Finding more Boolean functions with maximum algebraic immunity based on univariate polynomial representation

Authors:
Yusong Du;Fangguo Zhang
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China
Venue:
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
Year:
2011

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Abstract

Algebraic immunity is an important cryptographic property for Boolean functions against algebraic attacks. Constructions of Boolean functions with the maximum algebraic immunity (MAI Boolean functions) by using univariate polynomial representation of Boolean functions over finite fields have received more and more attention. In this paper, how to obtain more MAI Boolean functions from a known MAI Boolean function under univariate polynomial representation is further investigated. The sufficient condition of Boolean functions having the maximum algebraic immunity obtained by changing a known MAI Boolean function under univariate polynomial representation is given. With this condition, more balanced MAI Boolean functions under univariate polynomial representation can be obtained. The algebraic degree and the nonlinearity of these Boolean functions are analyzed.