Results on characterizations of plateaued functions in arbitrary characteristic

Date

2016-01-01

Author

Mesnager, Sihem
Özbudak, Ferruh
Sınak, Ahmet

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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.

Subject Keywords

Bent functions , Plateaued functions , Vectorial functions

URI

https://hdl.handle.net/11511/45019

DOI

https://doi.org/10.1007/978-3-319-29172-7_2

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Department of Mathematics, Conference / Seminar

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Citation Formats

S. Mesnager, F. Özbudak, and A. Sınak, “Results on characterizations of plateaued functions in arbitrary characteristic,” 2016, vol. 9540, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45019.