Abstract
We construct differentially 4-uniform functions over GF(2n) through Albert’s finite commutative semifields, if n is even. The key observation there is that for some k with 0 ≤ k ≤ n − 1, the function \(f_{k}(x):=(x^{2^{k+1}}+x)/(x^{2}+x)\) is a two to one map on a certain subset D k (n) of GF(2n). We conjecture that f k is two to one on D k (n) if and only if (n,k) belongs to a certain list. For (n,k) in this list, f k is proved to be two to one. We also prove that if f 2 is two to one on D 2(n) then (n,2) belongs to the list.
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© 2007 Springer-Verlag Berlin Heidelberg
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Nakagawa, N., Yoshiara, S. (2007). A Construction of Differentially 4-Uniform Functions from Commutative Semifields of Characteristic 2. In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_11
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DOI: https://doi.org/10.1007/978-3-540-73074-3_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73073-6
Online ISBN: 978-3-540-73074-3
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