Elliptic Curves over p-adic field Q_p and its p-adic point addition

Abstract

Public-key cryptosystems with the Elliptic curve  over finite field  are an alternative to RSA with finite fields. In the context of improving the efficiency of cryptosystems with elliptic curves, the study of elliptic curves  over p-adic number field  was consequential. In this paper we first obtain all the points in the elliptic curve  over p-adic number field  as lifts of the points in  to  and then  to  and so on and then to evaluate the arithmetic on , we first proceed to describe the implementation of the arithmetic of points on  to points on  and then give the algorithms for the computations.