On cross-correlation indicators of an S-box

Authors:
Sheng Gao;Wenping Ma;Zepeng Zhuo;Fenghe Wang
Affiliations:
Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an, China 710071;Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an, China 710071;State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China 710071;Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an, China 710071
Venue:
Frontiers of Computer Science in China
Year:
2011

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Abstract

Substitution boxes (S-boxes) are often used as the most important nonlinear components in many symmetric encryption algorithms. The cryptographic properties of an S-box directly affect the security of the whole cipher system. Recently, generalized global avalanche characteristics (GGAC) were introduced to measure the correlation between two arbitrary Boolean functions. In this paper, to better evaluate the security of an S-box, we present two cross-correlation indicators for it. In addition, by studying the related properties of the cross-correlation between two balanced Boolean functions, we propose the lower bounds on the sum-of-squares indicator related to GGAC for two balanced functions and also for an S-box.