A Note on the Higher-order Nonlinearity of Niho Function

• Autorzy: Garg M.

Identyfikatory

DOI

10.3233/FI-2018-1712

• Języki publikacji: EN

Abstrakty

EN

Sun and Wu investigated the lower bound of higher-order nonlinearity of the niho Boolean function f(x)=Trⁿ₁n(λx^d) 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).

Słowa kluczowe

EN

Boolean function; higher order derivative; Niho power function; higher-order nonlinearity; Walsh spectrum

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2018
• Tom: Vol. 162, nr 1
• Strony: 37--42
• Opis fizyczny: Bibliogr. 5 poz., tab.

Twórcy

autor

Garg M.

• Department of Mathematics, The LNM Institue of Information Technology, Jaipur–302031, Rajasthan, INDIA

Bibliografia

• [1] Canteaut A, Charpin P, and Kyureghyan GM. A new class of monomial bent functions, Finite Fields and their Applications, 2008;14:221-241. URL https://doi.org/10.1016/j.ffa.2007.02.004.
• [2] Carlet C. Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications, IEEE Trans. Inf. Theory, 2008;54(3):1262-1272. doi:10.1109/TIT.2007.915704.
• [3] Garg M, and Khalyavin A. Higher order-nonlinearity of Kasami function, International Journal of Computer Mathematics, Taylor Francis, 2012;89(1)):1311-1318. URL https://doi.org/10.1080/00207160.2012.687725.
• [4] Macwilliams FJ, Solane NJA. The theory of Error-correcting Codes, Amsterdam: North-Holland Publishing Company, vol. 16, 1-st edition 1978. ISBN:9780444851932.
• [5] Sun G, and Wu C. Higher Order Nonlinearity pf Niho Function, Fundamenta Informaticae, 2015; 137(3):403-412. doi:10.3233/FI-2015-1187.