RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Mat. Zametki, 2004, Volume 76, Issue 2, Pages 237–257 (Mi mz103)  

This article is cited in 1 scientific paper (total in 1 paper)

New Series of Rational Approximations and Some of Their Applications

V. E. Tarakanov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the well-known discrete logarithm problem in a finite simple field $GF(p)$, where $p$ is a prime number, which has several application in problems of information protection. In Sec. 1, we introduce and study some number sequences arising in the continued fraction expansion of a real number. The results obtained are used in Sec. 2, where we introduce a new algorithm based on rational approximations for solving the problem of representing the discrete logarithm of a given number as the sum of logarithms of small primes; this problem is an important part of the discrete logarithm problem. We obtain several results necessary to construct and justify the representation algorithm. This algorithm is stated exactly in Sec. 3. We present several experimental results illustrating the work of the algorithm for prime numbers of the order of $10^16$$10^31$.

DOI: https://doi.org/10.4213/mzm103

Full text: PDF file (252 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2004, 76:2, 219–237

Bibliographic databases:

Document Type: Article
UDC: 519.6+511
Received: 21.07.2003

Citation: V. E. Tarakanov, “New Series of Rational Approximations and Some of Their Applications”, Mat. Zametki, 76:2 (2004), 237–257; Math. Notes, 76:2 (2004), 219–237

Citation in format AMSBIB
\Bibitem{Tar04}
\by V.~E.~Tarakanov
\paper New Series of Rational Approximations and Some of Their Applications
\jour Mat. Zametki
\yr 2004
\vol 76
\issue 2
\pages 237--257
\mathnet{http://mi.mathnet.ru/mz103}
\crossref{https://doi.org/10.4213/mzm103}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2098995}
\zmath{https://zbmath.org/?q=an:1069.11028}
\transl
\jour Math. Notes
\yr 2004
\vol 76
\issue 2
\pages 219--237
\crossref{https://doi.org/10.1023/B:MATN.0000036760.37456.f9}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000223760500025}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-4043091268}


Linking options:
  • http://mi.mathnet.ru/eng/mz103
  • https://doi.org/10.4213/mzm103
  • http://mi.mathnet.ru/eng/mz/v76/i2/p237

    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. V. E. Tarakanov, “O skhodimosti iteratsii v metode resheniya zadachi predstavleniya diskretnogo logarifma metodom ratsionalnykh approksimatsii”, Matem. vopr. kriptogr., 1:4 (2010), 111–125  mathnet  crossref
  • Математические заметки Mathematical Notes
    Number of views:
    This page:192
    Full text:70
    References:27
    First page:3

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