Improved Cryptographic Schemes Based on Hessian and Twisted Hessian Elliptic Curves Using Some Techniques of AIVM

  • Manoj Kumar, Ankur Kumar

Abstract

The proposed schemes are implemented in the form of algorithms of points addition and point doubling for the Hessian elliptic curves using techniques of AIVM (ancient Indian Vedic mathematics). In particular, we improve timings in the cryptographic operations for the Hessian elliptic curves. We use some techniques of ancient mathematics namely Urdhva-tiryagbhyam for multiplication, Dvandva-yoga for squaring of any digits. We introduce cryptographic formulae namely, addition and doubling of points for HEC (Hessian 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    8-bits and 16-bits.

Published
2020-10-03
How to Cite
Manoj Kumar, Ankur Kumar. (2020). Improved Cryptographic Schemes Based on Hessian and Twisted Hessian Elliptic Curves Using Some Techniques of AIVM. International Journal of Advanced Science and Technology, 29(04), 10190 -. Retrieved from http://sersc.org/journals/index.php/IJAST/article/view/33057