## A new tool for assurance of perfect nonlinearity.(English)Zbl 1206.94048

Golomb, Solomon W. (ed.) et al., Sequences and their applications – SETA 2008. 5th international conference, Lexington, KY, USA, September 14–18, 2008 Proceedings. Berlin: Springer (ISBN 978-3-540-85911-6/pbk). Lecture Notes in Computer Science 5203, 415-419 (2008).
Summary: Let $$f(x)$$ be a mapping $$f: \text{GF}(p ^{n }) \rightarrow \text{GF}(p ^{n })$$, where $$p$$ is prime and $$\text{GF}(p ^{n })$$ is the finite field with $$p ^{n }$$ elements. A mapping $$f$$ is called differentially $$k$$-uniform if $$k$$ is the maximum number of solutions $$x \in \text{GF}(p ^{n })$$ of $$f(x + a) - f(x) = b$$, where $$a, b \in \text{GF}(p ^{n })$$ and $$a \neq 0$$. 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.
For the entire collection see [Zbl 1155.94003].

### MSC:

 94A60 Cryptography 11T71 Algebraic coding theory; cryptography (number-theoretic aspects)

### Keywords:

perfect nonlinear; equivalence of functions
Full Text:

### References:

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