Two results on maximum nonlinear functions |
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Authors: | Doreen Hertel Alexander Pott |
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Affiliation: | (1) Institute for Algebra and Geometry, Otto-von-Guericke-University Magdeburg, Magdeburg, 39016, Germany |
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Abstract: | Maximum nonlinear functions are widely used in cryptography because the coordinate functions F β (x) := tr(β F(x)), , have large distance to linear functions. Moreover, maximum nonlinear functions have good differential properties, i.e. the equations F(x + a) − F(x) = b, , have 0 or 2 solutions. Two classes of maximum nonlinear functions are the Gold power functions , gcd(k, m) = 1, and the Kasami power functions , gcd(k, m) = 1. The main results in this paper are: (1) We characterize the Gold power functions in terms of the distance of their coordinate functions to characteristic functions of subspaces of codimension 2 in . (2) We determine the differential properties of the Kasami power functions if gcd(k,m) ≠ 1. |
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Keywords: | Maximum nonlinear Gold power function Walsh transform Difference set Finite field Kasami power function Almost perfect nonlinear |
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