Title: Differential properties of power functions

Authors: Celine Blondeau, Anne Canteaut, Pascale Charpin

Addresses: 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

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.

Keywords: differential uniformity; APN function; almost perfect nonlinear function; Boolean function; power function; power permutations; cyclic codes; weight enumerator; differential cryptanalysis; monomials bijective mappings.

DOI: 10.1504/IJICOT.2010.032132

International Journal of Information and Coding Theory, 2010 Vol.1 No.2, pp.149 - 170

Published online: 10 Mar 2010 *

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