OPTIMIZED ELLIPTIC CURVE CRYPTOGRAPHIC COMPUTATIONS USING ANCIENT INDIAN VEDIC MATHEMATICS TECHNIQUES

Abstract

This study investigates the integration of Ancient Indian Vedic Mathematics (AIVM) into contemporary cryptographic frameworks, with a particular emphasis on Elliptic Curve Cryptography (ECC). Cryptographic computations in ECC require substantial computational resources and execution time, especially during core operations such as point addition, point doubling, and modular multiplication. The AIVM system, based on sixteen Sutras and fourteen Sub-sutras, offers efficient and high-speed arithmetic techniques. This paper examines the applicability and performance benefits of the Urdhva-Tiryagbhyam sutra for multiplication, the Dvandva-Yoga sutra for squaring operations, and the Nikhilam Navatashcaramam Dashatah sutra for handling large-number computations. By implementing these ancient techniques, the computational latency and hardware complexity of systems like RSA and ECC can be significantly reduced. The survey demonstrates that Vedic algorithms not only accelerate encryption and decryption processes but also optimize hardware resource utilization, making them highly suitable for high-speed security applications.

Keywords: ECC, Vedic Mathematics, Dhvajanka, Cryptography, Dvandva-Yoga, Urdhva-Tiryagbhyam, Nikhilam Navatashcaramam Dashatah.