1. Constructing APN Functions Through Isotopic Shifts.
- Author
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Budaghyan, Lilya, Calderini, Marco, Carlet, Claude, Coulter, Robert S., and Villa, Irene
- Subjects
- *
INFORMATION theory , *CODING theory , *BOOLEAN functions , *MATHEMATICAL equivalence , *MATHEMATICS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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