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IJSTR >> Volume 8 - Issue 8, August 2019 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Some Algorithms of Various Projective Coordinate Systems for ECC Using Ancient Indian Vedic Mathematics Sutras

[Full Text]



Manoj Kumar, Ankur Kumar



Dvandva-Yoga, Elliptic Curve Cryptography, Jacobian Projective, Lopez-Dahab Projective, Point addition, Point doubling, Standard Projective, Urdhva-Tiryagbhyam.



In this present approach, Some Algorithms of Various Projective Coordinate Systems for ECC (Elliptic Curve Cryptography) using AIVM (Ancient Indian Vedic Mathematics) sutras, has been studied. This work explained some useful Vedic sutra for multiplication calculation in cryptographic operations. In this paper, we have used some Vedic Mathematics Sutra to get minimum steps in the calculation of the addition algorithm, doubling algorithm and for improving the speed of processing time in the cryptographic operations, such as point addition, point doubling which occurs in the Elliptic curve cryptography over projective coordinate systems (Standard Projective, Jacobian Projective, Lopez-Dahab Projective). The coding and synthesis are done in MATLAB. The results proved that the Vedic Mathematics based schemes show better performance compared to the conventional method. The total delay in computation is reduced by Vedic mathematics Sutras (Urdhva-Tiryagbhyam, Dvandva-Yoga) with the help of MATLAB software.



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