Littérature scientifique sur le sujet « Number system for modular arithmetic »
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Articles de revues sur le sujet "Number system for modular arithmetic"
Khani, Elham. « Efficient Montgomery Modular Multiplication by using Residue Number System ». INTERNATIONAL JOURNAL OF MANAGEMENT & ; INFORMATION TECHNOLOGY 2, no 1 (27 novembre 2012) : 56–62. http://dx.doi.org/10.24297/ijmit.v2i1.1410.
Texte intégralGuzhov, Vladimir I., Ilya O. Marchenko, Ekaterina E. Trubilina et Dmitry S. Khaidukov. « Comparison of numbers and analysis of overflow in modular arithmetic ». Analysis and data processing systems, no 3 (30 septembre 2021) : 75–86. http://dx.doi.org/10.17212/2782-2001-2021-3-75-86.
Texte intégralKrasnobayev, V. A., A. S. Yanko et D. M. Kovalchuk. « METHODS FOR TABULAR IMPLEMENTATION OF ARITHMETIC OPERATIONS OF THE RESIDUES OF TWO NUMBERS REPRESENTED IN THE SYSTEM OF RESIDUAL CLASSES ». Radio Electronics, Computer Science, Control, no 4 (3 décembre 2022) : 18. http://dx.doi.org/10.15588/1607-3274-2022-4-2.
Texte intégralShevelev, S. S. « RECONFIGURABLE COMPUTING MODULAR SYSTEM ». Radio Electronics, Computer Science, Control 1, no 1 (31 mars 2021) : 194–207. http://dx.doi.org/10.15588/1607-3274-2021-1-19.
Texte intégralSchevelev, S. S. « Reconfigurable Modular Computing System ». Proceedings of the Southwest State University 23, no 2 (9 juillet 2019) : 137–52. http://dx.doi.org/10.21869/2223-1560-2019-23-2-137-152.
Texte intégralSelianinau, Mikhail, et Yuriy Povstenko. « An Efficient CRT-Base Power-of-Two Scaling in Minimally Redundant Residue Number System ». Entropy 24, no 12 (14 décembre 2022) : 1824. http://dx.doi.org/10.3390/e24121824.
Texte intégralChernov, V. M. « Number systems in modular rings and their applications to "error-free" computations ». Computer Optics 43, no 5 (octobre 2019) : 901–11. http://dx.doi.org/10.18287/2412-6179-2019-43-5-901-911.
Texte intégralKalmykov, Igor Anatolyevich, Vladimir Petrovich Pashintsev, Kamil Talyatovich Tyncherov, Aleksandr Anatolyevich Olenev et Nikita Konstantinovich Chistousov. « Error-Correction Coding Using Polynomial Residue Number System ». Applied Sciences 12, no 7 (25 mars 2022) : 3365. http://dx.doi.org/10.3390/app12073365.
Texte intégralRahn, Alexander, Eldar Sultanow, Max Henkel, Sourangshu Ghosh et Idriss J. Aberkane. « An Algorithm for Linearizing the Collatz Convergence ». Mathematics 9, no 16 (9 août 2021) : 1898. http://dx.doi.org/10.3390/math9161898.
Texte intégralChervyakov, Nikolay, Pavel Lyakhov, Mikhail Babenko, Irina Lavrinenko, Maxim Deryabin, Anton Lavrinenko, Anton Nazarov, Maria Valueva, Alexander Voznesensky et Dmitry Kaplun. « A Division Algorithm in a Redundant Residue Number System Using Fractions ». Applied Sciences 10, no 2 (19 janvier 2020) : 695. http://dx.doi.org/10.3390/app10020695.
Texte intégralThèses sur le sujet "Number system for modular arithmetic"
Néto, João Carlos. « Método de multiplicação de baixa potência para criptosistema de chave-pública ». Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/3/3141/tde-23052014-010449/.
Texte intégralThis thesis studies the use of computer arithmetic for Public-Key Cryptography (PKC) and investigates alternatives on the level of the hardware cryptosystem architecture that can lead to a reduction in the energy consumption by considering low power and high performance in energy-limited portable devices. Most of these devices are battery powered. Although performance and area are the two main hardware design goals, low power consumption has become a concern in critical system designs. PKC is based on arithmetic functions such as modular exponentiation and modular multiplication. It produces an authenticated key-exchange scheme over an insecure network between two entities and provides the highest security solution for most applications that must exchange sensitive information. Modular multiplication is widely used, and this arithmetic operation is more complex because the operands are extremely large numbers. Hence, computational methods to accelerate the operations, reduce the energy consumption, and simplify the use of such operations, especially in hardware, are always of great value for systems that require data security. Currently, one of the most successful modular multiplication methods is Montgomery Multiplication. Efforts to improve this method are always important to designers of dedicated cryptographic hardware and security in embedded systems. This research deals with algorithms for low-power cryptography. It covers operations required for hardware implementations of modular exponentiation and modular multiplication. In particular, this thesis proposes a new architecture for modular multiplication called Parallel k-Partition Montgomery Multiplication and an innovative hardware design to perform modular exponentiation using Residue Number System (RNS).
Dosso, Fangan Yssouf. « Contribution de l'arithmétique des ordinateurs aux implémentations résistantes aux attaques par canaux auxiliaires ». Electronic Thesis or Diss., Toulon, 2020. http://www.theses.fr/2020TOUL0007.
Texte intégralThis thesis focuses on two currently unavoidable elements of public key cryptography, namely modular arithmetic over large integers and elliptic curve scalar multiplication (ECSM). For the first one, we are interested in the Adapted Modular Number System (AMNS), which was introduced by Bajard et al. in 2004. In this system of representation, the elements are polynomials. We show that this system allows to perform modular arithmetic efficiently. We also explain how AMNS can be used to randomize modular arithmetic, in order to protect cryptographic protocols implementations against some side channel attacks. For the ECSM, we discuss the use of Euclidean Addition Chains (EAC) in order to take advantage of the efficient point addition formula proposed by Meloni in 2007. The goal is to first generalize to any base point the use of EAC for ECSM; this is achieved through curves with one efficient endomorphism. Secondly, we propose an algorithm for scalar multiplication using EAC, which allows error detection that would be done by an attacker we detail
Marrez, Jérémy. « Représentations adaptées à l'arithmétique modulaire et à la résolution de systèmes flous ». Electronic Thesis or Diss., Sorbonne université, 2019. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2019SORUS635.pdf.
Texte intégralModular computations involved in public key cryptography applications most often use a standardized prime modulo, the choice of which is not always free in practice. The improvement of modular operations is fundamental for the efficiency and safety of these primitives. This thesis proposes to provide an efficient modular arithmetic for the largest possible number of primes, while protecting it against certain types of attacks. For this purpose, we are interested in the PMNS system used for modular arithmetic, and propose methods to obtain many PMNS for a given prime, with an efficient arithmetic on the representations. We also consider the randomization of modular computations via algorithms of type Montgomery and Babaï by exploiting the intrinsic redundancy of PMNS. Induced changes of data representation during the calculation prevent an attacker from making useful assumptions about these representations. We then present a hybrid system, HyPoRes , with an algorithm that improves modular reductions for any prime modulo. The numbers are represented in a PMNS with coefficients in RNS. The modular reduction is faster than in conventional RNS for the primes standardized for ECC. In parallel, we are interested in a type of representation used to compute real solutions of fuzzy systems. We revisit the global approach of resolution using classical algebraic techniques and strengthen it. These results include a real system called the real transform that simplifies computations, and the management of the signs of the solutions
Vonk, Jan Bert. « The Atkin operator on spaces of overconvergent modular forms and arithmetic applications ». Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:081e4e46-80c1-41e7-9154-3181ccb36313.
Texte intégralSchill, Collberg Adam. « The last two digits of mk ». Thesis, Linköpings universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-78532.
Texte intégralZhu, Dalin. « Residue number system arithmetic inspired applications in cellular downlink OFDMA ». Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/2070.
Texte intégralArnold-Roksandich, Allison F. « There and Back Again : Elliptic Curves, Modular Forms, and L-Functions ». Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/61.
Texte intégralYounes, 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.
Texte intégralPatel, Riyaz Aziz. « A study and implementation of parallel-prefix modular adder architectures for the residue number system ». Thesis, University of Sheffield, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434492.
Texte intégralHändel, Milene. « Circuitos aritméticos e representação numérica por resíduos ». reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2007. http://hdl.handle.net/10183/12670.
Texte intégralThis work shows various numerical representation systems, including the system normally used in current circuits and some alternative systems. A great emphasis is given to the residue number system. This last one presents very interesting characteristics for the development of arithmetic circuits nowadays, as for example, the high parallelization. The main architectures of adders and multipliers are also studied. Some descriptions of arithmetic circuits are made and synthesized. The architecture of arithmetic circuits using the residue number system is also studied and implemented. The synthesis data of these circuits are compared with the traditional arithmetic circuits results. Then it is possible to evaluate the potential advantages of using the residue number system in arithmetic circuits development.
Livres sur le sujet "Number system for modular arithmetic"
1946-, Soderstrand Michael A., dir. Residue number system arithmetic : Modern applications in digital signal processing. New York : Institute of Electrical and Electronics Engineers, 1986.
Trouver le texte intégralOmondi, Amos R. Residue number systems : Theory and implementation. London : Imperial College Press, 2007.
Trouver le texte intégralA, Soderstrand Michael, dir. Residue number system arithmetic : Modern applications in digital signal processing. NewYork : IEEE Press, 1986.
Trouver le texte intégralModuli spaces and arithmetic dynamics. Providence, R.I : American Mathematical Society, 2012.
Trouver le texte intégralContemporary's number power : Fractions, decimals, and percents. Lincolnwood, Ill : Contemporary Books, 2000.
Trouver le texte intégralContemporary's number power : Addition, subtraction, multiplication, and division. Lincolnwood, Ill., USA : Contemporary Books, 2000.
Trouver le texte intégralHowett, Jerry. Contemporary's number power : A real world approach to math. Chicago, Ill : McGraw-Hill/Wright Group, 2000.
Trouver le texte intégralJamīl, T̤āriq. Complex Binary Number System : Algorithms and Circuits. India : Springer India, 2013.
Trouver le texte intégralElliptic curves, modular forms, and their L-functions. Providence, R.I : American Mathematical Society, 2011.
Trouver le texte intégralContemporary's number power 2 : Fractions, decimals and percents. Chicago : Contemporary Books, 1988.
Trouver le texte intégralChapitres de livres sur le sujet "Number system for modular arithmetic"
Pirlo, Giuseppe. « Non-Modular Operations of the Residue Number System : Functions for Computing ». Dans Embedded Systems Design with Special Arithmetic and Number Systems, 49–64. Cham : Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49742-6_3.
Texte intégralHunacek, Mark. « Congruences and Modular Arithmetic ». Dans Introduction to Number Theory, 31–53. Boca Raton : Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003318712-3.
Texte intégralFaltings, Gerd. « Arithmetic theory of Siegel modular forms ». Dans Number Theory, 101–8. Berlin, Heidelberg : Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0072976.
Texte intégralLowry-Duda, David. « Visualizing Modular Forms ». Dans Arithmetic Geometry, Number Theory, and Computation, 537–57. Cham : Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_19.
Texte intégralBest, Alex J., Jonathan Bober, Andrew R. Booker, Edgar Costa, John E. Cremona, Maarten Derickx, Min Lee et al. « Computing Classical Modular Forms ». Dans Arithmetic Geometry, Number Theory, and Computation, 131–213. Cham : Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_4.
Texte intégralFrey, Gerhard, et Michael Müller. « Arithmetic of Modular Curves and Applications ». Dans Algorithmic Algebra and Number Theory, 11–48. Berlin, Heidelberg : Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-59932-3_2.
Texte intégralArndt, Jörg. « Modular arithmetic and some number theory ». Dans Matters Computational, 764–821. Berlin, Heidelberg : Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14764-7_39.
Texte intégralWiese, Gabor. « Computational Arithmetic of Modular Forms ». Dans Notes from the International Autumn School on Computational Number Theory, 63–170. Cham : Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12558-5_2.
Texte intégralPaliouras, Vassilis, et Thanos Stouraitis. « Logarithmic Number System ». Dans Arithmetic Circuits for DSP Applications, 237–72. Hoboken, NJ, USA : John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119206804.ch7.
Texte intégralDonnelly, Steve, et John Voight. « A Database of Hilbert Modular Forms ». Dans Arithmetic Geometry, Number Theory, and Computation, 365–73. Cham : Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_12.
Texte intégralActes de conférences sur le sujet "Number system for modular arithmetic"
Didier, Laurent-Stephane, Fangan-Yssouf Dosso, Nadia El Mrabet, Jeremy Marrez et Pascal Veron. « Randomization of Arithmetic Over Polynomial Modular Number System ». Dans 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH). IEEE, 2019. http://dx.doi.org/10.1109/arith.2019.00048.
Texte intégralMeloni, Nicolas. « An Alternative Approach to Polynomial Modular Number System Internal Reduction ». Dans 2022 IEEE 29th Symposium on Computer Arithmetic (ARITH). IEEE, 2022. http://dx.doi.org/10.1109/arith54963.2022.00024.
Texte intégralHeinrich, Mark L., Ravindra A. Athale, Michael W. Haney et Charles W. Stirk. « Design of a 16- × 16-bit digital optical multiplier using the residue number system ». Dans OSA Annual Meeting. Washington, D.C. : Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.maa5.
Texte intégralLin, Shing-Hong. « An Optical Intensity and Polarization Coded Ternary Number System ». Dans Spatial Light Modulators and Applications. Washington, D.C. : Optica Publishing Group, 1988. http://dx.doi.org/10.1364/slma.1988.the1.
Texte intégralWei, Shugang. « Number conversions between RNS and mixed-radix number system based on Modulo (2p - 1) signed-digit arithmetic ». Dans the 18th annual symposium. New York, New York, USA : ACM Press, 2005. http://dx.doi.org/10.1145/1081081.1081124.
Texte intégralWei, Shugang. « Number Conversions between RNS and Mixed-Radix Number System Based on Modulo (2p - 1) Signed-Digit Arithmetic ». Dans 2005 18th Symposium on Integrated Circuits and Systems Design. IEEE, 2005. http://dx.doi.org/10.1109/sbcci.2005.4286850.
Texte intégralHeinrich, Mark L., Ravindra A. Athale et Michael W. Haney. « Optical Outer Product Look-up Table Architectures for Residue Arithmetic ». Dans Optical Computing. Washington, D.C. : Optica Publishing Group, 1989. http://dx.doi.org/10.1364/optcomp.1989.tuh1.
Texte intégralKucherov, N., V. Kuchukov, E. Golimblevskaia, N. Kuchukova, I. Vashchenko et E. Kuchukova. « Efficient implementation of error correction codes in modular code ». Dans 3rd International Workshop on Information, Computation, and Control Systems for Distributed Environments 2021. Crossref, 2021. http://dx.doi.org/10.47350/iccs-de.2021.09.
Texte intégralKucherov, N., M. Babenko, A. Tchernykh, V. Kuchukov et I. Vashchenko. « Increasing reliability and fault tolerance of a secure distributed cloud storage ». Dans The International Workshop on Information, Computation, and Control Systems for Distributed Environments. Crossref, 2020. http://dx.doi.org/10.47350/iccs-de.2020.16.
Texte intégralSorger, Volker J., Jiaxin Peng, Shuai Sun, Vikam K. Narayana et Tarek El-Ghazawi. « Integrated Photonic Residue Number System Arithmetic ». Dans Integrated Photonics Research, Silicon and Nanophotonics. Washington, D.C. : OSA, 2018. http://dx.doi.org/10.1364/iprsn.2018.iw2b.3.
Texte intégralRapports d'organisations sur le sujet "Number system for modular arithmetic"
Ostersetzer-Biran, Oren, et Jeffrey Mower. Novel strategies to induce male sterility and restore fertility in Brassicaceae crops. United States Department of Agriculture, janvier 2016. http://dx.doi.org/10.32747/2016.7604267.bard.
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