Diskretnaya Matematika
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



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






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


Diskretnaya Matematika, 1998, Volume 10, Issue 4, Pages 35–38
DOI: https://doi.org/10.4213/dm442
(Mi dm442)
 

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

Simplified justification of the probabilistic Miller–Rabin test for primality

S. B. Gashkov
Full-text PDF (359 kB) Citations (1)
Abstract: Let $m$ be a positive integer and $\mathbb Z_m^*$ be the set of all positive integeres which are no greater than $m$ and relatively prime to $m$. A number $s\in\mathbb Z_m^*$ is called a witness of primality of $m$ if the sequence
$$ s^{(m-1)2^{-i}} \pmod m,\quad i = 0,1,\ldots, r,\quad m-1 = 2^{r}t, $$
where $t$ is odd, consists only of ones, or begins with ones and continues by minus one and, may be, then by other integers.
We give a simple proof of the following known assertion that is a ground of the Miller–Rabin primality test: The cardinality of the set of witnesses of primality of a composite $m$ is no greater than $\varphi(m)/4$, where $\varphi(m)$ is Euler's totient function.
This work was supported by the Russian Foundation for Basic Research, grant 96–01–068.
Received: 02.02.1998
Bibliographic databases:
UDC: 519.7
Language: Russian
Citation: S. B. Gashkov, “Simplified justification of the probabilistic Miller–Rabin test for primality”, Diskr. Mat., 10:4 (1998), 35–38; Discrete Math. Appl., 8:6 (1998), 545–548
Citation in format AMSBIB
\Bibitem{Gas98}
\by S.~B.~Gashkov
\paper Simplified justification of the probabilistic Miller--Rabin test for primality
\jour Diskr. Mat.
\yr 1998
\vol 10
\issue 4
\pages 35--38
\mathnet{http://mi.mathnet.ru/dm442}
\crossref{https://doi.org/10.4213/dm442}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1673119}
\zmath{https://zbmath.org/?q=an:0985.11065}
\transl
\jour Discrete Math. Appl.
\yr 1998
\vol 8
\issue 6
\pages 545--548
Linking options:
  • https://www.mathnet.ru/eng/dm442
  • https://doi.org/10.4213/dm442
  • https://www.mathnet.ru/eng/dm/v10/i4/p35
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
    Statistics & downloads:
    Abstract page:1264
    Full-text PDF :535
    References:1
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025