|
|
|
| Global Avalanche Characteristics and Nonlinearity of Boolean Function with the Hamming Weight k |
| Zhou Yu①; Wang Wei-qiong①②; Xiao Guo-zhen① |
| ①National Key Lab of Integrated Service Network, Xidian University, Xi’an 710071, China;②College of Science, Chang’an University, Xi’an 710064, China |
|
|
|
|
Abstract Some properties of autocorrelation coefficient and cross-correlation coefficient are given. The restricted relationship among n(n variables, wt(f) (the Hamming weight of Boolean function f (x) and t (t-th propagation criteria) was derived, then a lower bound on the sum-of-squares of any Boolean functions with Hamming weight k is concluded. Finally, the results generalized a upper bound on nonlinearity of Boolean function only depending on Hamming weight. This paper improved known results.
|
|
Received: 03 August 2007
|
|
|
|
|
|
|
|
|
2009, Vol. 31 
