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Abstract

Let f(x) be a mapping f: GF(p n ) →GF(p n ), where p is prime and GF(p n ) is the finite field with p n elements. A mapping f is called differentially k-uniform if k is the maximum number of solutions x ∈ GF(p n ) of f(x + a) − f(x) = b, where a, b ∈ GF(p n ) and a ≠ 0. A 1-uniform mapping is called perfect nonlinear (PN). In this paper, we propose an approach for assurance of perfect nonlinearity which involves simply checking a trace condition.

Keywords  perfect nonlinear - equivalence of functions

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