Elliptic curve cryptography arithmetic in terms of one variable polynomial division
Santoshi Pote, Virendra R. Sule, B. K. Lande · Journal of Discrete Mathematical Sciences and Cryptography · 2020
This paper develops an approach for point addition and doubling on elliptic curves over finite fields using one variable polynomial arithmetic based on Euclidean division. This approach succeeds in computing these operations on realistic curves over large finite fields due to a striking observation about computing the gcd of two polynomials one which represents the elliptic curve as its roots and the other representing the lines which intersect or are tangent to the curve. This paper provides a verification of correctness of this approach for different finite fields. The resulting algorithm is tested on realistic elliptic curves and is shown to be practically scalable to perform the computations.