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dc.contributor.author Amer I.
dc.contributor.author Ishmukhametov S.
dc.date.accessioned 2020-01-15T22:14:54Z
dc.date.available 2020-01-15T22:14:54Z
dc.date.issued 2019
dc.identifier.issn 2541-7746
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/157219
dc.description.abstract © 2019, Kazan Federal University. All rights reserved. In this paper, methods of acceleration of GCD algorithms for natural numbers based on the k-ary GCD algorithm have been studied. The k-ary algorithm was elaborated by J. Sorenson in 1990. Its main idea is to find for given numbers A, B and a parameter k, co-prime to both A and B, integers x and y satisfying the equation Ax + By ≡ 0 mod k. Then, integer C = (Ax+By)/k takes a value less than A. At the next iteration, a new pair (B, C) is formed. The k-ary GCD algorithm ensures a significant diminishing of the number of iterations against the classical Euclidian scheme, but the common productivity of the k-ary algorithm is less than the Euclidian method. We have suggested a method of acceleration for the k-ary algorithm based on application of preliminary calculated tables of parameters like as inverse by module k . We have shown that the k-ary GCD algorithm overcomes the classical Euclidian algorithm at a sufficiently large k when such tables are used.
dc.relation.ispartofseries Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
dc.subject Binary GCD algorithm
dc.subject Euclidian GCD algorithm
dc.subject Greatest common divisor for natural numbers
dc.subject K-ary GCD algorithm
dc.title On acceleration of the k-ary GCD algorithm
dc.type Article
dc.relation.ispartofseries-issue 1
dc.relation.ispartofseries-volume 161
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 110
dc.source.id SCOPUS25417746-2019-161-1-SID85071981073


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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