There is an explosive growth of confidential data transmission over the internet with resource-constrained applications. Real time applications require a high-speed and area-efficient cryptography system with higher security. Elliptic curve cryptography (ECC) offers a widely acknowledged secure environment for the exchange of confidential data in resource-constrained embedded system applications such as network servers, internet banking, smart card-based transactions, defence services, medical services, wireless sensor networks, the internet, etc. ECC provides a superior solution for enhanced security with reduced resource utilization, and it is currently the globally accepted method for transferring confidential data. This paper presents the design and implementation of a high-speed and low area-based ECC system on field-programmable gate array (FPGA). The proposed system is designed for national institute of standards and technology (NIST) recommended prime field. The proposed design has implemented and simulated on the Xilinx Vivado platform using Verilog language. We have proposed restructure point addition and point doubling modules for the Montgomery algorithm to improve the speed. The implementation of the proposed ECC architecture improved the speed of cryptographic operation by an average of 10% to 20% and optimized area by an average of 5% to 10% compared to the previous work. The simulation results confirm that this designed system has state-of-the-art architecture as well as the highest versatility for the ECC design.