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.
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Yu Zhou, Senior Engineer, received the BS, MS in Mathematics from Lanzhou University and PhD in Communication from Xidian University, China, in 2003, 2006 and 2009 respectively. In 2010, he joined the Science and Technology on Communication Security Laboratory, China. His research interests include sequence design, coding theory and Boolean functions.
Weiguo Zhang, associate professor, received the BS and PhD from Xidian University, China, in 2001 and 2007, respectively. In 2007, he joined State Key Laboratory of Integrated Service Networks at Xidian University. His research interests include cryptography and sequence design.
Juan Li, Engineer, received the BS and MS from Sichuan International Studies University, Sichuan International Studies University and University of Electronic Science and Technology of China, in 2004, 2010 respectively. In 2011, she joined Southwest Jiaotong University. Her research interests include communication.
Xinfeng Dong, Engineer, received the BS and MS, Sichuan University, China, in 2006, 20009 respectively. In 2010, he joined the Science and Technology on Communication Security Laboratory. His research interests include Boolean functions.
Guozhen Xiao, professor, received the BS in Mathematics from Northeast Normal University, Changchun, China, in 1954, and the MS in Mathematics from the East China Normal University, Shanghai, China, in 1956. From 1956 to 1960, he was an associate instructor in Northeast Normal University. He joined Xidian University, China, in 1960, and became a full professor in 1981. His research interests include cryptography, coding, and information theory.
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Zhou, Y., Zhang, W., Li, J. et al. The autocorrelation distribution of balanced Boolean function. Front. Comput. Sci. 7, 272–278 (2013). https://doi.org/10.1007/s11704-013-2013-x
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DOI: https://doi.org/10.1007/s11704-013-2013-x