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Mat. Vopr. Kriptogr., 2010, Volume 1, Issue 2, Pages 31–56 (Mi mvk9)  

This article is cited in 13 scientific papers (total in 13 papers)

Reconstruction of linear recurrent sequence over prime residue ring from its image

A. S. Kuz'mina, G. B. Marshalkob, A. A. Nechaeva

a Academy of Cryptography of Russian Federation, Moscow
b TVP Laboratory, Moscow

Abstract: We consider pseudorandom sequences $v$ over $\mathbb Z_p$, $p\ge3$, obtained from a primitive sequence $u$ over integer residue ring $\mathbb Z_{p^n}$ by means of some compressing map. We study sufficient conditions for the reconstruction of $u$ from known $v$ and suggest some methods of such reconstruction. The review of known results is presented also.

Key words: Compressing map, integer residue ring, linear recurrent sequence, primitive sequence.


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UDC: 511.216, 519.113.6
Received 22.IV.2010

Citation: A. S. Kuz'min, G. B. Marshalko, A. A. Nechaev, “Reconstruction of linear recurrent sequence over prime residue ring from its image”, Mat. Vopr. Kriptogr., 1:2 (2010), 31–56

Citation in format AMSBIB
\by A.~S.~Kuz'min, G.~B.~Marshalko, A.~A.~Nechaev
\paper Reconstruction of linear recurrent sequence over prime residue ring from its image
\jour Mat. Vopr. Kriptogr.
\yr 2010
\vol 1
\issue 2
\pages 31--56

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    This publication is cited in the following articles:
    1. D. N. Bylkov, “A class of injective compressing maps on linear recurring sequences over a Galois ring”, Problems Inform. Transmission, 46:3 (2010), 245–252  mathnet  crossref  mathscinet  isi
    2. A. S. Kuzmin, A. A. Nechaev, “Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence”, Discrete Math. Appl., 21:2 (2011), 145–178  mathnet  crossref  crossref  mathscinet  elib
    3. A. S. Kuzmin, G. B. Marshalko, “Vosstanovlenie lineinoi rekurrenty nad primarnym koltsom vychetov po ee uslozhneniyu. II”, Matem. vopr. kriptogr., 2:2 (2011), 81–93  mathnet  crossref
    4. D. N. Bylkov, O. V. Kamlovskii, “Parametry bulevykh funktsii, postroennykh s ispolzovaniem starshikh koordinatnykh posledovatelnostei lineinykh rekurrent”, Matem. vopr. kriptogr., 3:4 (2012), 25–53  mathnet  crossref
    5. O. V. Kamlovskii, “Frequency characteristics of coordinate sequences of linear recurrences over Galois rings”, Izv. Math., 77:6 (2013), 1130–1154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Zheng Q.-X., Qi W.-F., “Further Results on the Distinctness of Binary Sequences Derived From Primitive Sequences Modulo Square-Free Odd Integers”, IEEE Trans. Inf. Theory, 59:6 (2013), 4013–4019  crossref  mathscinet  zmath  isi  scopus
    7. E. M. Serebryakov, “Vosstanovlenie polinomialno uslozhnennoi lineinoi rekurrenty maksimalnogo perioda nad koltsom Galua po starshei koordinatnoi posledovatelnosti”, PDM, 2014, no. 2(24), 21–36  mathnet
    8. A. V. Akishin, “On groups with automorphisms generating recurrent sequences of the maximal period”, Discrete Math. Appl., 25:4 (2015), 187–192  mathnet  crossref  crossref  mathscinet  isi  elib
    9. D. N. Bylkov, “Postroenie novykh klassov filtruyuschikh generatorov, ne imeyuschikh ekvivalentnykh sostoyanii”, Matem. vopr. kriptogr., 5:4 (2014), 17–39  mathnet  crossref
    10. A. V. Akishin, “On groups of even orders with automorphisms generating recurrent sequences of the maximal period”, Discrete Math. Appl., 25:5 (2015), 253–259  mathnet  crossref  crossref  mathscinet  isi  elib
    11. S. A. Kuzmin, “On binary digit-position sequences over Galois rings, admitting an effect of reduction of period”, J. Math. Sci., 223:5 (2017), 642–647  mathnet  crossref  mathscinet  elib
    12. S. A. Kuzmin, “O dostatochnom uslovii dlya otsutstiya vozmozhnosti sokrascheniya perioda v starshikh dvoichnykh razryadnykh posledovatelnostyakh nad primarnymi koltsami”, PDM. Prilozhenie, 2016, no. 9, 12–14  mathnet  crossref
    13. Tsypyschev V.N., “Lower Bounds on Linear Complexity of Digital Sequences Products of Lrs and Matrix Lrs Over Galois Ring”, Cybernetics Approaches in Intelligent Systems: Computational Methods in Systems and Software 2017, Vol. 1, Advances in Intelligent Systems and Computing, 661, eds. Silhavy R., Silhavy P., Prokopova Z., Springer International Publishing Ag, 2018, 50–61  crossref  isi  scopus
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