Characterizations of Partially Bent and Plateaued Functions over Finite Fields

Date

2018-12-30

Author

Mesnager, Sihem
Özbudak, Ferruh
SINAK, AHMET

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Partially bent and plateaued functions over finite fields have significant applications in cryptography, sequence theory, coding theory, design theory and combinatorics. They have been extensively studied due to their various desirable cryptographic properties. In this paper, we study on characterizations of partially bent and plateaued functions over finite fields, with the aim of clarifying their structure. We first redefine the notion of partially bent functions over any finite field Fq , with q a prime power, and then provide a few characterizations of these functions in terms of their derivatives, Walsh power moments and autocorrelation functions. We next characterize partially bent (vectorial) functions over Fp , with p a prime, by means of their derivatives and Walsh power moments. We finally characterize plateaued functions over Fp in terms of their Walsh power moments, derivatives and autocorrelation functions.

Subject Keywords

p-ary function, q-ary functions, Partially bent, Plateaued, Additive character

URI

https://hdl.handle.net/11511/33263

DOI

https://doi.org/10.1007/978-3-030-05153-2_12

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Department of Mathematics, Conference / Seminar

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Citation Formats

S. Mesnager, F. Özbudak, and A. SINAK, “Characterizations of Partially Bent and Plateaued Functions over Finite Fields,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33263.