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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 11, Pages 30–38 (Mi ivm9298)  
This article is cited in 8 scientific papers (total in 8 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
Full-text PDF (198 kB) Citations (8)
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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.
Received: 24.06.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 11, Pages 26–33
DOI: https://doi.org/10.3103/S1066369X17110044
Bibliographic databases:
Document Type: Article
UDC: 511.1
Language: Russian
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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\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
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\vol 61
\issue 11
\pages 26--33
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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