Research and Modification of Montgomery Multiplication Algorithm

The article the discusses the realization of Montgomery Multiplication Algorithm, and the research and analysis of the values of program runtime divided by value P and program runtime from value N. Special attention was paid to the mathematical aspects of the execution of the Montgomery Multiplicati...

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Главные авторы:	Lapina, M. A., Лапина, М. А., Borodulin, I. V., Бородулин, И. В., Koronskiy, A., Коронский, А., Martemyanov, M. V., Мартемьянов, М. В.
Формат:	Статья
Язык:	English
Опубликовано:	Springer Science and Business Media Deutschland GmbH 2024
Темы:	Modular arithmetic Residue number system (RNS) Python Montgomery multiplication algorithm Modulo
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/29358
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spelling	ir-123456789-293582024-12-27T08:12:56Z Research and Modification of Montgomery Multiplication Algorithm Lapina, M. A. Лапина, М. А. Borodulin, I. V. Бородулин, И. В. Koronskiy, A. Коронский, А. Martemyanov, M. V. Мартемьянов, М. В. Modular arithmetic Residue number system (RNS) Python Montgomery multiplication algorithm Modulo The article the discusses the realization of Montgomery Multiplication Algorithm, and the research and analysis of the values of program runtime divided by value P and program runtime from value N. Special attention was paid to the mathematical aspects of the execution of the Montgomery Multiplication Algorithm, its realization in the Python programming language, as well as the optimization of the realization to obtain a range of values of the results of the program execution and the time of obtaining these values at different P (P – modulus of the operation of taking the remainder). As a result of the analysis, regularities and tendencies of change of the dependencies considered in the paper were revealed. 2024-12-11T09:10:57Z 2024-12-11T09:10:57Z 2024 Статья Lapina, M., Neelakandan, S., Borodulin, I., Koronskiy, A., Martemyanov, M. Research and Modification of Montgomery Multiplication Algorithm // Lecture Notes in Networks and Systems. - 2024. - 1207 LNNS. - pp. 142-150. - DOI: 10.1002/cbic.202400800 https://dspace.ncfu.ru/handle/123456789/29358 en Lecture Notes in Networks and Systems application/pdf Springer Science and Business Media Deutschland GmbH
institution	СКФУ
collection	Репозиторий
language	English
topic	Modular arithmetic Residue number system (RNS) Python Montgomery multiplication algorithm Modulo
spellingShingle	Modular arithmetic Residue number system (RNS) Python Montgomery multiplication algorithm Modulo Lapina, M. A. Лапина, М. А. Borodulin, I. V. Бородулин, И. В. Koronskiy, A. Коронский, А. Martemyanov, M. V. Мартемьянов, М. В. Research and Modification of Montgomery Multiplication Algorithm
description	The article the discusses the realization of Montgomery Multiplication Algorithm, and the research and analysis of the values of program runtime divided by value P and program runtime from value N. Special attention was paid to the mathematical aspects of the execution of the Montgomery Multiplication Algorithm, its realization in the Python programming language, as well as the optimization of the realization to obtain a range of values of the results of the program execution and the time of obtaining these values at different P (P – modulus of the operation of taking the remainder). As a result of the analysis, regularities and tendencies of change of the dependencies considered in the paper were revealed.
format	Статья
author	Lapina, M. A. Лапина, М. А. Borodulin, I. V. Бородулин, И. В. Koronskiy, A. Коронский, А. Martemyanov, M. V. Мартемьянов, М. В.
author_facet	Lapina, M. A. Лапина, М. А. Borodulin, I. V. Бородулин, И. В. Koronskiy, A. Коронский, А. Martemyanov, M. V. Мартемьянов, М. В.
author_sort	Lapina, M. A.
title	Research and Modification of Montgomery Multiplication Algorithm
title_short	Research and Modification of Montgomery Multiplication Algorithm
title_full	Research and Modification of Montgomery Multiplication Algorithm
title_fullStr	Research and Modification of Montgomery Multiplication Algorithm
title_full_unstemmed	Research and Modification of Montgomery Multiplication Algorithm
title_sort	research and modification of montgomery multiplication algorithm
publisher	Springer Science and Business Media Deutschland GmbH
publishDate	2024
url	https://dspace.ncfu.ru/handle/123456789/29358
work_keys_str_mv	AT lapinama researchandmodificationofmontgomerymultiplicationalgorithm AT lapinama researchandmodificationofmontgomerymultiplicationalgorithm AT boroduliniv researchandmodificationofmontgomerymultiplicationalgorithm AT boroduliniv researchandmodificationofmontgomerymultiplicationalgorithm AT koronskiya researchandmodificationofmontgomerymultiplicationalgorithm AT koronskija researchandmodificationofmontgomerymultiplicationalgorithm AT martemyanovmv researchandmodificationofmontgomerymultiplicationalgorithm AT martemʹânovmv researchandmodificationofmontgomerymultiplicationalgorithm
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Research and Modification of Montgomery Multiplication Algorithm

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