The autocorrelation distribution of balanced Boolean function

Authors:
Yu Zhou;Weiguo Zhang;Juan Li;Xinfeng Dong;Guozhen Xiao
Affiliations:
Science and Technology on Communication Security Laboratory, Chengdu, China 610041;State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China 710071 and State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing, China 100093;Foreign Language Department, Emei Campus, Southwest Jiaotong University, Emei, China 614202;Science and Technology on Communication Security Laboratory, Chengdu, China 610041;State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China 710071
Venue:
Frontiers of Computer Science: Selected Publications from Chinese Universities
Year:
2013

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Abstract

The global avalanche characteristics (the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. (1999) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function satisfying the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propagation criterion with respect to some vectors, we give three necessary and sufficient conditions on the auto-correlation distribution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator.