Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-01-13 , DOI: 10.1016/j.disc.2019.111698 Haode Yan; Deng Tang
Boolean functions used in symmetric-key cryptosystems must have high second-order nonlinearity to withstand several known attacks and some potential attacks which may exist but are not yet efficient and might be improved in the future. The second-order nonlinearity of Boolean functions also plays an important role in coding theory, since the maximal second-order nonlinearity of all Boolean functions in variables equals the covering radius of the Reed–Muller code with length and order . It is well-known that providing a tight lower bound on the second-order nonlinearity of a general Boolean function with high algebraic degree is a hard task, excepting a few special classes of Boolean functions. In this paper, we improve the lower bounds on the second-order nonlinearity of three classes of Boolean functions of the form in variables for and 3, where denotes the absolute trace mapping from to and ’s are of the form (1) and , (2) , with odd , and (3) and with even .