{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:05Z","timestamp":1760150885388,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T00:00:00Z","timestamp":1642982400000},"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>Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure the security of information in common technologies used today, such as cloud computing, the Internet of Things, and machine learning, among others. A primary disadvantage for its practical application is the low efficiency of sign and comparison operations. Several FHE schemes use the Residue Number System (RNS) to decrease the time complexity of these operations. Converting from the RNS to the positional number system and calculating the positional characteristic of a number are standard approaches for both operations in the RNS domain. In this paper, we propose a new method for comparing numbers and determining the sign of a number in RNS. We focus on the even ranges that are computationally simple due to their peculiarities. We compare the performance of several state-of-art algorithms based on an implementation in C++ and relatively simple moduli with a bit depth from 24 to 64 bits. The experimental analysis shows a better performance of our approach for all the test cases; it improves the sign detection between 1.93 and 15.3 times and the number comparison within 1.55\u201311.35 times with respect to all the methods and configurations.<\/jats:p>","DOI":"10.3390\/computation10020017","type":"journal-article","created":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T20:38:58Z","timestamp":1643143138000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5029-5212","authenticated-orcid":false,"given":"Andrei","family":"Tchernykh","sequence":"first","affiliation":[{"name":"Computer Science Department, CICESE Research Center, Ensenada 22860, Mexico"},{"name":"Control\/Management and Applied Mathematics, Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia"},{"name":"School of Electronic Engineering and Computer Science, South Ural State University, 454080 Chelyabinsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7066-0061","authenticated-orcid":false,"given":"Mikhail","family":"Babenko","sequence":"additional","affiliation":[{"name":"Control\/Management and Applied Mathematics, Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia"},{"name":"North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2359-1291","authenticated-orcid":false,"given":"Egor","family":"Shiriaev","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, 355017 Stavropol, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7384-7670","authenticated-orcid":false,"given":"Bernardo","family":"Pulido-Gaytan","sequence":"additional","affiliation":[{"name":"Computer Science Department, CICESE Research Center, Ensenada 22860, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7209-8324","authenticated-orcid":false,"given":"Jorge M.","family":"Cort\u00e9s-Mendoza","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Computer Science, South Ural State University, 454080 Chelyabinsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arutyun","family":"Avetisyan","sequence":"additional","affiliation":[{"name":"Control\/Management and Applied Mathematics, Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander Yu","family":"Drozdov","sequence":"additional","affiliation":[{"name":"School of Radio Engineering and Computer Technology, Moscow Institute of Physics and Technology, 141701 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viktor","family":"Kuchukov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, 355017 Stavropol, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,24]]},"reference":[{"key":"ref_1","first-page":"803","article-title":"A new class of monotone functions of the residue number system","volume":"7","author":"Pirlo","year":"2013","journal-title":"Int. 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