In this paper, a simple implementation for elliptic curve equation on Field Programmable Gate Array (FPGA) will be proposed. As Elliptic Curve Cryptography (ECC) offers a smaller key size without sacrificing security level. A brief survey on applying the main equation of Elliptic Curve (EC) with different values of the coefficients a and b. A comparison between results depended on the correlation coefficient of each value. Value of a and b implemented on FPGA according to correlation results between plaintext image and ciphertext image on MATLAB. This EC equation will be applied to an ultra-wide band (UWB) system to secure transmission of data in a wireless channel. Here, a brief survey on UWB technology has been implemented with software simulation for a secured system based on ECC algorithm.