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.