A Note on the Higher–order Nonlinearity of Niho Function

Article type: Research Article

Authors: Garg, Manish^{; *}

Affiliations: Department of Mathematics, The LNM Institue of Information Technology, Jaipur–302031, Rajasthan, INDIA, manishiitr8@gmail.com

Correspondence: [*] Address for correspondence: Department of Mathematics, The LNM Institue of Information Technology, Jaipur–302031, Rajasthan, India.

Abstract: Sun and Wu investigated the lower bound of higher-order nonlinearity of the niho Boolean function f(x)=Tr1n(λxd) over ᵓ2n; where λ∈F2n*,d=2n−12+23n−14−1 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).

Keywords: Boolean function, Higher-order derivative, Niho power function, Higher-order nonlinearity, Walsh-spectrum

DOI: 10.3233/FI-2018-1712

Journal: Fundamenta Informaticae, vol. 162, no. 1, pp. 37-42, 2018