract

In recent years, several classes of Boolean functions with good cryptographic properties have been constructed by using univariate (or bivariate) polynomial representation of Boolean functions over finite fields. The estimation of an incomplete additive character sum plays an important role in analyzing the nonlinearity of these functions. In this paper, we consider replacing this character sum with another incomplete additive character sum, whose estimation was firstly given by A. Winterhof in 1999. Based on Winterhof's estimation, we try to modify two of these functions and obtain better nonlinearity bound of them.