CCZ-equivalence is the most general currently known equivalence relation for functions over finite fields preserving planarity and APN properties. However, for the particular case of quadratic planar functions isotopic equivalence is more general than CCZ-equivalence. A recent construction method for APN functions over fields of even characteristic, so-called isotopic shift construction, was instigated by the notion of isotopic equivalence. In this paper we discuss possible applications of the idea of isotopic shift for the case of planar functions. We show that, surprisingly, some of the known planar functions are actually isotopic shifts of each other. This confirms practically the pertinence of the notion of isotopic shift not only for APN functions but also for planar maps.

On Isotopic Shift Construction for Planar Functions / Budaghyan, L.; Calderini, M.; Carlet, C.; Coulter, R.; Villa, I.. - 2019-:(2019), pp. 2962-2966. ((Intervento presentato al convegno 2019 IEEE International Symposium on Information Theory, ISIT 2019 tenutosi a La Maison de La Mutualite, fra nel 7th July-12th July 2019 [10.1109/ISIT.2019.8849339].

On Isotopic Shift Construction for Planar Functions

Calderini M.;Villa I.
2019

Abstract

CCZ-equivalence is the most general currently known equivalence relation for functions over finite fields preserving planarity and APN properties. However, for the particular case of quadratic planar functions isotopic equivalence is more general than CCZ-equivalence. A recent construction method for APN functions over fields of even characteristic, so-called isotopic shift construction, was instigated by the notion of isotopic equivalence. In this paper we discuss possible applications of the idea of isotopic shift for the case of planar functions. We show that, surprisingly, some of the known planar functions are actually isotopic shifts of each other. This confirms practically the pertinence of the notion of isotopic shift not only for APN functions but also for planar maps.
IEEE International Symposium on Information Theory - Proceedings
New York
Institute of Electrical and Electronics Engineers Inc.
21578095
Budaghyan, L.; Calderini, M.; Carlet, C.; Coulter, R.; Villa, I.
On Isotopic Shift Construction for Planar Functions / Budaghyan, L.; Calderini, M.; Carlet, C.; Coulter, R.; Villa, I.. - 2019-:(2019), pp. 2962-2966. ((Intervento presentato al convegno 2019 IEEE International Symposium on Information Theory, ISIT 2019 tenutosi a La Maison de La Mutualite, fra nel 7th July-12th July 2019 [10.1109/ISIT.2019.8849339].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/328852
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