Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary characteristic. Moreover, we present a new characterization of plateaued functions in terms of fourth power moments of their Walsh transforms. Furthermore, we give a new proof of the characterization of vectorial bent functions. Finally, we present the characterizations of vectorial s-plateaued functions in terms of moments of their Walsh transforms and the zeros of their second-order derivatives.
CITATION STYLE
Mesnager, S., Özbudak, F., & Sınak, A. (2016). Results on characterizations of plateaued functions in arbitrary characteristic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9540, pp. 17–30). Springer Verlag. https://doi.org/10.1007/978-3-319-29172-7_2
Mendeley helps you to discover research relevant for your work.