International Association
for Cryptologic Research

In this paper, by modifying a subclass of bent functions in

$\\mathcal P S_{ap}$, we construct another subclass of bent functions

in $\\mathcal P S^+$ with maximum algebraic degree. We demonstrate

that the algebraic immunity of the constructed functions is maximum.

The result is proved by using the well known conjecture proposed by

Tu and Deng (Des. Codes Cryptogr. 60(1), pp. 1-14, 2011) which has

been proved recently by Cohen and Flori (http://eprint.iacr.org/

2011/400.pdf). Finally, we identify a class of $\\cD_0$ type bent

functions constructed by modifying Dillon functions whose lower

bound on second-order nonlinearity is very high.