On the resistance of boolean functions against fast algebraic attacks

Authors:
Yusong Du;Fangguo Zhang;Meicheng Liu
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou, P.R. China,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,State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijin ...;State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, P.R. China
Venue:
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
Year:
2011

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Abstract

Boolean functions with large algebraic immunity resist algebraic attacks to a certain degree, but they may not resist fast algebraic attacks (FAA's). It is necessary to study the resistance of Boolean functions against FAA's. In this paper, we localize the optimal resistance of Boolean functions against FAA's and introduce the concept of e-fast algebraic immunity (e-FAI) for n-variable Boolean functions against FAA's, where e is a positive integer and $1 \leq ee-FAI. With e-FAI the problem of deciding the resistance of an n-variable Boolean function against FAA's can be converted into the problem of observing the properties of one given matrix. An algorithm for deciding e-FAI and the optimal resistance against FAA's is also described.