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Constructing APN Functions Through Isotopic Shifts.
- Source :
-
IEEE Transactions on Information Theory . Aug2020, Vol. 66 Issue 8, p5299-5309. 11p. - Publication Year :
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 144615690
- Full Text :
- https://doi.org/10.1109/TIT.2020.2974471