Higher-order nonlinearity of Kasami functions

作者：Garg Manish^*; Khalyavin Andrey

来源：International Journal of Computer Mathematics, 2012, 89(10): 1311-1318.

DOI：10.1080/00207160.2012.687725

• Boolean functions
• higher-order derivatives
• higher-order nonlinearity
• Kasami functions

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 f((lambda,d)) (x) = Tr-1(n) (lambda x(k)), where k = 2(2d) - 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.

• 出版日期2012