This book is based on the best papers accepted for presentation during the International Conference on Mathematics and its Applications in New Computer Systems (MANCS-2021), Russia.
The book includes research materials on modern mathematical problems, solutions in the field of cryptography, data analysis and modular computing, as well as scientific computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in mathematical solutions to cryptography issues are devoted to secret sharing schemes, public key systems, private key systems, n-degree comparisons, modular arithmetic of simple, addition of points of an elliptic curve, Hasse theorem, homomorphic encryption and learning with error, and modifications of the RSA system. Furthermore, issues in data analysis and modular computing include contributions in the field of mathematical statistics, machine learning methods, deep learning, and neural networks. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of cryptography, information security, parallel computing, computer technology, and mathematical education.
?Andrei Tchernykh is Full Professor in computer science at CICESE Research Center (Centro de Investigación Científica y de Educación Superior de Ensenada), Ensenada, Baja California, Mexico, and Adjunct Professor at ISP RAS—Institute for System Programming of the Russian Academy of Sciences, Russia. He is chairing “Parallel Computing Laboratory” at CICESE, Mexico, and “International Laboratory of Problem-Oriented Cloud Computing” at South Ural State University, Russia. He gained industrial experience as supercomputer design team leader in Advance Technical Products Corp and Supercomputer Design Department of Electro-Mechanical Enterprise. He received his Ph.D. degree in Computer Science from the IPMCE in 1986. He is Founding Member of the Mexican Supercomputer Society (RedMexSu), a Regional President of Global Association for Academic Supervision (GAAS) Latin America, and Member of the Mexican National Researchers System SNI level II. He has led a number of research projects and grants in different countries funded by CONACYT, NSF, ANII, Ochoa, INRIA, FNR, UC MEXUS, DAAD, LAFMI, AMEXCID, ANII, etc. He is awarded Global Scholars Fellow at Tsinghua University (China), German Academic Exchange Service fellowship at University of Göttingen, Dortmund University, Technische Universität Clausthal (Germany), and Severo Ochoa Fellowship at Barcelona Supercomputing Center (Spain). He is Editorial Board Member of several journals and served as Guest Editor for special issues including Mobile Networks & Applications (MONET) Springer, International Journal of Approximate Reasoning, Elsevier.
Anatoly Alikhanov has obtained his Ph.D. in Physical and Mathematical Sciences and is Dean of the Faculty of Mathematics and Computer Science named after Professor Chervyakov of the North Caucasus Federal University. He is Head of the Regional Scientific and Educational Mathematical Center "North Caucasian Center for Mathematical Research." Earlier, he worked as Visiting Member of the dissertation council at Southeast University, Department of Mathematics, Nanjing, China. In 2016, he was invited for an internship in the field of numerical methods for solving fractional differential equations at the Nanjing University of China. He is Member of the Editor Board of the Fractional Calculus and Applied Analysis Journal. He is Reviewer of over 30 reputable scientific journals in computational mathematics.
Mikhail Babenko is Head of the Department of Computational Mathematics and Cybernetics North-Caucasus Federal University. He is Member of the scientific school named after Professor Chervyakov “Neuromathematics, modular neurocomputers and high-performance computing.” He received Ph.D. in mathematical modeling, numerical methods, and software. He took internships in CICESE Research Center in México; Le Quy Don Technical University, Hanoi, Vietnam, in 2015; University of Lorraine, Nancy, France, in 2017. His research areas are: Security, Cryptography, Residue Number System, Big Data, Internet of Things, Fog-Edge-Cloud Computing, Trust, Uncertainty, Scalable and Reliable Systems, Elliptic Curve.
Irina Samoilenko, Ph.D., is Associate Professor at Informational Systems Department, Stavropol State Agrarian University, Russia. She received M.S. degree in Applied Mathematics and Informatics, and Ph.D. in System Analysis, Control and Processing of Information in North-Caucasus Federal University. She is Researcher in North-Caucasus Centre for Mathematical Research, North-Caucasus Federal University. She is Member of Association of Scientific Editors and Publishers, Russia. She participated in international conferences and internships in Italy, Turkey, Romania, and Czech Republic. Her research interests include wireless sensor networks, IoT, optimization tasks, and mathematical modeling.
