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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) |
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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.
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Received: 04 March 2010
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Corresponding Authors:
Li Xue-lian
E-mail: xuelian202@163.com
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