Relevant bibliographies by topics / RNS arithmetic

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'RNS arithmetic'

Author: Grafiati
Published: 17 May 2025
Last updated: 31 July 2025

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Journal articles on the topic "RNS arithmetic"

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Olatunbosun, L. O., A. A. Adam, and K. A. Gbolagade. "RNS Bases in Computer Architecture for DNA Sequence Application." International Journal of Engineering and Computer Science 9, no. 07 (2020): 25116–24. http://dx.doi.org/10.18535/ijecs/v9i07.4507.

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In this paper we present an RNS algorithm and architecture implementation of gene sequence applications based on an existing RNS arithmetic algorithm. Investigation was made on RNS application and its inherent arithmetic advantages; data conversion algorithm from Decimal/Binary to RNS; the forward conversion; Conversion from RNS to Binary/Decimal; the reverse conversion using the Chinese remainder theorem CRT, conversion from RNS to mixed radix form with capability for effective computation performance, and analysis of Smith Waterman Algorithm based on DNA sequence computing. Its limitations a
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Timarchi, Somayeh, and Keivan Navi. "Arithmetic Circuits of Redundant SUT-RNS." IEEE Transactions on Instrumentation and Measurement 58, no. 9 (2009): 2959–68. http://dx.doi.org/10.1109/tim.2009.2016793.

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Olatunbosun, Lukumon Olawale. "An Efficient RNS Arithmetic in Bioinformatics sequences." International Journal of Computer Science Issues 16, no. 6 (2019): 19–26. https://doi.org/10.5281/zenodo.3987076.

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This paper investigates the features and the limitation in the implementation of effective RNS computing algorithms using an special method of data representation and conversion in Residue Number System arithmetic as a helpful tool for enhancing Bioinformatics sequencing computing and to reduce the complexity of calculation in many applications. As required in DNA sequencing involving very high speed sequence comparator (VHSC) with real-time processing requirements. We consider and analyze different stages of data processing in RNS. Based on this analysis, we describe the process of conversion
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Khani, Elham. "Efficient Montgomery Modular Multiplication by using Residue Number System." INTERNATIONAL JOURNAL OF MANAGEMENT & INFORMATION TECHNOLOGY 2, no. 1 (2012): 56–62. http://dx.doi.org/10.24297/ijmit.v2i1.1410.

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Residue number system is a carry free system that performs arithmetic operation on residues instead of the weighted binary number. By applying Residue Number System (RNS) to Montgomery modular multiplication the delay of modular multiplication will be decreased. Modular multiplication over large number is frequently used in some application such as Elliptic Curve Cryptography, digital signal processing, and etc.By choosing appropriate RNS moduli sets the time consuming operation of multiplication can be replaced by smaller operations. In addition because of the property of RNS, arithmetic oper
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Parhami, B. "Digital Arithmetic in Nature: Continuous-Digit RNS." Computer Journal 58, no. 5 (2014): 1214–23. http://dx.doi.org/10.1093/comjnl/bxu060.

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Stamenkovic, Negovan, and Vladica Stojanovic. "Constant-coefficient FIR filters based on residue number system arithmetic." Serbian Journal of Electrical Engineering 9, no. 3 (2012): 325–42. http://dx.doi.org/10.2298/sjee1203325s.

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In this paper, the design of a Finite Impulse Response (FIR) filter based on the residue number system (RNS) is presented. We chose to implement it in the (RNS), because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC) unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.
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Elleithy, K. M., and M. A. Bayoumi. "Fast and flexible architectures for RNS arithmetic decoding." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 39, no. 4 (1992): 226–35. http://dx.doi.org/10.1109/82.136572.

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Hiasat, A. A. "RNS arithmetic multiplier for medium and large moduli." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 47, no. 9 (2000): 937–40. http://dx.doi.org/10.1109/82.868463.

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Taylor, F. J., G. Papadourakis, A. Skavantzos, and A. Stouraitis. "A Radix-4 FFT Using Complex RNS Arithmetic." IEEE Transactions on Computers C-34, no. 6 (1985): 573–76. http://dx.doi.org/10.1109/tc.1985.5009414.

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Murthy, C. Srinivasa, and K. Sridevi. "FPGA Implementation of high speed-low energy RNS based Reconfigurable-FIR Filter for Cognitive Radio Applications." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 16 (May 26, 2021): 278–93. http://dx.doi.org/10.37394/23203.2021.16.24.

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The Finite impulse response (FIR) filter is prominently employed in many digital signal processing (DSP) systems for various applications. In this paper, we present a high-performance RNS based FIR filter design for filtration in SDR applications. In general, the residue number system (RNS) gives significant metrics over FIR implementation with its inherent parallelism and data partitioning mechanism. But with increased bit width cause considerable performance trade-off due to both residue computation and reverse conversion. In this paper optimized Residue Number System (RNS) arithmetic is pro
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Dissertations / Theses on the topic "RNS arithmetic"

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Courtois, Jérôme. "Leak study of cryptosystem implementations in randomized RNS arithmetic." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS290.

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On parlera d'analyse forte pour une analyse qui permet de retrouver la clef d'un système cryptographique et d'une analyse faible dans le cas où on élimine des clefs candidates. Le but de cette thèse est essentiellement la compréhension du comportement de l'aléa des distances de Hamming produites par un système cryptographique de type ECC (Elliptic Curve for Cryptography) quand on utilise une représentation RNS (Residue Number System) avec la méthode des moduli aléatoires. Le Chapitre 2 introduit les différentes notions nécessaires à la compréhension de ce document. Il introduit brièvement l'al
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Vollmer, Morgane. "Contributions à l'arithmétique RNS pour la cryptographie logicielle." Electronic Thesis or Diss., Brest, 2024. http://www.theses.fr/2024BRES0122.

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La représentation modulaire des nombres (RNS) permet de découper de grands opérandes en plus petites valeurs et d’accélérer les calculs des implémentations logicielles et matérielles de différents domaines, dont la cryptographie. Cependant, certaines opérations, telles que les réductions modulaires ou les divisions, sont plus difficiles à effectuer en RNS et nécessitent une opération intermédiaire coûteuse : l’extension de base. Nous proposons différentes contributions à l’arithmétique RNS, conduisant à des implémentations logicielles encore plus efficaces que celles existantes. En particulier
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Eynard, Julien. "Approche arithmétique RNS de la cryptographie asymétrique." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066107/document.

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Cette thèse se situe à l'intersection de la cryptographie et de l'arithmétique des ordinateurs. Elle traite de l'amélioration de primitives cryptographiques asymétriques en termes d'accélération des calculs et de protection face aux attaques par fautes par le biais particulier de l'utilisation des systèmes de représentation des nombres par les restes (RNS). Afin de contribuer à la sécurisation de la multiplication modulaire, opération centrale en cryptographie asymétrique, un nouvel algorithme de réduction modulaire doté d'une capacité de détection de faute est présenté. Une preuve formelle ga
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Eynard, Julien. "Approche arithmétique RNS de la cryptographie asymétrique." Electronic Thesis or Diss., Paris 6, 2015. http://www.theses.fr/2015PA066107.

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Cette thèse se situe à l'intersection de la cryptographie et de l'arithmétique des ordinateurs. Elle traite de l'amélioration de primitives cryptographiques asymétriques en termes d'accélération des calculs et de protection face aux attaques par fautes par le biais particulier de l'utilisation des systèmes de représentation des nombres par les restes (RNS). Afin de contribuer à la sécurisation de la multiplication modulaire, opération centrale en cryptographie asymétrique, un nouvel algorithme de réduction modulaire doté d'une capacité de détection de faute est présenté. Une preuve formelle ga
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Métairie, Jérémy. "Contribution aux opérateurs arithmétiques GF(2m) et leurs applications à la cryptographie sur courbes elliptiques." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S023/document.

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La cryptographie et la problématique de la sécurité informatique deviennent des sujets de plus en plus prépondérants dans un monde hyper connecté et souvent embarqué. La cryptographie est un domaine dont l'objectif principal est de ''protéger'' l'information, de la rendre inintelligible à ceux ou à celles à qui elle n'est pas destinée. La cryptographie repose sur des algorithmes solides qui s'appuient eux-mêmes sur des problèmes mathématiques réputés difficiles (logarithme discret, factorisation des grands nombres etc). Bien qu'il soit complexe, sur papier, d'attaquer ces systèmes de protectio
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Händel, Milene. "Circuitos aritméticos e representação numérica por resíduos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2007. http://hdl.handle.net/10183/12670.

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Este trabalho mostra os diversos sistemas de representação numérica, incluindo o sistema numérico normalmente utilizado em circuitos e alguns sistemas alternativos. Uma maior ênfase é dada ao sistema numérico por resíduos. Este último apresenta características muito interessantes para o desenvolvimento de circuitos aritméticos nos dias atuais, como por exemplo, a alta paralelização. São estudadas também as principais arquiteturas de somadores e multiplicadores. Várias descrições de circuitos aritméticos são feitas e sintetizadas. A arquitetura de circuitos aritméticos utilizando o sistema numé
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Younes, Dina. "Využití systému zbytkových tříd pro zpracování digitálních signálů." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-233606.

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Předkládaná disertační práce se zabývá návrhem základních bloků v systému zbytkových tříd pro zvýšení výkonu aplikací určených pro digitální zpracování signálů (DSP). Systém zbytkových tříd (RNS) je neváhová číselná soustava, jež umožňuje provádět paralelizovatelné, vysokorychlostní, bezpečné a proti chybám odolné aritmetické operace, které jsou zpracovávány bez přenosu mezi řády. Tyto vlastnosti jej činí značně perspektivním pro použití v DSP aplikacích náročných na výpočetní výkon a odolných proti chybám. Typický RNS systém se skládá ze tří hlavních částí: převodníku z binárního kódu do RNS,
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Lin, Su-Hon, and 林蘇宏. "Fast RNS-Based Arithmetic Architecture Design and Its VLSI Implementation." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/00534157878874689319.

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碩士<br>國立雲林科技大學<br>電子與資訊工程研究所碩士班<br>90<br>Due to the computational arithmetic based on the conventional weighted number system inherently has carry chains, so that results in performance degradation of the designed system. The residue number system (RNS) offers carry-free, high degree of parallelism and modularity solution since there exists no digit dependence between result and each operand. In this paper, we firstly propose an efficient approach based on special three-channel PRNS to derive polynomial product with low quantity of calculation. It performs a large order range of pol
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Hsu, Di-cheng, and 許迪程. "Implementation of Long Word-length RNS Arithmetic Operations Using Custom Instructions on an Altera SOPC System." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/53393002563872348329.

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碩士<br>逢甲大學<br>資訊工程所<br>98<br>In designing mobile embedded systems, due to the requirement for low cost, low power, and high performance, 32-bit fixed-point processors with RISC architecture are used in these systems. As a result, the precision of these 32-bit processors is not sufficient for high-precision applications. To overcome this precision problem, this thesis proposes to implement long word-length arithmetic instructions on a 32-bit processor by adopting residue number system (RNS) arithmetic with moduli set {2n+1-1,2n,2n-1,2n-1-1}. By using custom instructions, we designed the functio
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Books on the topic "RNS arithmetic"

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Pickar, Gloria D. Dosage calculations. 6th ed. Delmar, 1999.

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Pickar, Gloria D. Dosage calculations. 3rd ed. Delmar Publishers, 1990.

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Pickar, Gloria D. Dosage calculations. 4th ed. Delmar Publishers, 1993.

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Pickar, Gloria D. Dosage calculations. Nelson Education, 2015.

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Pickar, Gloria D. Dosage calculations. 8th ed. Thomson Delmar Learning, 2008.

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Pickar, Gloria D. Dosage calculations. 2nd ed. Delmar, 1987.

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Pickar, Gloria D. Dosage calculations. 8th ed. Thomson Delmar Learning, 2008.

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author, Abernethy Amy Pickar, ed. Dosage calculations: A ratio-proportion approach. Cengage Learning, 2016.

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Campbell, Jamie I. D. How Abstract is Arithmetic? Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.024.

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What is the nature of the cognitive architecture that subserves memory for elementary arithmetic facts, such as 4 + 5 = 9 and 6 × 2 = 12? This article reviews research that has investigated the degree of dependence or independence of calculation processes on the conditions of problem encoding (e.g. by varying problem surface notation or semantic context). It also reviews evidence about the role of linguistic factors in the representation and performance of elementary arithmetic (e.g. transfer of practice within and between languages in bilinguals; effects of the linguistic structure for number
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Demopoulos, William, and Peter Clark. The Logicism of Frege, Dedekind, and Russell. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0005.

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This article is organized around logicism's answers to the following questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified? Although there are, as is seen in this article, important differences, the common thread that runs through all three of the authors discussed in this article their opposition to the Kantian thesis that reflection on reasoning with mere concepts (i.e., without attention to intuitions formed a priori) can never succeed in providing satisfactory answers to these three qu
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Book chapters on the topic "RNS arithmetic"

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Mohan, P. V. Ananda. "RNS-Based Arithmetic Circuits and Applications." In Arithmetic Circuits for DSP Applications. John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119206804.ch6.

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Plantard, Thomas, and Jean-Marc Robert. "Enhanced Digital Signature Using RNS Digit Exponent Representation." In Arithmetic of Finite Fields. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-55227-9_13.

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Chervyakov, Nikolay, and Pavel Lyakhov. "RNS-Based Image Processing." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_9.

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Zarandi, Azadeh Alsadat Emrani. "RNS Applications in Computer Networks." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_14.

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Matutino, Pedro Miguens, Ricardo Chaves, and Leonel Sousa. "RNS-Based Embedded Processor Design." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_2.

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Bajard, Jean-Claude, and Julien Eynard. "RNS Approach in Lattice-Based Cryptography." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_13.

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Cardarilli, Gian Carlo, Alberto Nannarelli, and Marco Re. "RNS Applications in Digital Signal Processing." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_8.

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Uma Maheshwari, J., M. Vaishnavi, P. Eshwar, Sangeeta Singh, and B. Anupama. "RNS integer arithmetic design for elliptic curve cryptography." In Recent Trends in VLSI and Semiconductor Packaging. CRC Press, 2025. https://doi.org/10.1201/9781003616399-37.

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Schinianakis, Dimitris, and Thanos Stouraitis. "RNS-Based Public-Key Cryptography (RSA and ECC)." In Embedded Systems Design with Special Arithmetic and Number Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_12.

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Negre, Christophe, and Guilherme Perin. "Trade-Off Approaches for Leak Resistant Modular Arithmetic in RNS." In Information Security and Privacy. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19962-7_7.

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Conference papers on the topic "RNS arithmetic"

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Bajard, Jean-Claude, Kazuhide Fukushima, Thomas Plantard, and Arnaud Sipasseuth. "Generating Very Large RNS Bases." In 2022 IEEE 29th Symposium on Computer Arithmetic (ARITH). IEEE, 2022. http://dx.doi.org/10.1109/arith54963.2022.00027.

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Bajard, J. C., M. Kaihara, and T. Plantard. "Selected RNS Bases for Modular Multiplication." In 2009 IEEE 19th IEEE Symposium on Computer Arithmetic (ARITH). IEEE, 2009. http://dx.doi.org/10.1109/arith.2009.20.

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Bajard, J., J. Eynard, and F. Gandino. "Fault Detection in RNS Montgomery Modular Multiplication." In 2013 IEEE 21st Symposium on Computer Arithmetic (ARITH). IEEE, 2013. http://dx.doi.org/10.1109/arith.2013.31.

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Lesavourey, Andrea, Christophe Negre, and Thomas Plantard. "Efficient Leak Resistant Modular Exponentiation in RNS." In 2017 IEEE 24th Symposium on Computer Arithmetic (ARITH). IEEE, 2017. http://dx.doi.org/10.1109/arith.2017.39.

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Didier, Laurent-Stephane, Jean-Marc Robert, Fangan Yssouf Dosso, and Nadia El Mrabet. "A software comparison of RNS and PMNS." In 2022 IEEE 29th Symposium on Computer Arithmetic (ARITH). IEEE, 2022. http://dx.doi.org/10.1109/arith54963.2022.00025.

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Peng, Jiaxin, Shuai Sun, Vikram Narayana, Tarek El-Ghazawi, and Volker Sorger. "Integrated Nanophotonics Enabled Residue Number System (RNS) Arithmetic." In 2019 IEEE Photonics Society Summer Topical Meeting Series (SUM). IEEE, 2019. http://dx.doi.org/10.1109/phosst.2019.8794943.

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Matutino, Pedro Miguens, Hector Pettenghi, Ricardo Chaves, and Leonel Sousa. "RNS Arithmetic Units for Modulo {2^n+-k}." In 2012 15th Euromicro Conference on Digital System Design (DSD). IEEE, 2012. http://dx.doi.org/10.1109/dsd.2012.114.

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Bajard, Jean-Claude, Julien Eynard, and Nabil Merkiche. "Multi-fault Attack Detection for RNS Cryptographic Architecture." In 2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH). IEEE, 2016. http://dx.doi.org/10.1109/arith.2016.16.

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Djath, Libey, Karim Bigou, and Arnaud Tisserand. "Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography." In 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH). IEEE, 2019. http://dx.doi.org/10.1109/arith.2019.00016.

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Palronik, Piotr, and Stanislaw J. Piestrak. "Design of a low-power RNS-enhanced arithmetic unit." In 2016 IEEE 7th Latin American Symposium on Circuits & Systems (LASCAS). IEEE, 2016. http://dx.doi.org/10.1109/lascas.2016.7451032.

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Reports on the topic "RNS arithmetic"

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Kirsch, Barry J., and Peter R. Turner. Modified Gaussian Elimination for Adaptive Beam Forming Using RNS Arithmetic. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada288809.

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