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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)
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