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Ancient Indian Vedic Mathematics (AIVM) and Elliptic Curve Cryptography (ECC) are the fundamental branches of Mathematics, this book aims to serve as a reference book for researchers. It can also be read with great interest by students of engineering and UG & PG courses in mathematics and computer science. The book's material has been arranged into sections spread out over seven chapters. Each chapter begins with a brief introduction which provides motivation and a keen desire to proceed with the material of the chapter. Some examples have been given for reference for solving problems in Cryptography and Vedic Maths. Remarks and notes at places and exercises have been given at the end of each section to increase the knowledge by applying previous results. The exercises have also been graded appropriately and followed by answers. We can get better performance if we use Vedic Mathematics sutras in ECC algorithms of Cryptography. This Book explained the coding of Vedic Mathematics Sutras in MATLAB and concluded that AIVM sutras in ECC improve the speed, memory, smaller key sizes, and performance in terms of calculation time, processing speed, and power consumption of the cryptosystem.