Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, mathematics and information theory. In this paper we deduce a new method for constructing APN functions by studying the isotopic equivalence, concept defined for quadratic planar functions in fields of odd characteristic. In particular, we construct a family of quadratic APN functions which provides a new example of an APN mapping over {mathbb F}_{2{9}} and includes an example of another APN function x{9}+ mathop {mathrm {Tr}}nolimits (x{3}) over {mathbb F}_{2{8}} , known since 2006 and not classified up to now. We conjecture that the conditions for this family are satisfied by infinitely many APN functions.

Constructing APN Functions through Isotopic Shifts / Budaghyan, L.; Calderini, M.; Carlet, C.; Coulter, R. S.; Villa, I.. - In: IEEE TRANSACTIONS ON INFORMATION THEORY. - ISSN 0018-9448. - 66:8(2020), pp. 5299-5309. [10.1109/TIT.2020.2974471]

Constructing APN Functions through Isotopic Shifts

Calderini M.;Villa I.
2020

Abstract

Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, mathematics and information theory. In this paper we deduce a new method for constructing APN functions by studying the isotopic equivalence, concept defined for quadratic planar functions in fields of odd characteristic. In particular, we construct a family of quadratic APN functions which provides a new example of an APN mapping over {mathbb F}_{2{9}} and includes an example of another APN function x{9}+ mathop {mathrm {Tr}}nolimits (x{3}) over {mathbb F}_{2{8}} , known since 2006 and not classified up to now. We conjecture that the conditions for this family are satisfied by infinitely many APN functions.
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Budaghyan, L.; Calderini, M.; Carlet, C.; Coulter, R. S.; Villa, I.
Constructing APN Functions through Isotopic Shifts / Budaghyan, L.; Calderini, M.; Carlet, C.; Coulter, R. S.; Villa, I.. - In: IEEE TRANSACTIONS ON INFORMATION THEORY. - ISSN 0018-9448. - 66:8(2020), pp. 5299-5309. [10.1109/TIT.2020.2974471]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/328824
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