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In this paper we describe Cryptography by using Karatsuba multipliers and ASCII codes implementing through coordinate geometry for data encryption and decryption with its code in matlab. Elliptic curve cryptography is an asymmetric key cryptography. It includes (i) public key generation on the elliptic curve and its declaration for data encryption and (ii) private key generation and its use in data decryption depended on the points on two dimensional elliptical curve. We also discuss the implementation of ECC on binary field. An overview of ECC implementation on two dimensional representation of ASCII codes with coordinate systems and data encryption through Elgamal Encryption technique has been discussed. Karatsuba multiplier is a fast process to solve the Elliptic curve cryptography problems. Here we have applied Karatsuba multiplier for point multiplication. Much attention has been given on the mathematical implementation of elliptic curves through Karatsuba multiplier. For cryptographic purposes, specifically results of the group formed by an elliptic curve over a finite field E(F 2 m ), and showing how this can form public key cryptographic systems for use in both encryption and key exchange. Finally we describe how to encrypt and decrypt the data with the ASCII codes through Karatsuba multiplier and its implimentation through matlab.

Cryptography By Karatsuba Multiplier with ASCII Codes