Explicit Characterizations for Plateaued-ness of p-ary (Vectorial) Functions

Plateaued (vectorial) functions have an important role in the sequence and cryptography frameworks. Given their importance, they have not been studied in detail in general framework. Several researchers found recently results on their characterizations and introduced new tools to understand their structure and to design such functions. In this work, we mainly extend some of the observations made in characteristic 2 and given in (Carlet, IEEE Trans. Inf. Theor. 61(11), 6272- 6289, 2015) to arbitrary characteristic. We first extend to arbitrary characteristic the characterizations of plateaued (vectorial) Boolean functions by the autocorrelation functions, next their characterizations in terms of the secondorder derivatives, and finally their characterizations via the moments of the Walsh transform.