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Erschienen in:
2011 | OriginalPaper | Buchkapitel
On Known and New Differentially Uniform Functions
verfasst von : Claude Carlet
Erschienen in: Information Security and Privacy
Verlag: Springer Berlin Heidelberg
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We give a survey on the constructions of APN and differentially 4-uniform functions suitable for designing S-boxes for block ciphers. We recall why the search for more of such functions is necessary. We propose a way of designing functions which can possibly be APN or differentially 4-uniform and be bijective. We illustrate it with an example of a differentially 4-uniform (
n
,
n
)-permutation for
n
odd, based on the power function
x
3
over the second order Galois extension of
${\Bbb F}_{2^{n+1}}$
, and related to the Dickson polynomial
D
3
over this field. These permutations have optimal algebraic degree and their nonlinearity happens to be rather good (but worse than that of the multiplicative inverse functions).
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