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.