Highly nonlinear plateaued functions

The authors describe a method for producing Boolean functions of degree d  ≥ 3 in n  = 2 dk  − 1 ( k  = 1, 2, …) variables, such that the functions are plateaued and balanced, have high nonlinearity and have no linear structures. The nonlinearity is 2 n −1  − 2 ( n −1)/2 , which is the same as the largest possible nonlinearity for a quadratic function in n (odd) variables (the so‐called ‘quadratic bound’). Their theorem uses some new ideas to generalise a theorem, which gave the case d  = 3, in a 2009 paper by Fengrong Zhang et al . They discuss the cryptographic properties and applications for the functions.