Prikladnaya Diskretnaya Matematika. Supplement
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Prikl. Diskr. Mat. Suppl.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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}
Linking options:
  • https://www.mathnet.ru/eng/pdma527
  • https://www.mathnet.ru/eng/pdma/y2021/i14/p46
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Prikladnaya Diskretnaya Matematika. Supplement
    Statistics & downloads:
    Abstract page:184
    Full-text PDF :160
    References:22
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024