Cubic bent functions Original Research Article

For any Boolean function f on GF(2)m, we define a sequence of ranks ri(f), 1 ⩽ i ⩽ m, which are invariant under the action of the general linear group GL(m, 2). If f is a cubic bent function in 2k variables, we show that when r3(f)⩽k, f is either obtained from a cubic bent function in 2k − 2 variables, or is in a well-known family of bent functions. We also determine all cubic bent functions in eight variables.