Implementation of point addition & point doubling for Elliptic Curve

Abstract

This paper describes the verilog implementation of point addition and doubling used in Elliptic Curve Point Multiplication. Based on the theory of Elliptic Curve Cryptography, this paper has carried out modular addition, Elliptic Curve Point doubling and addition, modular squaring and projective to affine coordinates system. Elliptical Curve Cryptography is a public key encryption technique depend on elliptic curve theory. It can be used to make faster, smaller, and more efficient cryptographic keys. ECC generate key through the properties of the elliptic curve equation. Key is designed using scalar point multiplication algorithm, applying digit-serial computation with the help of Galois Field multiplication. For digit serial computations, there are various methods. Out of which target planned is to develop Montgomery ladder Point algorithm using projective coordinate system over Galois Field. The desired objective is to design circuit of multiplier using scalar point multiplication algorithm in GF (2m) for Elliptic Curve Cryptography using Xilinx.