The Techniques of Vedic Mathematics for ECC Over Weierstrass Elliptic Curve Y2 = X3 + Ax + B

Abstract

An analysis is presented to the study, the proficient implementation of ancient mathematics formulae for multiplications and squares in the cryptographic system. In this approach, we have used ancient mathematics techniques and algorithms in the different projective coordinates system (Jacobian, Chudnovsky-Jacobian, Modified Jacobian coordinates system) to get minimum steps in the calculation of addition algorithm, doubling algorithm and for improving the speed of processing time in the operations of ECC (points addition, points doubling). The coding and synthesis are done in MATLAB for 16-bit digit multiplications and squares. The results proved that the Vedic mathematics-based scheme shows better performance compared to the conventional method and total delay in computation is reduced by Vedic mathematics Sutras (Urdhva-tiryagbhyam, Dvandva-yoga). The results of some AVIM techniques over ECC were obtained and discussed in the form of tables and graphs.