Differential properties of power functions

Authors:
Celine Blondeau;Anne Canteaut;Pascale Charpin
Affiliations:
INRIA Paris-Rocquencourt, Project-Team SECRET, B.P. 105, Le Chesnay Cedex 78153, France.;INRIA Paris-Rocquencourt, Project-Team SECRET, B.P. 105, Le Chesnay Cedex 78153, France.;INRIA Paris-Rocquencourt, Project-Team SECRET, B.P. 105, Le Chesnay Cedex 78153, France
Venue:
International Journal of Information and Coding Theory
Year:
2010

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Abstract

Some properties of power permutations, that is, monomials bijective mappings on double-struck capital F_{2ⁿ, are investigated. In particular, the differential spectrum of these functions is shown to be of great interest for estimating their resistance to some variants of differential cryptanalysis. The relationships between the differential spectrum of a power permutation and the weight enumerator of a cyclic code with two zeroes are provided. The functions with a two-valued differential spectrum are also studied and the differential spectra of several infinite families of exponents are computed.}