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The autocorrelation distribution of balanced Boolean function |
Yu ZHOU1( ), Weiguo ZHANG2,4, Juan LI3, Xinfeng DONG1, Guozhen XIAO2 |
| 1. Science and Technology on Communication Security Laboratory, Chengdu 610041, China; 2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China; 3. Foreign Language Department, Emei Campus, Southwest Jiaotong University, Emei 614202, China; 4. State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing 100093, China |
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Abstract The global avalanche characteristics (the sumof- 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 sumof- 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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| Keywords
Boolean functions
auto-correlation distribution
global avalanche characteristics
balanced
propagation criterion
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Corresponding Author(s):
ZHOU Yu,Email:zhouyu.zhy@tom.com
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Issue Date: 01 April 2013
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