This book explores cryptographic techniques by integrating Elliptic and Jacobian Elliptic Curve Cryptography with Ancient Indian Mathematics, optimizing security and computational efficiency. As digital security becomes vital, the rich mathematical heritage of ancient India offers profound insights into cryptography, bridging historical wisdom with cutting-edge security solutions.
Key frameworks- algebra, analysis, and optimization- enhance point operations like addition and doubling in cryptographic protocols. The book explores trilinear pairing and cryptographic schemes over specialized rings, leveraging projective geometry and algebraic structures to enhance encryption and decryption methods. Covering foundational concepts, algorithms, and applications, the book highlights how ancient Indian insights can improve Elliptic Curve Cryptography, Jacobian Elliptic Curve Cryptography, and trilinear pairing.
Applications span secure vehicular communication using fog computing, blockchain-based authentication, and cloud security. It is targeted at cryptographers, mathematicians, and computer scientists and provides algorithmic innovations, security proofs, structured exercises, and real-world case studies.

Autorentext

Anita Tomar is the Professor and Head of the Department of Mathematics at Pt. L.M.S. Campus, Sri Dev Suman Uttarakhand University, Rishikesh. Her research interests encompass real and complex dynamics, focusing on chaos, fractals, mathematical modeling, and fixed point theory. She has contributed significantly to these fields, authoring 95 research papers and 10 book chapters, and edited books titled "Fixed Point Theory & its Applications to Real World Problems" and Banach Contraction Principle: A Centurial Journey . In addition to this, Prof. Tomar has been actively involved in applied mathematics and the history of mathematics. She has delivered talks in various countries, including Senegal, Turkey, Nepal, Taiwan, and Thailand, as well as across India. She has supervised two research scholars, co-authored textbooks, and served as a guest editor for special issues in journals such as the Journal of Function Spaces, Journal of Mathematical Sciences, and Demonstratio Mathematica.
Prof. Tomar is also a reviewer for Mathematical Reviews (AMS) and has reviewed numerous papers indexed in MathSciNet, ZbMATH, and Scopus. She holds life memberships in the Indian Mathematical Society and the Indian Society for History of Mathematics. Her accolades include the "Teacher of the Year" award in 2020, the "Leading Women Scientist" award in 2021, and the "Chief Minister's Excellence and Good Governance Award" in 2022, Excellence in Research award in 2023.
Beyond her research, Prof. Tomar has contributed to syllabus development under NEP 2020 for universities in Uttarakhand and actively participates in both academic and administrative roles. She serves on several key university bodies, including the Director, Centre of Excellence in Entrepreneurship and Incubation, Director, Faculty Development Centre, Executive Council, Academic Council, Board of Studies, Research Degree Committee (RDC), and Interview Boards.
She is deeply committed to advancing mathematics through innovative research, fostering interdisciplinary collaboration, and promoting excellence in education.

Dr. Ankur Nehra is working as an Assistant Professor in the Department of Mathematics at Govt. Aided Dhanauri P.G. College, Dhanauri, Haridwar, Uttarakhand (INDIA) 247667. He has nine years of teaching and research experience. He serves as the Head of the SC/ST/OBC CELL and the Head of the Counselling & Placement Cell at Dhanauri P.G. College, Dhanauri, Haridwar, Uttarakhand, India 247667. His research areas, Fuzzy Theory, Graph Theory, and Ancient Indian Mathematics, and their Applications in Cryptography have resulted in an impressive scholarly record. With 30 publications in renowned journals and five publications as chapters in edited books, it has significantly contributed to the field. His book, "Some Vedic Mathematics Sutras for Elliptic Curve Cryptography," is published in an international publishing house. He has made contributions to mentoring and academic leadership. He is co-supervising two research scholars. Being a Life member of the ISCA chapter Haridwar, He actively engages in scholarly communities. His role as a Reviewer for Mathematical Reviews, a division of the Journal of Extension Education, Coimbatore, India, reflects his commitment to mathematical research. His contributions have been recognized through various awards, including the "Young Scientist Award (08-09 Nov. 2023). His accolades underscore her dedication to advancing mathematical research and education.