Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestnik Moskov. Univ. Ser. 1. Mat. Mekh.:
Year:
Volume:
Issue:
Page:
Find






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


Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, Number 5, Pages 8–14 (Mi vmumm569)  

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

Mathematics

Fast algorithm of square rooting in some odd charactećistic finite field

S. B. Gashkova, I. B. Gashkovb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Karlstads University, Sweden

Abstract: It was proved that the complexity of square root computation in the Galois field $GF(3^s),$ $s=2^kr,$ is equal to $O(M(2^k)M(r)k+M(r)\log_2 r)+2^k kr^{1+o(1)},$ where $M(n)$ is the complexity of multiplication of polynomials of degree $n$ over fields with characteristics $3.$ The complexity of multiplication and division in the field $GF(3^s)$ is equal to $O(M(2^k)M(r))$ and $O(M(2^k)M(r))+r^{1+o(1)}$, respectively. If the basis in the field $GF(3^r)$ is determined by an irreducible binom over $GF(3)$ or is an optimal normal basis, then the summands $2^k kr^{1+o(1)}$ and $r^{1+o(1)}$ can be omitted. For $M(n)$ one may take $n\log_2 n\psi(n) $, where $\psi(n)$ grows slower than any iteration of the logarithm. If $k$ grows and $r$ is fixed, than all the estimates presented here have the form $O_r(M(s)\log_2 s)=s (\log_2 s)^2\psi(s).$

Key words: finite fields, square root computation, Boolean complexity.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00337
17-01-00485


Full text: PDF file (245 kB)
References: PDF file   HTML file

English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2018, 73:5, 176–181

Bibliographic databases:

UDC: 519.95
Received: 22.11.2017

Citation: S. B. Gashkov, I. B. Gashkov, “Fast algorithm of square rooting in some odd charactećistic finite field”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 5, 8–14; Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 73:5 (2018), 176–181

Citation in format AMSBIB
\Bibitem{GasGas18}
\by S.~B.~Gashkov, I.~B.~Gashkov
\paper Fast algorithm of square rooting in some odd charactećistic finite field
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2018
\issue 5
\pages 8--14
\mathnet{http://mi.mathnet.ru/vmumm569}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3878529}
\zmath{https://zbmath.org/?q=an:07023559}
\transl
\jour Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin
\yr 2018
\vol 73
\issue 5
\pages 176--181
\crossref{https://doi.org/10.3103/S0027132218050029}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000450666000002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056086358}


Linking options:
  • http://mi.mathnet.ru/eng/vmumm569
  • http://mi.mathnet.ru/eng/vmumm/y2018/i5/p8

    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. S. B. Gashkov, “Bystrye algoritmy resheniya uravnenii stepeni ne vyshe chetvertoi v nekotorykh konechnykh polyakh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2021, no. 3, 22–31  mathnet
  • Number of views:
    This page:128
    Full text:30
    References:5
    First page:10

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021