RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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


Prikl. Diskr. Mat. Suppl., 2016, Issue 9, Pages 14–16 (Mi pdma290)  

Theoretical Foundations of Applied Discrete Mathematics

On groups generated by mixed type permutations and key addition groups

B. A. Pogorelova, M. A. Pudovkinab

a Academy of Cryptography of Russian Federation, Moscow
b National Engineering Physics Institute (MEPhI), Moscow

Abstract: Three groups are often used as key addition groups in iterated block ciphers: $V_n^+$, $\mathbb Z_{2^n}^+$ and $\mathbb Z_{2^n+1}^\odot$. They are the regular permutation representations, respectively, of the group of vector key addition, of the additive group of the residue ring $\mathbb Z_{2^n}$, and of the multiplicative group of the residue ring $\mathbb Z_{2^n+1}$, where $2^n+1$ is a prime number. In this paper, we describe some properties of the extensions of the group ${G_n}=\langle V_n^+,\mathbb Z_{2^n}^+\rangle$ by transformations and groups related to cryptographic applications. The groups $\mathbb Z_{2^d}^+ \times V_{n-d}^+$, $V_{n-d}^+\times\mathbb Z_{2^d}^+$ and a pseudoinverse permutation of the field $\operatorname{GF}(2^n)$ or the Galois ring $\operatorname{GR}(2^{md},2^m)$ are examples of such groups and transformations.

Keywords: key addition group, additive regular group, wreath product, multiplicative group of the residue ring, Galois ring.

DOI: https://doi.org/10.17223/2226308X/9/5

Full text: PDF file (492 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.7

Citation: B. A. Pogorelov, M. A. Pudovkina, “On groups generated by mixed type permutations and key addition groups”, Prikl. Diskr. Mat. Suppl., 2016, no. 9, 14–16

Citation in format AMSBIB
\Bibitem{PogPud16}
\by B.~A.~Pogorelov, M.~A.~Pudovkina
\paper On groups generated by mixed type permutations and key addition groups
\jour Prikl. Diskr. Mat. Suppl.
\yr 2016
\issue 9
\pages 14--16
\mathnet{http://mi.mathnet.ru/pdma290}
\crossref{https://doi.org/10.17223/2226308X/9/5}


Linking options:
  • http://mi.mathnet.ru/eng/pdma290
  • http://mi.mathnet.ru/eng/pdma/y2016/i9/p14

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Prikladnaya Diskretnaya Matematika. Supplement
    Number of views:
    This page:74
    Full text:26
    References:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019