Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography]
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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}
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  • 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
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