Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Vopr. Kriptogr.:
Year:
Volume:
Issue:
Page:
Find






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


Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography], 2013, Volume 4, Issue 2, Pages 59–72
DOI: https://doi.org/10.4213/mvk83
(Mi mvk83)
 

This article is cited in 9 scientific papers (total in 9 papers)

Skew LRS of maximal period over Galois rings

M. A. Goltvanitsaa, A. A. Nechaevb, S. N. Zaitseva

a Moscow State Technical University of Radio Engineering, Electronics and Automatics, Moscow
b Academy of Cryptography of the Russian Federation, Moscow
Full-text PDF (135 kB) Citations (9)
References:
Abstract: Let $p$ be a prime number, $R=\mathrm{GR}(q^d,p^d)$ be a Galois ring with $q^d=p^{rd}$ elements and characteristic $p^d$. Denote by $S=\mathrm{GR}(q^{nd},p^d)$ a Galois extension of the ring $R$ of dimension $n$ and by $\breve S$ the ring of all linear transformations of the module $_RS$. A sequence $v$ over the ring $S$ satisfying the recursion $\forall i\in\mathbb N_0\colon v(i+m)=\psi_{m-1}(v(i+m-1))+\dots+\psi_0(v(i))$, $\psi_0,\dots,\psi_{m-1}\in\breve S$, is called a skew LRS over $S$ with a characteristic polynomial $\Psi(x)=x^m-\sum_{t=0}^{m-1}\psi_tx^t\in\breve S[x]$. We investigate the problem of construction the polynomials $\Psi$ generating LRS $v$ with the maximal possible period $\tau=(q^{mn}-1)p^{d-1}$.
Key words: Galois ring, Frobenius automorphism, skew linear recurrence of maximal period, skew MP-polynomial, rank of a sequence.
Received 18.IX.2012
Document Type: Article
UDC: 512.53+519.113.6
Language: English
Citation: M. A. Goltvanitsa, A. A. Nechaev, S. N. Zaitsev, “Skew LRS of maximal period over Galois rings”, Mat. Vopr. Kriptogr., 4:2 (2013), 59–72
Citation in format AMSBIB
\Bibitem{GolNecZai13}
\by M.~A.~Goltvanitsa, A.~A.~Nechaev, S.~N.~Zaitsev
\paper Skew LRS of maximal period over Galois rings
\jour Mat. Vopr. Kriptogr.
\yr 2013
\vol 4
\issue 2
\pages 59--72
\mathnet{http://mi.mathnet.ru/mvk83}
\crossref{https://doi.org/10.4213/mvk83}
Linking options:
  • https://www.mathnet.ru/eng/mvk83
  • https://doi.org/10.4213/mvk83
  • https://www.mathnet.ru/eng/mvk/v4/i2/p59
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические вопросы криптографии
    Statistics & downloads:
    Abstract page:617
    Full-text PDF :300
    References:77
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024