Research Article
New bounds on the sum-of-squares indicator
@INPROCEEDINGS{10.1109/ChinaCom.2012.6417470, author={YU ZHOU and Xinfeng Dong and Wenzheng Zhang and Bing Zeng}, title={New bounds on the sum-of-squares indicator}, proceedings={7th International Conference on Communications and Networking in China}, publisher={IEEE}, proceedings_a={CHINACOM}, year={2012}, month={9}, keywords={boolean functions walsh spectrum nonlinearity gac balanced sac}, doi={10.1109/ChinaCom.2012.6417470} }- YU ZHOU
Xinfeng Dong
Wenzheng Zhang
Bing Zeng
Year: 2012
New bounds on the sum-of-squares indicator
CHINACOM
IEEE
DOI: 10.1109/ChinaCom.2012.6417470
Abstract
The two indicators the sum-of-squares indicator and the absoluate indicator between two different Boolean functions f and g are introduced by Yu Zhou, Min Xie, Guozhen Xiao, On the global avalanche characteristics of two Boolean functions and the higher order nonlinearity. Information Sciences. 180(2010) 256-265, to measure of cryptographic behavior in a global manner. In this paper, we derive a new bound on the sum-of-squares indicator. Moreover, we obtain some bounds on the sum-of-squares indicator of a Boolean function f by using two decomposition functions f1,f2. Finally, we give a method to construct balanced Boolean functions with n(n>=6) variables by the disjoint spectra functions, where n is an even integer, satisfying strict avalanche criterion, high nonlinearity and lower GAC.