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Applied Sciences
Special Issues
Emerging Residue Number System Technologies and Applications
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Emerging Residue Number System Technologies and Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: closed (20 December 2022) | Viewed by 3980

Special Issue Editors

Dr. Mikhail Babenko

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Guest Editor
Department of Computational Mathematics and Cybernetics, North-Caucasus Federal University, 355009 Stavropol, Russia
Interests: residue number system; elliptic curve; cloud computing; cryptography; Internet of Things
Dr. Maxim Deryabin

E-Mail Website
Guest Editor
Computing Platform Lab, Samsung Advanced Institute of Technology, Samsung Electronics, Suwon 16678, Republic of Korea
Interests: residue number system; computer arithmetic; cryptography; lattice-based cryptography; homomorphic encryption; circuit design
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Andrei Tchernykh

E-Mail Website
Guest Editor
1. CICESE Research Center, carr. Tijuana-Ensenada 3918, 22860 Ensenada, BC, Mexico
2. Ivannikov Institute for System Programming, Alexander Solzhenitsyn 25, 109004 Moscow, Russia
3. South Ural State University, Prospekt Lenina 76, 454080 Chelyabinsk, Russia
Interests: residue number system; multi-objective resource optimization; security; scheduling; heuristics and meta-heuristics; uncertainty; adaptive resource allocation; cloud computing; privacy-preserving
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The residue number system has attracted the attention of researchers and engineers for many years due to its versatility, high potential, and variety of possible applications. RNS works well with modern parallel processing environments and platforms, and this fact makes RNS one of the foundational tools of modern high-performance computing systems. In applying RNS, its properties allow reducing the computational complexity of cryptographic primitives, digital signal processing algorithms, and artificial neural networks. In addition, due to its unique combination of properties, RNS can be used to construct error correction codes and distributed storage schemes.

This Special Issue is aimed at reflecting modern developments in the field of RNS and its applications, trends, and problems in the development and application of this technology. Submissions researching and generalizing knowledge in the field of the residue number system, from both the theoretical and the practical side, are invited.

Specific topics of interest include, but are not limited to, the following areas:

  • Design of high-performance devices using the residue number system
  • Challenges and advances of using the residue number system in the field of cryptography
  • High-performance digital signal processing methods based on the residue number system
  • Error correction and control of data integrity in various applications based on the residue number system
  • Residue number system applications in artificial intelligence and machine learning
  • Communications and networking using the residue number system

Dr. Mikhail Babenko
Dr. Maxim Deryabin
Prof. Dr. Andrei Tchernykh
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

22 pages, 383 KiB  
Article
Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
by Viktor Kuchukov, Dmitry Telpukhov, Mikhail Babenko, Ilya Mkrtchan, Alexander Stempkovsky, Nikolay Kucherov, Tatiana Ermakova and Marine Grigoryan
Appl. Sci. 2022, 12(23), 12355; https://doi.org/10.3390/app122312355 - 2 Dec 2022
Viewed by 1335
Abstract
The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional [...] Read more.
The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional number system. The methods of reverse conversion for general form moduli based on the Chinese remainder theorem and the mixed-radix conversion are considered, as well as the optimized methods for special form moduli. In this paper, a method is proposed that develops the authors’ ideas based on the modified mixed-radix conversion and reference points. The modified method based on the mixed-radix conversion in this case makes it possible to replace the operation of finding the residue of division by a large modulo with the sequential calculation of the residue. The method of reference points allows to reduce the size of the stored information compared to the use of ROM to store all the residues of RNS. The application of this approach makes it possible to find a balance between the speed of the calculation and the hardware used, by varying the number of moduli of one method and the other. Full article
(This article belongs to the Special Issue Emerging Residue Number System Technologies and Applications)
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29 pages, 2578 KiB  
Article
Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding
by Mikhail Babenko, Anton Nazarov, Maxim Deryabin, Nikolay Kucherov, Andrei Tchernykh, Nguyen Viet Hung, Arutyun Avetisyan and Victor Toporkov
Appl. Sci. 2022, 12(1), 463; https://doi.org/10.3390/app12010463 - 4 Jan 2022
Cited by 2 | Viewed by 1592
Abstract
Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge [...] Read more.
Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs. Full article
(This article belongs to the Special Issue Emerging Residue Number System Technologies and Applications)
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