Cryptology ePrint Archive: Report 2018/769

Constructing APN functions through isotopic shifts

Lilya Budaghyan and Marco Calderini and Claude Carlet and Robert S. Coulter and Irene Villa

Abstract: Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, information theory as well as mathematics. Building new APN families is a challenge which has not been successfully addressed for more than seven years now. The most general known equivalence relation preserving APN property in characteristic 2 is CCZ-equivalence. Extended to general characteristic, it also preserves planarity. In the case of quadratic planar functions, it is a particular case of isotopic equivalence. We apply the idea of isotopic equivalence to transform APN functions in characteristic 2 into other functions, some of which can be APN. We deduce new quadratic APN functions and a new quadratic APN family.

Category / Keywords: secret-key cryptography / Boolean function, APN, isotopic equivalence,

Date: received 16 Aug 2018, last revised 10 Sep 2018

Contact author: Irene Villa at uib no

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Version: 20180910:135329 (All versions of this report)

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