Higher-order nonlinearity of Kasami functions

On the second-order nonlinearities of some bent functions

“…In 2008, the second author presented in [2] a general approach for determining the lower bound on the rth-order nonlinearity of a given Boolean function and applied it to several classical cryptographic functions including the inverse function. Based on this approach, some new results about the lower bound on the rth-order nonlinearity (r P 2) of some specific Boolean functions were given recently in [2,5,16,17,19,18,20,26,[30][31][32]34].…”

Higher Order Nonlinearity of Niho Functions

“…Since the results obtained by Carlet are very general in nature, identifying special classes of Boolean functions which have high lower bounds on the r-th order nonlinearities for some values of r remains an open problem. Garg and Khalyavin [18] have found the higher-order nonlinearities of Kasami functions. Gode and Gangopadhyay [19] have obtained the lower bounds of the third order nonlinearities for a subclass of Kasami functions.…”