Prikladnaya Diskretnaya Matematika. Supplement
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Prikladnaya Diskretnaya Matematika. Supplement, 2021, Issue 14, Pages 46–48
DOI: https://doi.org/10.17223/2226308X/14/7
(Mi pdma527)
 

Discrete Functions

On properties of additive differential probabilities of XOR

N. Mouhaa, N. A. Kolomeetsb, D. A. Ahtyamovc, I. A. Sutorminb, M. A. Panferovd, K. M. Titovad, T. A. Bonichd, E. A. Ishchukovae, N. N. Tokarevabdf, B. F. Zhantulikovd

a Strativia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Hebrew University of Jerusalem
d Novosibirsk State University
e Southern Federal University, Rostov-on-Don
f JetBrains Research
References:
Abstract: The additive differential probability of exclusive-or $\mathrm{adp}^{\oplus}(\alpha, \beta, \gamma)$, where $\alpha, \beta, \gamma \in \mathbb{Z}_{2}^{n}$, is studied. It is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as Addition-Rotation-XOR (ARX) constructions. We focus on the maximal differentials which are helpful when constructing differential trails. It is proven that $\max_{\alpha, \beta} \mathrm{adp}^{\oplus}(\alpha,\beta,\gamma) = \mathrm{adp}^{\oplus}(0,\gamma,\gamma)$. In addition, there exist either $2$ or $8$ distinct pairs ($\alpha$, $\beta$) such that $\mathrm{adp}^{\oplus}(\alpha,\beta,\gamma) = \mathrm{adp}^{\oplus}(0,\gamma,\gamma)$. Also, we obtain a simplified representation of $\mathrm{adp}^{\oplus}(0,\gamma,\gamma)$ and formula for $\min_{\gamma}\mathrm{adp}^{\oplus}(0,\gamma,\gamma)$.
Keywords: ARX, XOR, modular addition, differential cryptanalysis.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
Document Type: Article
UDC: 519.7
Language: Russian
Citation: N. Mouha, N. A. Kolomeets, D. A. Ahtyamov, I. A. Sutormin, M. A. Panferov, K. M. Titova, T. A. Bonich, E. A. Ishchukova, N. N. Tokareva, B. F. Zhantulikov, “On properties of additive differential probabilities of XOR”, Prikl. Diskr. Mat. Suppl., 2021, no. 14, 46–48
Citation in format AMSBIB
\Bibitem{MouKolAht21}
\by N.~Mouha, N.~A.~Kolomeets, D.~A.~Ahtyamov, I.~A.~Sutormin, M.~A.~Panferov, K.~M.~Titova, T.~A.~Bonich, E.~A.~Ishchukova, N.~N.~Tokareva, B.~F.~Zhantulikov
\paper On properties of additive differential probabilities of XOR
\jour Prikl. Diskr. Mat. Suppl.
\yr 2021
\issue 14
\pages 46--48
\mathnet{http://mi.mathnet.ru/pdma527}
\crossref{https://doi.org/10.17223/2226308X/14/7}
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