Bundles, presemifields and nonlinear functions
Bundles, presemifields and nonlinear functions
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DOI：
10.1007/s10623-008-9172-z
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发表时间：
2008-12
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影响因子：
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通讯作者：
K. Horadam;David G. Farmer
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文献类型：
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作者：
K. Horadam;David G. Farmer
Bundles are equivalence classes of functions derived from equivalence classes of transversals. They preserve measures of resistance to differential and linear cryptanalysis. For functions overGF(2n), affine bundles coincide with EA-equivalence classes. From equivalence classes (“bundles”) of presemifields of orderpn, we derive bundles of functions overGF(pn) of the formλ(x)*ρ(x), whereλ, ρare linearised permutation polynomials and * is a presemifield multiplication. We prove there are exactlypbundles of presemifields of orderp2and give a representative of each. We compute all bundles of presemifields of orderspn≤ 27 and in the isotopism class ofGF(32) and we measure the differential uniformity of the derivedλ(x)*ρ(x). This technique produces functions with low differential uniformity, including PN functions (podd), and quadratic APN and differentially 4-uniform functions (p= 2).
