Bundles, presemifields and nonlinear functions
نویسندگان
چکیده
Bundles are equivalence classes of functions derived from equivalence classes of transversals. They preserve measures of resistance to differential and linear cryptanalysis. For functions over G F(2n), affine bundles coincide with EA-equivalence classes. From equivalence classes (“bundles”) of presemifields of order pn , we derive bundles of functions over G F(pn) of the form λ(x)∗ρ(x), where λ, ρ are linearised permutation polynomials and ∗ is a presemifield multiplication. We prove there are exactly p bundles of presemifields of order p2 and give a representative of each. We compute all bundles of presemifields of orders pn ≤ 27 and in the isotopism class of G F(32) and we measure the differential uniformity of the derived λ(x) ∗ ρ(x). This technique produces functions with low differential uniformity, including PN functions (p odd), and quadratic APN and differentially 4-uniform functions (p = 2).
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ورودعنوان ژورنال:
- Des. Codes Cryptography
دوره 49 شماره
صفحات -
تاریخ انتشار 2008