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Research Article

JCR. 2020; 7(19): 5787-5799


IMPROVED PERFORMANCE OF CRYPTOSYSTEM BASED ON EDWARDS AND TWISTED EDWARDS ELLIPTIC CURVES USING SOME TECHNIQUES OF AIVM

Manoj Kumar, Ankur Kumar.

Abstract
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.

Key words: Finite field, Urdhva-tiryagbhyam technique, Dvandva-yoga technique, Edwards elliptic curve, Edwards elliptic curve, Points addition, Point doubling.



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