Industries attention is lots more on Elliptic Curve Cryptography (ECC). ECC offers equal security for smaller bit size than RSA where larger key size is required, which reduces the processing complexity. Encryption and Decryption methods of ECC will not work on messages but is on curve performance. In this paper fast mapping method based on a matrix approach for ECC is studied, where high security for the encrypted message is offered. Initially, the alphabets present in the message is mapped to the points present on an elliptic curve. Later those points are encoded using ElGamal encryption method by using a non-singular matrix. The original message is obtained by decrypting the encoded message using ElGamal decryption technique, the decoded matrix is multiplied with the inverse of non-singular matrix. The Verilog Code is used. FPGA simulate and synthesize the proposed design