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Prikl. Diskr. Mat. Suppl., 2014, Issue 7, Pages 36–37 (Mi pdma181)  

This article is cited in 3 scientific papers (total in 3 papers)

Theoretical Foundations of Applied Discrete Mathematics

Vectorial Boolean functions on distance one from APN functions

G. I. Shushuev

Faculty of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk

Abstract: The metric properties of the class of vectorial Boolean functions are studied. A vectorial Boolean function $F$ in $n$ variables is called a differential $\delta$-uniform function if the equation $F(x)\oplus F(x\oplus a)=b$ has at most $\delta$ solutions for any vectors $a,b$, where $a\neq0$. In particular, if it is true for $\delta=2$, then the function $f$ is called APN. The distance between vectorial Boolean functions $F$ and $G$ is the cardinality of the set $\{x\in\mathbb Z_2^n\colon F(x)\neq G(x)\}$. It is proved that there are only differential $4$-uniform functions which are on the distance 1 from an APN function.

Keywords: vectorial Boolean function, differentially $\delta$-uniform function, APN function.

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UDC: 519.7

Citation: G. I. Shushuev, “Vectorial Boolean functions on distance one from APN functions”, Prikl. Diskr. Mat. Suppl., 2014, no. 7, 36–37

Citation in format AMSBIB
\Bibitem{Shu14}
\by G.~I.~Shushuev
\paper Vectorial Boolean functions on distance one from APN functions
\jour Prikl. Diskr. Mat. Suppl.
\yr 2014
\issue 7
\pages 36--37
\mathnet{http://mi.mathnet.ru/pdma181}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Vitkup, “O nekotorykh otkrytykh voprosakh v oblasti APN-funktsii”, PDM. Prilozhenie, 2014, no. 7, 11–13  mathnet
    2. G. I. Shushuev, “O svoistvakh mnozhestva znachenii proizvolnoi vektornoi bulevoi funktsii”, PDM. Prilozhenie, 2015, no. 8, 51–53  mathnet  crossref
    3. G. I. Shushuev, “Funktsii na rasstoyanii odin ot APN-funktsii ot malogo chisla peremennykh”, PDM. Prilozhenie, 2016, no. 9, 39–40  mathnet  crossref
  • Prikladnaya Diskretnaya Matematika. Supplement
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