Affiliations: College of Sciences, Hohai University, Nanjing, 210098, China. sgh1976@gmail.com | State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100095, China
Note: [] This work was supported by the Natural Science Foundation of China under Grant No. 61103184, No. 61173134, and No. 61272542. Address for correspondence: College of Sciences, Hohai University, Nanjing, 210098, China
Abstract: 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 $\lambda \isin F_2_n^*$, $d = 2^{(n-1)/2} + 2^{(n-1)/4} - 1$ when n = 1 mod 4 or $d = 2^{(n-1)/2} + 2^{(3n-1)/4} - 1$ when n = 3 mod 4.
