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A Note on the Higher-order Nonlinearity of Niho Function

Garg M.

Fundamenta Informaticae

2018

Vol. 162, nr 1

37--42

Sun and Wu investigated the lower bound of higher-order nonlinearity of the niho Boolean function f(x)=Trn1n(λxd) over F*2ⁿ; where λ∈F*2ⁿ,[formula] when n ≡ 3 mod 4 in second case of Theorem 3.6 of the paper titled higher-order nonlinearity of niho functions published in Fundamenta Informaticae 137 (2015) 403–412. Unfortunately, the proof of finding the lower bound of higher-order nonlinearities of the niho Boolean function f(x) is not correct in the above mentioned paper. In this paper the author gives the correct proof of lower bound of higher-order nonlinearities of the niho Boolean function f(x).

A Lower Bound of the Second-order Nonlinearities of Boolean Bent Functions

Garg M., Gangopadhyay S.

Fundamenta Informaticae

2011

Vol. 111, nr 4

413-422

In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = [formula], where d1 and d2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a recent result of Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is shown in Section 3, by a direct computation, that for large values of n, the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao.