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Computation
Volume 10
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10.3390/computation10020017
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Article

An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges

by
Andrei Tchernykh
1,2,3,*,
Mikhail Babenko
2,4,
Egor Shiriaev
5,
Bernardo Pulido-Gaytan
1,
Jorge M. Cortés-Mendoza
3,
Arutyun Avetisyan
2,
Alexander Yu Drozdov
6 and
Viktor Kuchukov
5
1
Computer Science Department, CICESE Research Center, Ensenada 22860, Mexico
2
Control/Management and Applied Mathematics, Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia
3
School of Electronic Engineering and Computer Science, South Ural State University, 454080 Chelyabinsk, Russia
4
North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, Russia
5
Department of Applied Mathematics and Mathematical Modeling, North-Caucasus Federal University, 355017 Stavropol, Russia
6
School of Radio Engineering and Computer Technology, Moscow Institute of Physics and Technology, 141701 Moscow, Russia
*
Author to whom correspondence should be addressed.
Computation 2022, 10(2), 17; https://doi.org/10.3390/computation10020017
Submission received: 20 December 2021 / Revised: 14 January 2022 / Accepted: 19 January 2022 / Published: 24 January 2022
(This article belongs to the Special Issue Advanced Information, Computation, and Control Systems for Distributed Environments)
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Abstract

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 1.55–11.35 times with respect to all the methods and configurations.
Keywords: residue number system; weighted number system; approximate method; parity number; core functions; mixed number system; non-modular operations; determining the sign of a number residue number system; weighted number system; approximate method; parity number; core functions; mixed number system; non-modular operations; determining the sign of a number

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MDPI and ACS Style

Tchernykh, A.; Babenko, M.; Shiriaev, E.; Pulido-Gaytan, B.; Cortés-Mendoza, J.M.; Avetisyan, A.; Drozdov, A.Y.; Kuchukov, V. An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges. Computation 2022, 10, 17. https://doi.org/10.3390/computation10020017

AMA Style

Tchernykh A, Babenko M, Shiriaev E, Pulido-Gaytan B, Cortés-Mendoza JM, Avetisyan A, Drozdov AY, Kuchukov V. An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges. Computation. 2022; 10(2):17. https://doi.org/10.3390/computation10020017

Chicago/Turabian Style

Tchernykh, Andrei, Mikhail Babenko, Egor Shiriaev, Bernardo Pulido-Gaytan, Jorge M. Cortés-Mendoza, Arutyun Avetisyan, Alexander Yu Drozdov, and Viktor Kuchukov. 2022. "An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges" Computation 10, no. 2: 17. https://doi.org/10.3390/computation10020017

APA Style

Tchernykh, A., Babenko, M., Shiriaev, E., Pulido-Gaytan, B., Cortés-Mendoza, J. M., Avetisyan, A., Drozdov, A. Y., & Kuchukov, V. (2022). An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges. Computation, 10(2), 17. https://doi.org/10.3390/computation10020017

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