Coding Theory, Cryptography, and Finite Fields

Coding Theory, Cryptography, and Finite Fields explores the theory and applications of finite fields, from basic concepts such as the modular arithmetic and polynomial interpolation to advanced topics such construction and counting of polynomials. This book:

• Addresses a wide range of topics within coding theory, cryptography, and finite fields, offering a holistic understanding of these interconnected fields
• Discusses cutting-edge subjects such as quantum cryptography and multimedia security, making it relevant to current and future technological advancements
• Explores polynomials over finite fields and their applications in coding theory and cryptography to enhance the reader's understanding of the mathematical foundations critical to these areas
• Emphasizes real-world applications of theoretical concepts, particularly in error correction, data security, and encryption algorithms
• Explains critical challenges in protecting multimedia data, offering cutting-edge techniques for securing images, videos, and audio files against unauthorized access and piracy

The text is primarily written for senior undergraduates, graduate students, and academic researchers in electrical engineering, electronics and communications engineering, computer science and engineering, and information technology.

Anand Nayyar received Ph.D (Computer Science) from Desh Bhagat University in 2017 in the area of Wireless Sensor Networks, Swarm Intelligence and Network Simulation. He is currently working in School of Computer Science-Duy Tan University, Da Nang, Vietnam as Professor, Scientist, Vice-Chairman (Research) and Director- IoT and Intelligent Systems Lab. A Certified Professional with 275+ Professional certifications from CISCO, Microsoft, CompTIA, Amazon, Alibaba Cloud, Oracle, Google, Tableau, FinOps, Beingcert, EXIN, GAQM, Cyberoam and many more. Published more than 200+ Research Papers in various High-Quality ISI-SCI/SCIE/SSCI Impact Factor- Q1, Q2, Q3, Q4 Journals cum Scopus/ESCI indexed Journals, 80+ Papers in International Conferences indexed with Springer, IEEE and ACM Digital Library, 60+ Book Chapters in various SCOPUS/WEB OF SCIENCE Indexed Books with Springer, CRC Press, Wiley, IET, Elsevier with Citations: (Google Scholar): 19500+, H-Index: 72 and I-Index: 286; (Scopus): 11000+; H-index: 54. Member of more than 60+ Associations as Senior and Life Member like: IEEE (Senior Member) and ACM (Senior Member). He has authored/co-authored cum Edited 70+ Books of Computer Science. Associated with more than 600+ International Conferences as Programme Committee/Chair/Advisory Board/Review Board member. He has completed 1 Grassroot and 1 ASEAN Project. He has 18 Australian Patents, 16 German Patents, 4 Japanese Patents, 43 Indian Design cum Utility Patents, 13 UK Patents, 1 USA Patent, 3 Indian Copyrights and 2 Canadian Copyrights to his credit in the area of Wireless Communications, Artificial Intelligence, Cloud Computing, IoT, Healthcare, Drones, Robotics and Image Processing. Awarded 55 Awards for Teaching and Research―Young Scientist, Best Scientist, Best Senior Scientist, Asia Top 50 Academicians and Researchers, Young Researcher Award, Outstanding Researcher Award, Excellence in Teaching, Best Senior Scientist Award, DTU Best Professor and Researcher Award- 2019, 2020-2021, 2022, 2022-2023, 2023-2024, Distinguished Scientist Award by National University of Singapore, Obada Prize 2023, Lifetime Achievement Award 2023, 2024; Asian Admirable Achievers 2024; Distinguished Academic Leader 2024, Lifetime Achievement Award 2024 and many more.

He is listed in Top 2% Scientists as per Stanford University (2019, 2020, 2021, 2022, 2023), Ad Index (Rank No:1 Duy Tan University, Rank No:2 Computer Science in Viet Nam) and Listed on Research.com (Top Scientist of Computer Science in Viet Nam- National Ranking: 2; D-Index: 56; World Ranking: 3694).

He is acting as Associate Editor for several reputed journals. He is acting as Managing Editor and Editor-in-Chief of prestigious journals. He has reviewed more than 5100+ Articles for diverse Web of Science and Scopus Indexed Journals. He is currently researching in the area of Wireless Sensor Networks, Internet of Things, Swarm Intelligence, Cloud Computing, Artificial Intelligence, Drones, Blockchain, Cyber Security, Healthcare Informatics, Big Data and Wireless Communications.

R .S. Raja Durai is currently a Professor in the Mathematics Department of JUIT (Jan 2023 - Present). He served as an Associate Professor in the Mathematics Department of JUIT (2013-December 2022). He joined the institute as an Assistant Professor in 2008. He received his bachelor's degree (Loyola college) and master's degree (IIT Madras) in Mathematics in 1997 and 1999, respectively. In 2004, he completed his doctoral research in the field of Algebraic Coding Theory from Department of Mathematics, Indian Institute of Technology Madras. He has then carried out his first post-doctoral research on sequence design for mobile and wireless communications under the supervision of Prof. Naoki Suehiro at the University of Tsukuba, Japan. His second post-doctoral project was a research-cum-implementation work on distributed video coding with IRISA/INRIA, France. He is primarily interested in the research and implementation of his research work to real channels.

Shalini Gupta received an M. Sc. degree in Mathematics and an M. Phil. Degree in Computer Applications from the University of Roorkee, Roorkee (Presently IIT Roorkee) in the year 1991 and 1992 respectively. She completed her Ph. D. degree from the Department of Mathematics and Statistics, Himachal Pradesh University, Shimla (H. P.), India in 2018. She has teaching experience of 14 years. Presently she is working as an Associate Professor and Chairperson of Mathematics in the Department of Mathematics and Statistics, at Himachal Pradesh University, Shimla (H.P.). She has published 35 Research papers in reputed international/ national journals and presented 24 research papers in various international/ national conferences. She delivered seven invited talks on various topics. Her research interests are Rhotrices, Finite Field, Cryptography, and Coding Theory. She recently completed a minor research project awarded by Himachal Pradesh University, Shimla. She is a member of the Cryptology Research Society of India, Himachal Ganita Parishad, Indian Mathematical Society, and Indian Science Congress Association Kolkata. Two students have completed Ph. D. and one student has completed M. Phil. under her supervision. Presently, six students are pursuing Ph. D. under her supervision. She has published one book entitled “Exploring Number Theory”.

Neetu Dhiman is currently working as an Assistant Professor at the University Institute of Technology, Himachal Pradesh University, Shimla. Before this, she was appointed as an Assistant Professor in the Government. Degree College Khundian, Kangra, in the Department of Higher Education. She also served in the government. Hydro Engineering College, Bandla, Bilaspur, as an Assistant Professor. She has been awarded a Gold Medal in M.Sc. Mathematics (2010), and have also qualified National Eligibility Test (NET) and the State Level Eligibility Test (SLET). I have completed my Ph. D. from the Department of Mathematics & Statistics, Himachal Pradesh University, Shimla in 2018. My research area includes Finite Fields, Boolean Bent Functions, Fuzzy Sets, Cryptography, and Rhotrices. She has published 12 research papers in reputed National & International Journals. She has guided one M.Phil student successfully. Currently, four students are pursuing Ph.D. under her supervision.

Ashwini Kumar received his bachelor's and master’s degree in mathematics in 2012 and 2015, respectively. He received a Master of Philosophy in Applied Mathematics in 2016 from Himachal Pradesh University. He completed his doctoral research in Algebraic Coding Theory in 2023, under the supervision of Dr. R. S. Raja Durai at the Department of Mathematics, Jaypee University of Information Technology, Solan (H.P.), India. Currently, he is working as an Assistant Professor at Department of Applied Sciences, Chitkara University, Punjab, India.

His research focuses on developing error-control coding schemes for reliable and efficient data transmission in mobile and wireless networks, bridging the gap between theory and practice. He is driven by a passion for making significant contributions to the field of information theory and communications and is dedicated to collaborating with international experts to advance the field of communications technology.