PERFORMANCE ANALYSIS OF EDWARDS ELLIPTIC CURVES USING VEDIC MATHEMATICS FOR SECURE AUTHENTICATION PROTOCOLS IN ECC

Abstract

In order to create effective implementations of point addition and point doubling algorithms for Edwards elliptic curves, this paper investigates the use of Vedic mathematical approaches. The goal of the suggested approach is to improve Edwards elliptic curve cryptography (ECC) procedures processing efficiency. In particular, the Urdhva-Tiryagbhyam sutra is used to optimize multiplication procedures, and the Dvandva-yoga method is used to speed up squaring operations. These methods are used to provide two optimized cryptographic formulations for Edwards elliptic curves: point addition and point doubling. In terms of execution speed, processing time, and lower multiplier power consumption, experimental evaluations show that the Vedic mathematics-based methodology performs noticeably better than traditional arithmetic methods. Point addition and scalar operations are implemented in MATLAB utilizing 16-bit and 32-bit operands. Additionally, a number of Vedic mathematical methods are examined to determine how they affect elliptic curve calculations; the findings are displayed using detailed tables and graphical representations. The results demonstrate how Vedic mathematics can significantly increase the effectiveness and performance of elliptic curve cryptography systems.