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On a Family of Planar Mappings
Gohar Kyureghyan, Yin Tan
175 - 178
10.3233/978-1-60750-002-5-175
NATO Science for Peace and Security Series - D: Information and Communication Security
Volume 23: Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes
Abstract

A mapping f : GF(q) → GF(q) is called planar if for every nonzero a ∊ GF(q) the difference mapping Df,a : x f(x + a) - f(x) - f(a) is a permutation of GF(q). In this note we show that for certain choices of β,γ the mapping f(x) = Tr(βxq+1) + γx2 is planar on GF(q3).

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