IMPROVED PERFORMANCE OF CRYPTOSYSTEM BASED ON EDWARDS AND TWISTED EDWARDS ELLIPTIC CURVES USING SOME TECHNIQUES OF AIVM
Manoj Kumar, Ankur Kumar · Journal of Critical Reviews · 2020
This paper is on some efficient algorithms implementation of points addition and points doubling for the Edwards elliptic curves using techniques of ancient mathematics. In particular, we improve timings in the cryptographic operations for the Edwards elliptic curves. We use some techniques of ancient mathematics namely Urdhva-triyagbhaym for multiplication, Dvandva-yoga for squaring of any digits. We introduce cryptographic formulae (Point Addition and Point Doubling) for Edwards elliptic curves. We discuss that the techniques of the ancient mathematics-based scheme show better performance in speed, processing time and power consumption of multipliers compared to the conventional method. The coding and synthesis are done in MATLAB for the algorithm of multiplications and squaring using 16-bits and 32-bits. The effect of some Ancient Mathematical techniques over elliptic curves was investigated and the obtained results are explained in the form of tables and graphs. We discuss the significance of these optimizations for elliptic curve cryptography.