RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Diskr. Mat., 2014, Volume 26, Issue 4, Pages 43–50 (Mi dm1303)  

This article is cited in 8 scientific papers (total in 8 papers)

Images of subset of finite set under iterations of random mappings

A. M. Zubkov, A. A. Serov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Let $\mathcal{N}$ be a set of $N$ elements and $F_1,F_2,\ldots$ be a sequence of random independent equiprobable mappings $\mathcal{N}\to\mathcal{N}$. For a subset $S_0\subset \mathcal{N}, |S_0|=n$, we consider a sequence of its images $S_k=F_k(\ldots F_2(F_1(S_0))\ldots), k=1,2\ldots$, and a sequence of their unions $\Psi_k=S_1\cup\ldots\cup S_k, k=1,2\ldots$  An approach to the exact computation of distribution of $|S_k|$ and $|\Psi_k|$ for moderate values of $N$ is described. Two-sided inequalities for $\mathbf{M}|S_k|$ and $\mathbf{M}|\Psi_k|$ such that upper bound are asymptotically equivalent to lower ones for $N,n,k\to\infty, nk=o(N)$ are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

Keywords: iterations of random mappings, time-memory tradeoff algorithm.

DOI: https://doi.org/10.4213/dm1303

Full text: PDF file (450 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2015, 25:3, 179–185

Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.213.21
Received: 20.06.2014

Citation: A. M. Zubkov, A. A. Serov, “Images of subset of finite set under iterations of random mappings”, Diskr. Mat., 26:4 (2014), 43–50; Discrete Math. Appl., 25:3 (2015), 179–185

Citation in format AMSBIB
\Bibitem{ZubSer14}
\by A.~M.~Zubkov, A.~A.~Serov
\paper Images of subset of finite set under iterations of random mappings
\jour Diskr. Mat.
\yr 2014
\vol 26
\issue 4
\pages 43--50
\mathnet{http://mi.mathnet.ru/dm1303}
\crossref{https://doi.org/10.4213/dm1303}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3467224}
\elib{http://elibrary.ru/item.asp?id=22834160}
\transl
\jour Discrete Math. Appl.
\yr 2015
\vol 25
\issue 3
\pages 179--185
\crossref{https://doi.org/10.1515/dma-2015-0017}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000366854000006}
\elib{http://elibrary.ru/item.asp?id=24049599}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84931050021}


Linking options:
  • http://mi.mathnet.ru/eng/dm1303
  • https://doi.org/10.4213/dm1303
  • http://mi.mathnet.ru/eng/dm/v26/i4/p43

    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

    This publication is cited in the following articles:
    1. A. A. Serov, “Images of a finite set under iterations of two random dependent mappings”, Discrete Math. Appl., 26:3 (2016), 175–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. M. Zubkov, A. A. Serov, “Limit theorem for the size of an image of subset under compositions of random mappings”, Discrete Math. Appl., 28:2 (2018), 131–138  mathnet  crossref  crossref  isi  elib
    3. A. M. Zubkov, V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe $k$-kratnoi iteratsii sluchainogo ravnoveroyatnogo otobrazheniya”, Matem. vopr. kriptogr., 8:4 (2017), 63–74  mathnet  crossref  mathscinet  elib
    4. Kogan D., Manohar N., Boneh D., “T/Key: Second-Factor Authentication From Secure Hash Chains”, Ccs'17: Proceedings of the 2017 Acm Sigsac Conference on Computer and Communications Security, Assoc Computing Machinery, 2017, 983–999  crossref  isi  scopus
    5. A. M. Zubkov, A. A. Serov, “Estimates of the mean size of the subset image under composition of random mappings”, Discrete Math. Appl., 28:5 (2018), 331–338  mathnet  crossref  crossref  isi  elib
    6. V. G. Mikhailov, V. O. Mironkin, “O mnozhestve obrazov $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 9:3 (2018), 99–108  mathnet  crossref  elib
    7. V. O. Mironkin, “Ob otsenkakh raspredeleniya dliny otrezka aperiodichnosti v grafe $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, PDM, 2018, no. 42, 6–17  mathnet  crossref
    8. V. O. Mironkin, “Sloi v grafe $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 10:1 (2019), 73–82  mathnet  crossref
  • Дискретная математика
    Number of views:
    This page:255
    Full text:50
    References:42
    First page:61

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