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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).

Higher Order Nonlinearity of Niho Functions

Sun G., Wu C.

Fundamenta Informaticae

2015

Vol. 137, nr 3

403--412

The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. In this paper we investigate the lower bound of the higher-order nonlinearity of Niho Boolean functions f(x) = tr(λxd) over F2n, where... [formula]

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.

Dedicated spectral method of Boolean function decomposition

Porwik P., Stanković R. S.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 2

271-278

Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using the Walsh transform and autocorrelation characteristics.