Elliptic Curve Cryptography (ECC) gained a lot of attention in industry. The key attraction of ECC over RSA is that it offers equal security even for smaller bit size, thus reducing the processing complexity. ECC Encryption and Decryption methods can only perform encrypt and decrypt operations on the curve but not on the message. This paper presents a fast mapping method based on matrix approach for ECC, which offers high security for the encrypted message. First, the alphabetic message is mapped on to the points on an elliptic curve. Later encode those points using Elgamal encryption method with the use of a non-singular matrix. And the encoded message can be decrypted by Elgamal decryption technique and to get back the original message, the matrix obtained from decoding is multiplied with the inverse of non-singular matrix. The coding is done using Verilog. The design is simulated and synthesized using FPGA.