A characterization of a class of maximum nonlinear functions
نویسندگان
چکیده
Maximum nonlinear functions F : F2m → F2m are widely used in cryptography because the coordinate functions Fβ(x) := tr(βF (x)), β ∈ F ∗ 2m, have large distance to linear functions. More precisely, the Hamming distance to the characteristic functions of hyperplanes is large. One class of maximum nonlinear functions are the Gold power functions x2 k+1, gcd(k,m) = 1. We characterize these functions in terms of the distance of their coordinate functions to characteristic functions of subspaces of codimension 2 in F2m.
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