The Lower Bounds on the Second Order Nonlinearity of Bent Functions and Semi-bent Functions
Li Xue-lian① Hu Yu-pu② Gao Jun-tao②
①(Department of Applied Mathematics, Xidian University, Xi’ an 710071, China) ②(Key Laboratory of Computer networks & Information Security, Xidian University, Xi’ an 710071, China)
Abstract：This paper studies the lower bounds on the second order nonlinearity of bent functions and semi-bent functions f(x,y) with n+1 variables, where x∈GF(2n), y∈GF(2). Firstly, the values of the nonlinearity of the 2n-1 derivatives of the Boolean function f(x,y) are given. Then, the tight lower bounds on the other 2n derivatives of f(x,y) are deduced. Furthermore, the tight lower bounds on the second order nonlinearity of f(x,y) are presented. The derived bounds are better than the existing general ones. The results show that these functions f(x,y) have higher second order nonlinearity, and can resist the quardratic and affine approximation attacks.
李雪莲, 胡予濮, 高军涛. bent函数和半bent函数的二阶非线性度下界[J]. 电子与信息学报, 2010, 32(10): 2521-2525.
Li Xue-Lian, Hu Yu-Pu, Gao Jun-Tao. The Lower Bounds on the Second Order Nonlinearity of Bent Functions and Semi-bent Functions. , 2010, 32(10): 2521-2525.
2010, Vol. 32 
