{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:42:20Z","timestamp":1760402540020,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003443","name":"The Ministry of Education and Science of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2020-915"],"award-info":[{"award-number":["075-15-2020-915"]}],"id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.<\/jats:p>","DOI":"10.3390\/computation10010009","type":"journal-article","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T10:57:37Z","timestamp":1642071457000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Improved Modular Division Implementation with the Akushsky Core Function"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7066-0061","authenticated-orcid":false,"given":"Mikhail","family":"Babenko","sequence":"first","affiliation":[{"name":"North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, Russia"},{"name":"Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5029-5212","authenticated-orcid":false,"given":"Andrei","family":"Tchernykh","sequence":"additional","affiliation":[{"name":"Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia"},{"name":"CICESE Research Center, Ensenada 22860, Mexico"},{"name":"School of Electrical Engineering and Computer Science, South Ural State University, 454080 Chelyabinsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viktor","family":"Kuchukov","sequence":"additional","affiliation":[{"name":"North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","unstructured":"Akushsky, I.Y., and Yuditsky, D.I. 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