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Switching construction of planar functions on finite fields. (English) Zbl 1232.11127

Hasan, M. Anwar (ed.) et al., Arithmetic of finite fields. Third international workshop, WAIFI 2010, Istanbul, Turkey, June 27–30, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-13796-9/pbk). Lecture Notes in Computer Science 6087, 135-150 (2010).
Summary: A function \(f: \mathbb F_{p^n}\to\mathbb F_{p^n}\) is planar, if \(f(x+a) - f(x) = b\) has precisely one solution for all \(a,b\in\mathbb F_{p^n}\), \(a \neq 0\). In this paper, we discuss possible extensions of the switching idea developed in [Y. Edel and the first author, Adv. Math. Commun. 3, No. 1, 59–81 (2009; Zbl 1231.11140)] to the case of planar functions. We show that some of the known planar functions can be constructed from each other by switching.
For the entire collection see [Zbl 1191.11003].

MSC:

11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
11T06 Polynomials over finite fields
12K10 Semifields

Citations:

Zbl 1231.11140
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