Cryptographic Algorithms

Elliptic and Jacobian, Elliptic Curve Cryptography and Computational Security

Anita Tomar, Ankur Nehra

• Publisher: De Gruyter
• Year: 2026
• Topic: Mathematics
• eBook ISBN:
  9783112221907
• Subtopic: Cyber Security
• Index: Mathematics

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.

Table of contents

• Title Page
• Copyright
• Contents
• Frontmatter
• Dedication
• Contents
• List of Acronyms
• About the Authors
• Chapter 1 Ancient Indian Mathematics
• Chapter 2 The Concept of Cryptography
• Chapter 3 The Elliptic Curve Cryptography (ECC)
• Chapter 4 Jacobian Elliptic Curve Cryptography (JECC) Based on Ancient Indian Mathematics
• Chapter 5 Trilinear Pairing in Cryptography Using Ancient Vedic Sutras
• Chapter 6 ECC over Ring A4 Using Ancient Indian Mathematics
• Chapter 7 Vehicular Communication Based on Fog Computing Using Ancient Indian Mathematics
• Chapter 8 The Ancient Indian Sutras for Cryptography: A Review
• Chapter 9 Conclusion and Future Work
• Index