Higher-order nonlinearity of Kasami functions

Abstract

The rth-order nonlinearity of a Boolean function is an important cryptographic criterion in analysing the security of stream ciphers and block ciphers. In this paper, we compute the lower bounds on the (r=d)th-order nonlinearity of Kasami Boolean function , where k=22d −2 d +1. We also compare the values of lower bound obtained in a theorem in this paper to the values of general lower bound obtained by Carlet [Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications, IEEE Trans. Inform. Theory 54(3) (2008), pp. 1262–1272]. It is also shown that our lower bound is better than the lower bound obtained by Carlet.