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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 11, Pages 30–38 (Mi ivm9298)  

This article is cited in 4 scientific papers (total in 4 papers)

Calculation of Bezout's coefficients for $k$-ary algorithm of greatest common divisor

Sh. T. Ishmukhametova, B. G. Mubarakova, Kamal Maad Al-Annib

a Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
b University of Strasbourg, 4 Rue Blaise Pascal, Strasbourg, 67081 France

Abstract: Bezout's equation is a representation of the greatest common divisor $d$ of two integers $A$ and $B$ as a linear combination $Ax+By=d$, where $x$ and $y$ are integers called Bezout's coefficients. Usually Bezout's coefficients are caclulated using the extended version of the classical Euclidian algorithm.
We elaborate a new algorithm for calculating Bezout's coefficients based on the $k$-ary GCD algorithm. This problem has numerous applications in the number theory and cryptography, for example, for calculation of multiplicative inverse elements in modular arithmetic.

Keywords: Euclidian algorithm, extended Euclidian algorithm, $k$-ary GCD algorithm, calculation of inverse elements by module.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:11, 26–33

Bibliographic databases:

UDC: 511.1
Received: 24.06.2016

Citation: Sh. T. Ishmukhametov, B. G. Mubarakov, Kamal Maad Al-Anni, “Calculation of Bezout's coefficients for $k$-ary algorithm of greatest common divisor”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 11, 30–38; Russian Math. (Iz. VUZ), 61:11 (2017), 26–33

Citation in format AMSBIB
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\by Sh.~T.~Ishmukhametov, B.~G.~Mubarakov, Kamal~Maad~Al-Anni
\paper Calculation of Bezout's coefficients for $k$-ary algorithm of greatest common divisor
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 11
\pages 30--38
\mathnet{http://mi.mathnet.ru/ivm9298}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 11
\pages 26--33
\crossref{https://doi.org/10.3103/S1066369X17110044}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85032342338}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Dolgov, “O rasshirennom algoritme Dzhebeleana–Vebera–Sedzhelmasi vychisleniya naibolshego obschego delitelya”, Chebyshevskii sb., 19:2 (2018), 421–431  mathnet  crossref  elib
    2. I. Amer, Sh. T. Ishmukhametov, “Ob uskorenii $k$-arnogo algoritma vychisleniya NOD naturalnykh chisel”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2019, 110–118  mathnet  crossref  elib
    3. R. R. Enikeev, “Effektivnoe udalenie delitelei v $k$-arnom algoritme”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2019, 393–404  mathnet  crossref
    4. Al Khalidi Arkan Mokhammed, Sh. T. Ishmukhametov, “Effektivnoe programmirovanie protsedury vychisleniya NOD naturalnykh chisel”, Izv. vuzov. Matem., 2020, no. 6, 3–8  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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