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New families of APN functions in characteristic 3 or 5. (English) Zbl 1354.11073

Aubry, Yves (ed.) et al., Arithmetic, geometry, cryptography and coding theory. 13th conference on arithmetic, geometry, cryptography and coding theory, CIRM, Marseille, France, March 14–18, 2011 and Geocrypt 2011, Bastia, France, June 19–24, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-7572-8/pbk; 978-0-8218-9027-1/ebook). Contemporary Mathematics 574, 115-123 (2012).
From the text: In this paper, we prove two conjectures of H. Dobbertin et al. [Discrete Math. 267, No. 1–3, 95–112 (2003; Zbl 1028.11076)] in characteristic 3. We also give a new family of APN power mappings in characteristic 5.
In the last section, we make some remarks about theorems of Z.-B. Zha and X.-L. Wang [Sci. China, Math. 53, No. 8, 1931–1940 (2010; Zbl 1246.12007)].
For the entire collection see [Zbl 1248.11004].

MSC:

11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
12E10 Special polynomials in general fields
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