The modular inversion operation is an essential hardware design for computing speed when we use it in cryptography applications. Through this work, we present a FSM based design methodology to achieve speed, area and high-performance modular binary inversion algorithm over 256-bit prime field. The proposed architecture implemented using Xilinx Virtex-7 FPGA device, it achieves 37% reduction in area-delay product and 15% and 16% of improvement in speed and throughput respectively, when compared with existing designs. Also, ASIC based implementation is done using TSMC 65nm CMOS technology, the synthesis results achieved the maximum operating clock frequency is 833 MHz and throughput of 626Mbps, which makes it suitable for speed-critical cryptoapplications.